# JWST UNCOVER: Discovery of $z>9$ Galaxy Candidates Behind the Lensing
Cluster Abell 2744

Hakim Atek1, Iryna Chemerynska1, Bingjie Wang2,3,4, Lukas Furtak5, Andrea
Weibel6, Pascal Oesch6, John R. Weaver7, Ivo Labbé8, Rachel Bezanson9, Pieter
van Dokkum10, Adi Zitrin5, Pratika Dayal11, Christina C. Williams12, Themiya
Nannayakkara8, Sedona H. Price9, Gabriel Brammer 13, Andy D. Goulding14 Joel
Leja 2,3,4, Danilo Marchesini15, Erica J. Nelson16, Richard Pan15, Katherine
E. Whitaker7,13
1Institut d’Astrophysique de Paris, CNRS, Sorbonne Université, 98bis Boulevard
Arago, 75014, Paris, France
2 Department of Astronomy & Astrophysics, The Pennsylvania State University,
University Park, PA 16802, USA
3 Institute for Computational & Data Sciences, The Pennsylvania State
University, University Park, PA 16802, USA
4 Institute for Gravitation and the Cosmos, The Pennsylvania State University,
University Park, PA 16802, USA
5Physics Department, Ben-Gurion University of the Negev, P.O. Box 653, Be’er-
Sheva 84105, Israel
6Department of Astronomy, University of Geneva, Chemin Pegasi 51, 1290
Versoix, Switzerland
7Department of Astronomy, University of Massachusetts, Amherst, MA 01003, USA
8Centre for Astrophysics and Supercomputing, Swinburne University of
Technology, Melbourne, VIC 3122, Australia
9Department of Physics and Astronomy and PITT PACC, University of Pittsburgh,
Pittsburgh, PA 15260, USA
10Department of Astronomy, Yale University, New Haven, CT 06511, USA
11Kapteyn Astronomical Institute, University of Groningen, P.O. Box 800, 9700
AV Groningen, The Netherlands
12NSF’s National Optical-Infrared Astronomy Research Laboratory, 950 N. Cherry
Avenue, Tucson, AZ 85719, USA
13 Cosmic Dawn Center (DAWN), Niels Bohr Institute, University of Copenhagen,
Jagtvej 128, København N, DK-2200, Denmark
14 Department of Astrophysical Sciences, Princeton University, Princeton, NJ
08544, USA
15Department of Physics and Astronomy, Tufts University, 574 Boston Ave.,
Medford, MA 02155, USA
16Department for Astrophysical and Planetary Science, University of Colorado,
Boulder, CO 80309, USA E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We present the results of a search for high-redshift ($z>9$) galaxy candidates
in the JWST UNCOVER survey, using deep NIRCam and NIRISS imaging in 7 bands
over $\sim 45$ arcmin2 and ancillary HST observations. The NIRCam observations
reach a $5-\sigma$ limiting magnitude of $\sim 29.2$ AB. The identification of
high$-z$ candidates relies on a combination of a dropout selection and
photometric redshifts. We find 16 candidates at $9<z<12$ and 3 candidates at
$12<z<13$, eight candidates are deemed very robust. Their lensing
amplification ranges from $\mu=1.2$ to 11.5. Candidates have a wide range of
(lensing-corrected) luminosities and young ages, with low stellar masses
($6.8<$ log(M⋆/M⊙) $<9.5$) and low star formation rates (SFR=0.2-7 M⊙ yr-1),
confirming previous findings in early JWST observations of $z>9$. A few
galaxies at $z\sim 9-10$ appear to show a clear Balmer break between the F356W
and F444W/F410M bands, which helps constrain their stellar mass. We estimate
blue UV continuum slopes between $\beta=-1.8$ and $-2.3$, typical for early
galaxies at $z>9$ but not as extreme as the bluest recently discovered
sources. We also find evidence for a rapid redshift-evolution of the mass-
luminosity relation and a redshift-evolution of the UV continuum slope for a
given range of intrinsic magnitude, in line with theoretical predictions.
These findings suggest that deeper JWST observations are needed to reach the
fainter galaxy population at those early epochs, and follow-up spectroscopy
will help better constrain the physical properties and star formation
histories of a larger sample of galaxies.

###### keywords:

galaxies: high-redshift – dark ages, reionization, first stars – galaxies:
dwarfs – galaxies: evolution – gravitational lensing: strong – cosmology:
observations

††pubyear: 2023††pagerange: JWST UNCOVER: Discovery of $z>9$ Galaxy Candidates
Behind the Lensing Cluster Abell 2744–LABEL:lastpage

##  1 Introduction

While the Hubble Space Telescope (HST) and ground-based observatories have
uncovered more than two thousands galaxies at redshifts greater than $z\sim 6$
(Atek et al., 2015; Finkelstein et al., 2015; Bouwens et al., 2021), only a
handful of galaxies were known at $z>9$ (Oesch et al., 2018; Bowler et al.,
2020; Bagley et al., 2022a). This observational frontier is mainly due to the
near-infrared (NIR) wavelength coverage of HST which is limited to $\lambda<2$
µm, whereas the rest-frame ultraviolet (UV) light of early galaxies is
increasingly shifted towards longer wavelengths. With its NIRCam (Near-
Infrared Camera) instrument covering the $\sim 1-5$ µm domain, coupled with a
significantly higher sensitivity compared to its NIR predecessors (Rigby et
al., 2022; Rieke et al., 2023), JWST is poised to revolutionize our views of
the early stages of galaxy formation.

In the early months of operation, several studies have reported the discovery
of $z>9$ galaxy candidates in the first JWST imaging observations: the Early
Release Observations (ERO; Pontoppidan et al., 2022), Early Release Science
(ERS) programs CEERS (Bagley et al., 2022b) and GLASS (Treu et al., 2022).
Among these early results, Naidu et al. (2022) reported candidates at $z\sim
12-13$, Finkelstein et al. (2022b) a candidate at $z\sim 12$, while samples of
$z\sim 9-16$ candidates have been presented in Atek et al. (2023); Donnan et
al. (2023); Harikane et al. (2023); Adams et al. (2023); Austin et al. (2023).
Many of these galaxy candidates broke the previous distance record held by HST
observations (Oesch et al., 2016). More recently, several programs have
started to spectroscopically confirm some of these high-redshift candidates
(Roberts-Borsani et al., 2022; Morishita et al., 2022), with the highest-
redshift galaxy located at $z\sim 13$ (Robertson et al., 2022; Curtis-Lake et
al., 2022). At the same time, the high-redshift solution of some of these
candidates have been ruled out by NIRSpec follow-up observations. For example,
the highest-redshift candidate at z$\sim 16.7$ (Donnan et al., 2023) has been
confirmed to be a dusty galaxy at $z\sim 4.9$ with intense rest-frame optical
emission lines (Arrabal Haro et al., 2023).

However, more than their distance, the most striking aspect perhaps is their
combined number density and brightness. Indeed, the inferred number density is
significantly larger than theoretical predictions based on galaxy formation
models, or extrapolation of lower-redshift luminosity functions (Bouwens et
al., 2022; Atek et al., 2023; Mason et al., 2022; Naidu et al., 2022; Donnan
et al., 2023). While some of these candidates have been confirmed at $z\sim
12$ or 13 (e.g, Curtis-Lake et al., 2022; Arrabal Haro et al., 2023), others
turned out to be low$-z$ dusty interlopers, which always warrants caution in
their interpretation. Also, a sample of red massive galaxies at $z=7-9$,
reported by (Labbe et al., 2022), appear to have stellar masses approaching
that of the present-day Milky Way, in potential tension with standard
$\Lambda$-CDM models (Boylan-Kolchin, 2022).

Several studies have attempted to understand these early observations and
interpret these surprising results. In particular, the high number density of
luminous galaxies at $z>12$ has been attributed to the decreasing amount of
dust attenuation at higher redshift (Ferrara et al., 2022), higher star
formation efficiency in early galaxies and/or non-standard initial mass
function (IMF; Ziparo et al., 2022; Mason et al., 2022), or even
non-$\Lambda$-CDM cosmologies (Menci et al., 2022; Boylan-Kolchin, 2022). In
the meantime, a larger area of deep JWST surveys and spectroscopic follow-up
observations are needed to confirm this claim by increasing the sample size of
confirmed $z>9$ galaxies.

During the first cycle of JWST operations, our UNCOVER (Ultradeep NIRSpec and
NIRCam ObserVations before the Epoch of Reionization) Treasury survey has
obtained deep multi-wavelength NIRCam imaging of the lensing cluster Abell
2744 (Bezanson et al., 2022). UNCOVER deep NIRCam imaging consists of a mosaic
in 7 filters for $\sim 4-6$ hour per band, reaching a magnitude limit of $\sim
29.2$ AB. Following on the steps of the Hubble frontier fields (HFF), the
program relies on the gravitational lensing boost to push beyond blank fields
limits. In fact, assuming an average amplification of 5, UNCOVER is
intrinsically the deepest observing program of Cycle 1. In addition, the
program will obtain spectra for the intrinsically faintest distant galaxies to
date with 5–20 hours of NIRSpec Prism follow-up observations. In addition to
our program, NIRISS imaging of A2744 was obtained as part of ERS GLASS
program, and NIRCam imaging as part of the DDT program ID 2756. We combined
all these imaging data to increase the depth and the area of our survey.

In this paper, we present the detection of $z>9$ galaxy candidates in the
NIRCam and NIRISS imaging data, determine their physical properties, and
compare them to theoretical predictions. Using imaging data in 15 broad-band
filters, the identification of galaxy candidates is based on a combination of
photometric dropout criteria and photometric redshifts derived from Spectral
Energy Distribution (SED) fitting with both BEAGLE and Eazy codes. We describe
the imaging dataset in Section 2 and the sample selection in Section 3. We
present our estimates of the physical parameters and their redshift-evolution
in Section 4. Our conclusions are given in Section 5. We use AB magnitudes
(Oke & Gunn, 1983) and a standard cosmology with H${{}_{0}}=70$ km s-1 Mpc-1,
$\Omega_{\Lambda}=0.7$, and $\Omega_{m}=0.3$.

##  2 Observations

The UNCOVER observations are described in the survey article (Bezanson et al.,
2022), which is accompanied by our first data release of the imaging mosaics,
available at the UNCOVER webpage111uncover.github. Here we describe briefly
the content of the data and their photometric characteristics.

The NIRCam data consists of short wavelength SW imaging in 3 broadband filters
(F115W, F150W, F200W) and long wavelength LW imaging in 3 broadband filters
(F277W, F356W, F444W) and one medium band filter (F410M). The exposure times
and the resulting magnitude limits in all filters are listed in Table
LABEL:tab:obs. Simultaneously to the NIRCam observations, NIRISS imaging is
obtained in parallel using 5 broadband filters (F115W, F150W, F200W, F356W,
and F444W). Our analysis also includes data from the GLASS survey (Treu et
al., 2022) obtained with NIRISS, which adds the F090W band in a fraction of
the UNCOVER area. In addition, we incorporate NIRCam imaging from the DDT
program ID 2756, which uses a similar set of filters to UNCOVER, except the
F410M filter, and shorter exposure times. Using the grizli software (Brammer
et al. in prep.), the data were then reduced and drizzled into mosaics with a
common pixel scale of 0.4″ pix-1 and a total field of view of $\sim 45$
arcmin2.

The cluster core of A2744 is covered by deep HST imaging from the HFF program,
and a slightly wider area with shallower observations from the BUFFALO program
(Steinhardt et al., 2020). The HST observations include Advanced Camera for
Surveys (ACS) imaging in three filters (F435W, F606W, F814W), and Wide-Field
Camera Three (WCF3) in four filters (F105W, F125W, F140W, F160W). Furthermore,
the UNCOVER NIRISS parallels overlap with deep HST ACS F814W imaging in the
A2744 parallel field. All these observations are drizzled to the same pixel
scale and aligned to the UNCOVER images. Detailed characterization of the data
are presented in Weaver et al. (2023).

Filter | Depth | Area
---|---|---
| ($5~{}\sigma$ AB) | (arcmin2)
| HST |
F435W | 29.28 | 18.54
F606W | 28.86 | 36.21
F814W | 28.47 | 31.26
F105W | 28.14 | 20.22
F125W | 28.14 | 20.08
F140W | 28.79 | 5.62
F160W | 28.27 | 20.15
| JWST |
F090W | 28.93 | 12.91
F115W | 28.85 | 45.12
F150W | 28.87 | 45.50
F200W | 28.92 | 44.71
F277W | 29.34 | 44.98
F356W | 29.45 | 45.67
F410M | 28.85 | 28.73
F444W | 29.10 | 45.11
Table 1: Limiting AB magnitudes at 5$\sigma$, quoted in 0.32″diameter
apertures, correspond to the area-weighted 50th percentiles. Area reflects the
union of the LW detection footprint with that of each band.

##  3 High-redshift Sample Selection

###  3.1 Photometric Catalogs

For our sample selection and analysis, we compared two photometric catalogs:
(i) the general UNCOVER catalog published in Weaver et al. (2023) which has
been designed to fit most of the scientific investigations covered by this
dataset, (ii) a custom photometric catalog specifically tailored to the
detection of high-redshift galaxies. the main differences reside in the
aperture size, the deblending parameters, and the aperture corrections.

####  3.1.1 General catalog

The object detection and photometry are performed in images that were
previously corrected for contamination from intra-cluster light (ICL) and
bright cluster galaxies, following methods developed in Shipley et al. (2018).
All images are matched to the point spread function (PSF) of the longest-
wavelength image in the F444W filter. The detection image consists of a co-
addition of the three long-wavelength JWST filters F277W, F356W, and F444W.
Photometry is measured in 0.32″ apertures using the python version of Source
Extractor SEP (Bertin & Arnouts, 1996; Barbary, 2016). We adopted the
following parameters for the SEP extraction: a detection threshold of
$1.5\sigma$, a deblending threshold of 16, and deblending contrast of 3e-3.
The total fluxes are estimated by applying a correction derived from
elliptical Kron apertures (Kron, 1980). Details of the PSF-matching procedure,
and additional photometric corrections, are described in Weaver et al. (2023)

####  3.1.2 High$-z$ catalog

In addition, we produce a photometric source catalog using the SExtractor tool
(Bertin & Arnouts, 1996) in dual mode on each available image, using the F444W
as the detection image. We adopt a detection threshold of 0.9 (relative to the
rms image), a minimum detection area of 6 pixels, and a deblending threshold
of 3e-4. We measured individual fluxes in 0.24″ circular apertures in each
filter. The total fluxes were obtained by using a scaling factor derived from
the ratio of the aperture flux to the AUTO_FLUX obtained from SExtractor in
the F444W image. To account for the missing flux due to the PSF wings, we
measured the aperture flux as a function of the aperture radius in the PSF of
the F444W band. For each object, we computed the equivalent circularized
radius as $r=\sqrt{a\times b}~{}\times$ kron_radius, and divided the encircled
flux by the flux fraction in the PSF-F444W for this radius. This correction
typically increases all the fluxes by $\sim 10-20$%.

In the end, the comparison between the two catalogs shows that the latter is
better suited for high-redshift sources, particularly in deblending the small
objects, and in estimating the object and background fluxes.

###  3.2 Dropout selection

Following the color-color criteria defined in Atek et al. (2023) we select
$9<z<11$ galaxies that satisfy:

$\begin{array}[]{l}M_{115}-M_{150}>1.0\\\
M_{115}-M_{150}>1.5+1.4(M_{150}-M_{200})\\\ M_{150}-M_{200}<0.5\end{array}$
(1)

This selection window, illustrated in Figure 1, has been designed to minimize
potential contamination from low-redshift interlopers and cool stars. To
determine the color-color space of these contaminants, we generated quiescent
galaxy templates from the SWIRES library (Polletta et al., 2007), applied
different dust attenuation values $A_{V}=[0,0.25,1]$ assuming an SMC dust law,
and computed synthetic photometry in the set of broadband filters used in this
paper. The resulting color-color tracks are shown in Figure 1. We also compute
the color tracks of cold red stars and brown dwarfs using stellar templates
from Chabrier et al. (2000) and Allard et al. (2001).

In addition to these selection criteria, we require that sources are detected
in all LW filters with a minimum SNR$=5$ and that they remain undetected in
F090W, when available, and all HST optical bands at a $2~{}\sigma$ level. For
sources that are not detected in the dropout filter, we assign a $1\sigma$
lower limit corresponding to the filter limiting magnitude to ensure a minimum
continuum break of one magnitude.

For $z\sim 12-15$ candidates, we adopt the following criteria:

$\begin{array}[]{l}M_{150}-M_{200}>1.5\\\
M_{150}-M_{200}>1.6+1.8(M_{200}-M_{277})\\\ M_{200}-M_{277}<0.5\end{array}$
(2)

Similarly, we require high-significance detection in the LW filters and that
none of these candidates are detected in the bands blueward of the Lyman
break, i.e. in the HST, and JWST F090W, F115W filters.

Figure 1: Color-color selection identification of high-redshift dropouts. Each
panel shows the selection window (white area) defined by the criteria of
equations 1, 2 for the identification of candidates in the redshift range
$9<z<11$ and $11<z<15$, respectively. Each candidate (magenta diamond) is
marked with its associated best-fit photometric redshift. The blue-solid lines
are the expected color-color space of typical starburst galaxies at $z>9$
based on galaxy templates generated using BEAGLE. We also show the color-color
tracks of quiescent galaxies (dashed lines), which represent potential low-
redshift contaminants, generated from GRASIL (Silva et al., 1998). We applied
different dust attenuation values in the range $A_{V}=[0,0.25,1]$ illustrated
by different colors (yellow to red) assuming an SMC dust law. In addition, the
green stars indicate the colors of cool stars (brown dwarfs and M-class),
another source of contamination, based on Chabrier et al. (2000) and Allard et
al. (2001) libraries.

###  3.3 Spectral energy distribution fitting

In parallel, we estimate photometric redshifts by running spectral energy
distribution (SED) fitting. We apply 5% error floor to all photometric
measurements to reflect the calibration uncertainties of JWST NIRCam data. To
minimize the propagation of lensing uncertainties, both of the following
procedures are based on the observed flux densities without correction for
magnification. The derived parameters are then unlensed a posteriori. We first
use the Eazy software (Brammer et al., 2022), over an allowed redshift range
of $0.01<z<20$, adopting the CORR_SFHZ set of galaxy templates, which include
redshift-dependent SFHs informed by the most recent results of JWST
observations of high$-z$ galaxies (Carnall et al., 2023; Larson et al.,
2022a). As shown in Weaver et al. (2023), these templates perform better than
the default FSPS_FULL library in recovering the true redshift. Improvements
over the Eazy FSPS templates have also been presented in Larson et al.
(2022b), which include bluer UV slopes based on BPASS (Stanway & Eldridge,
2018) and nebular emission models.

Second, we run the Beagle (BayEsian Analysis of GaLaxy sEds) SED-fitting
software (Chevallard & Charlot, 2016) on the same photometric data. The
procedure uses stellar population models from (Bruzual & Charlot, 2003) and
nebular emission models from Gutkin et al. (2016). In the first run of the SED
fitting, we are mostly interested in the best redshift solution. We adopt a
simple star formation history with a constant star formation rate, a uniform
distribution of the age priors
$\log(t_{\mathrm{age}}/\mathrm{yr})\in[7,t_{\mathrm{universe}}]$, and a fixed
metallicity of $Z=0.1\,\mathrm{Z}_{\odot}$.

In order to identify spurious objects, or sources affected by artifacts, we
flag objects that meet the following criteria: objects whose segmentation
apertures overlap with the edge of the detector or are next to bright stars,
are affected by bad pixels, whose size is 1 pixel or less, or are likely to be
stars. For the latter, we combine information from both the SExtractor
stellarity parameter CLASS_STAR and the $\chi^{2}$ of the Eazy SED-fitting run
using a set of dwarf star templates through the fit_phoenix_stars function. In
addition, all the sources that pass these filters are visually inspected for
potential contamination (diffraction spikes, detector artifacts, etc.)

All the candidates have best-fit photometric redshifts consistent with the
dropout selection. Conversely, when first selecting candidates using
photometric redshift criteria, limiting the sample to best-fit solutions with
$\chi^{2}<30$, 31 candidates satisfy the selection. The dropout selection
rejects 13 candidates. For the majority of these rejected candidates, the
high$-z$ solution is due to fitting failures, where the best-fit SED does not
match the photometry. Some objects do not show a clear Lyman break, or are
clearly detected in the blue bands. Also, in few cases, the signal-to-noise
level in the detection bands is simply below our selection threshold.

The final sample of high-redshift candidates consists of a total of 16
galaxies in the redshift range $9<z<11$ and 3 galaxies at $11<z<15$. The
complete list and properties of the high$-z$ sample are reported in Tab. 2.

Table 2: Photometric and physical properties of the sample of high-redshift candidates identified through the A2744 cluster at $9<z<11$ and $12<z<15$. The photometric redshift $z_{phot}$ is derived from the Eazy SED-fitting. The UV absolute magnitude, stellar mass and SFR are corrected by the amplification factor $\mu$, which was computed with the latest UNCOVER lensing model. Column 2 provides the quality of the candidate based on the robustness of the photometric redshift, Q=1 being the most secure candidates. ID | Q | RA | Dec | $z_{\mathrm{phot}}$ | $M_{\mathrm{UV}}$ | $\beta$ | $\log(M_{\star}/\mathrm{M}_{\odot})$ | SFR ($\mathrm{M}_{\odot}~{}\mathrm{yr}^{-1})$ | $\mu$
---|---|---|---|---|---|---|---|---|---
$z\sim 9-11$ candidates
1870 | 3 | 3.648010 | -30.426616 | $9.32_{-6.95}^{+0.96}$ | -19.78 $\pm$ 0.18 | -2.09 $\pm$ 0.14 | $8.00_{-0.21}^{+0.17}$ | $1.16_{-0.45}^{+0.54}$ | $1.30_{-0.01}^{+0.01}$
2065 | 1 | 3.617194 | -30.425536 | $9.50_{-0.08}^{+0.34}$ | -21.67 $\pm$ 0.12 | -2.03 $\pm$ 0.04 | $8.57_{--0.06}^{+0.44}$ | $4.27_{--0.58}^{+7.33}$ | $1.65_{-0.03}^{+0.02}$
3148 | 3 | 3.646481 | -30.421615 | $9.40_{-7.14}^{+0.88}$ | -20.51 $\pm$ 0.18 | -1.92 $\pm$ 0.12 | $8.47_{-0.25}^{+0.55}$ | $3.41_{-1.51}^{+8.66}$ | $1.31_{-0.01}^{+0.02}$
3160 | 2 | 3.591436 | -30.421663 | $10.74_{-1.45}^{+0.37}$ | -19.06 $\pm$ 0.15 | -1.79 $\pm$ 0.08 | $8.15_{--0.13}^{+0.74}$ | $1.55_{--0.58}^{+6.40}$ | $2.49_{-0.08}^{+0.09}$
10619 | 1 | 3.594996 | -30.400738 | $9.69_{-0.12}^{+0.33}$ | -17.57 $\pm$ 0.13 | -2.16 $\pm$ 0.05 | $6.78_{-0.45}^{+0.35}$ | $0.68_{-0.45}^{+0.30}$ | $11.50_{-0.50}^{+0.40}$
17987 | 3 | 3.641572 | -30.382825 | $9.41_{-7.12}^{+0.60}$ | -19.39 $\pm$ 0.18 | -2.05 $\pm$ 0.14 | $7.57_{-0.45}^{+0.20}$ | $0.42_{-0.27}^{+0.25}$ | $1.31_{-0.01}^{+0.01}$
21623 | 1 | 3.567067 | -30.377869 | $10.01_{-0.26}^{+0.36}$ | -19.01 $\pm$ 0.14 | -2.30 $\pm$ 0.07 | $7.86_{-0.05}^{+0.06}$ | $0.83_{-0.09}^{+0.12}$ | $3.72_{-0.18}^{+0.14}$
22360 | 2 | 3.637111 | -30.376780 | $10.73_{-1.19}^{+0.44}$ | -19.85 $\pm$ 0.18 | -2.08 $\pm$ 0.12 | $8.33_{-0.11}^{+0.17}$ | $2.47_{-0.54}^{+1.17}$ | $1.33_{-0.01}^{+0.01}$
26928 | 1 | 3.511925 | -30.371861 | $9.47_{-0.07}^{+0.44}$ | -20.36 $\pm$ 0.12 | -1.97 $\pm$ 0.04 | $9.02_{-0.09}^{+0.26}$ | $6.54_{-0.29}^{+3.30}$ | $1.67_{-0.09}^{+0.07}$
31763 | 3 | 3.519867 | -30.366428 | $11.31_{-8.63}^{+0.20}$ | -18.89 $\pm$ 0.17 | -2.13 $\pm$ 0.11 | $7.73_{-0.13}^{+0.09}$ | $0.61_{-0.16}^{+0.14}$ | $1.92_{-0.11}^{+0.11}$
39074 | 1 | 3.590115 | -30.359743 | $10.60_{-0.31}^{+0.21}$ | -20.03 $\pm$ 0.14 | -2.21 $\pm$ 0.07 | $8.16_{-0.07}^{+0.08}$ | $1.65_{-0.24}^{+0.32}$ | $1.89_{-0.06}^{+0.05}$
46026 | 3 | 3.605690 | -30.352664 | $10.86_{-8.30}^{+0.32}$ | -19.92 $\pm$ 0.16 | -2.06 $\pm$ 0.14 | $8.31_{-0.15}^{+0.67}$ | $2.34_{-0.70}^{+8.57}$ | $1.47_{-0.03}^{+0.04}$
52008 | 2 | 3.478739 | -30.345535 | $10.37_{-1.09}^{+0.32}$ | -19.90 $\pm$ 0.14 | -2.11 $\pm$ 0.07 | $7.69_{-0.32}^{+0.15}$ | $0.56_{-0.29}^{+0.23}$ | $1.26_{-0.02}^{+0.02}$
73667 | 1 | 3.451412 | -30.321807 | $10.68_{-0.31}^{+0.21}$ | -20.55 $\pm$ 0.13 | -2.24 $\pm$ 0.05 | $8.37_{-0.01}^{+0.01}$ | $2.73_{-0.08}^{+0.07}$ | $1.17_{-0.01}^{+0.01}$
81198 | 1 | 3.451367 | -30.320717 | $10.50_{-0.66}^{+0.23}$ | -19.90 $\pm$ 0.14 | -2.33 $\pm$ 0.08 | $8.08_{-0.02}^{+0.02}$ | $1.38_{-0.06}^{+0.07}$ | $1.17_{-0.01}^{+0.01}$
83338 | 2 | 3.454706 | -30.316898 | $9.55_{-0.57}^{+0.91}$ | -19.24 $\pm$ 0.18 | -1.80 $\pm$ 0.12 | $9.29_{-0.10}^{+0.11}$ | $0.19_{-0.19}^{+0.37}$ | $1.17_{-0.01}^{+0.01}$
$z\sim 11-15$ candidates
42329 | 3 | 3.513568 | -30.356804 | $11.83_{-7.93}^{+1.05}$ | -19.13 $\pm$ 0.18 | -2.05 $\pm$ 0.12 | $9.31_{--0.00}^{+0.54}$ | $0.36_{-0.35}^{+0.58}$ | $1.57_{-0.05}^{+0.06}$
46075 | 3 | 3.546722 | -30.352425 | $12.23_{-0.50}^{+1.38}$ | -19.10 $\pm$ 0.19 | -2.43 $\pm$ 0.20 | $7.72_{-0.05}^{+0.04}$ | $0.61_{-0.06}^{+0.06}$ | $1.82_{-0.05}^{+0.11}$
70846 | 1 | 3.498983 | -30.324758 | $12.50_{-0.15}^{+0.46}$ | -20.79 $\pm$ 0.12 | -2.27 $\pm$ 0.04 | $9.50_{-2.72}^{+0.82}$ | $7.06_{-6.99}^{+29.90}$ | $1.27_{-0.02}^{+0.02}$

###  3.4 Gravitational lensing model

In order to compute the gravitational magnifications of the sample and the
effective survey area, we use the new UNCOVER cluster mass model derived by
Furtak et al. (2022). This parametric strong lensing model is based on
existing and newly-discovered multiple-image systems in the deep NIRCam
imaging of UNCOVER. Thanks to the wide NIRCam coverage, the total survey area
with an amplification factor $\mu>2$ is about 3.5 arcmin2, which is a
significant improvement over the HFF-derived area of $\sim 0.9$ arcmin2.
Figure 2 shows the cumulative surface area as a function of magnification. The
amplification factors shown in Table 2 range between $\mu=1.2$ and $\mu=11.5$,
and were derived using the photometric redshifts.

Figure 2: The cumulative surface area behind A2744 at $z=9$ (blue curve) as a
function of gravitational magnification $\mu$ (cf. section 3.4), expressed in
magnitudes. also shown for reference, the area as a function of magnification
derived from HFF observations by the CATS team. The total unlensed survey area
of UNCOVER is $\sim 35$ arcmin2. For reference, the observed area is about 45
arcmin2. Figure 3: Coordinates of the high-redshift candidates overlaid on the
F277W image, which has been corrected for bCG and ICL contamination. The
footprint includes UNCOVER, GLASS, DDT observations (see text for details).
The field of view of the full frame is about $12\times 9$ arcmin.

##  4 Results

###  4.1 High-redshift candidates

We find 16 candidates in the range $9<z<11$, among which 8 objects have best-
fit photometric redshifts above $z=10$. Among the total sample, we identify 7
robust candidates that have a narrow high$-z$ solution with no secondary
low$-z$ solution. These candidates have about 70-90% of their total
probability enclosed within $\Delta z=1$ around the best-fit solution.
Examples of these high-confidence candidates are shown in Figure 4. These are
ranked as the best candidates in the sample and are assigned a quality flag
Q=1 in Table 2. The lower-quality Q=2 sample includes galaxies that show a
significant secondary solution, with a total probability within 50-70% around
their high$-z$ peak. Four galaxies lie in this category. Finally, 5 sources
belong to the Q=3 category because of disagreements between their Eazy and
BEAGLE best-fit solutions or a total probability of less than 50% around their
high$-z$ peak. Castellano et al. (2022) recently identified 7 candidates at
$z\sim 10$ in the A2744 region. We recover 6 of their candidates in our
sample. Five of these overlapping sources are in the Q=1 category. One of
their source, GHZ9, is ranked in the Q=2 of our sample. Source GHZ4 in their
catalog is not included in our selection because it has SNR=4.8, which is
slightly below our color-color selection criteria. In table 3 we compare the
photometric redshifts of the sources that have been identified in both
studies. Overall, there is a good agreement between these independent
determinations, whose differences remain within the $1\sigma$ uncertainties,
in most cases.

We also identify three candidates in the redshift selection range $12<z<15$.
Among these, one candidate is classified as robust Q=1, while the remaining
two candidates have a Q=3 score according to the criteria defined earlier.
Overall, these candidates are among the highest-redshift candidates identified
in recent JWST observations, as can be seen in Figure 6. This sample spans a
large dynamic range in intrinsic luminosity from $M_{\rm UV}$=-17.6 to -21.7
mag.

We examined the recent JWST spectroscopic observations of A2744 as part of the
GLASS program, utilizing both NIRSpec and NIRISS grism observations.

  * •

Candidate ID 2065 in our sample has a spectroscopic confirmation at $z=9.3$ as
reported by Boyett et al. (2023), in good agreement with the estimated
photometric redshift of $z=9.50_{-0.08}^{+0.34}$. The NIRSpec observations of
this spatially-resolved galaxy show prominent emission lines of O, Ne, and H,
as well as a clear Lyman break. By combining the photometric and spectroscopic
data, the best-fit SED provides a stellar mass of log(M⋆/M⊙$\sim$ 9.17).

  * •

Candidate ID 10619 is one of the three multiple images of a candidate galaxy
previously identified in the HFF data by (Zitrin et al., 2014). It has the
highest magnification ($\mu\sim 11.5$). It has been spectroscopically
confirmed at $z=9.76$ with NIRSpec prism spectroscopy by Roberts-Borsani et
al. (2022). This value is in good agreement with our photometric redshift
estimate of $z=9.69_{-0.12}^{+0.33}$.

ID | GLASS ID |  $z_{phot}$(Eazy) |  $z_{phot}$(BEAGLE) | GLASS $z_{phot}$
---|---|---|---|---
2065 | DHZ1 | $9.50_{-0.08}^{+0.34}$ | $9.78_{-0.34}^{+1.05}$ | 9.45
21623 | UHZ1 | $10.01_{-0.26}^{+0.36}$ | $10.17_{-0.05}^{+0.77}$ | 10.32
26928 | GHZ1 | $9.47_{-0.07}^{+0.44}$ | $9.95_{-0.17}^{+0.88}$ | 10.47
52008 | GHZ9 | $10.37_{-1.09}^{+0.32}$ | $9.47_{-0.35}^{+0.36}$ | 9.35
81198 | GHZ7 | $10.50_{-0.66}^{+0.23}$ | $10.17_{-0.05}^{+0.66}$ | 10.62
73667 | GHZ8 | $10.68_{-0.31}^{+0.21}$ | $10.63_{-0.51}^{+0.20}$ | 10.85
Table 3: Comparison between the photometric redshifts derived in our analysis
with Eazy and BEAGLE with the results of Castellano et al. (2022) for common
objects in the two samples.

Figure 4: Imaging data and best-fit solutions for 4 of the high-redshift
candidates in the range $9<z<11$. The top row of each panel shows image
cutouts in the 7 JWST filters. The bottom panel shows the best-fit SEDs with
Eazy (orange curve) and BEAGLE (blue curve) together with object ID and the
best fit $\chi^{2}$ from both codes. The purple diamonds represent the
observed photometric data points (and their associated 1$\sigma$
uncertainties) measured in HST and JWST images. The orange and blue circles
represent the best fit magnitudes in their respective bands for Eazy and
BEAGLE solutions, respectively. We also show the probability distribution
function (PDF) of the photometric redshift solutions (for both codes) on the
right, together with the best-ft $z_{phot}$ and the total probability enclosed
in a redshift width of $\Delta z=1$ around the Eazy best-fit solution.

Figure 5: same as figure 4 but for one of the candidates in the $12<z<15$
range. Figure 6: Absolute UV magnitude as a function of redshift for the
present sample compared to literature results. The gray circles (stars)
represent a compilation of known galaxies with photometric (spectroscopic)
redshifts at $z>8$. The rest of the circles represents photometrically-
selected galaxies from recent JWST observations (Finkelstein et al., 2022a;
Atek et al., 2023; Austin et al., 2023; Whitler et al., 2023). the colored
stars show galaxies with spectroscopic confirmations by NIRSpec observations
(Curtis-Lake et al., 2022; Bunker et al., 2023).

###  4.2 Physical properties

In addition to computing photometric redshifts, we perform a second SED
fitting run with BEAGLE to refine our estimates of physical parameters, this
time using a Gaussian prior for the redshift based on the first-run photo$-z$
solution. We adopt this time a more flexible SFH using a delayed exponential
form SFR $\propto$ t exp($-t/\tau$), and a potential SF burst episode in the
last 10 Myr. We use a constant metallicity of $Z=0.1Z_{\odot}$, which has been
shown to have little effect on the photometry of high-redshift galaxies
(Furtak et al., 2021). We also assume an SMC extinction law, which is more
appropriate for high-redshift galaxies (Capak et al., 2015; Reddy et al.,
2018). We limit the fit to 4 physical parameters using the following priors:

  * •

Stellar mass with a log-uniform distribution prior in the range log(M⋆/M⊙)
$\in$ [6-10]

  * •

SFR averaged over the last 10 Myr with a log-uniform distribution prior
log($\psi$ /M⊙ yr-1) $\in$ [-4,4]

  * •

Maximum stellar age for $t$=$\tau$, with a log-uniform prior log($t_{age}$/yr)
$\in$ [6, $t_{universe}$], where $t_{universe}$ is the age of the universe at
the redshift of the galaxy.

  * •

Dust attenuation as traced by the optical depth measured in the V band with a
uniform prior $\tau_{V}\in$ [0, 0.5]. The prior distribution is based on UV
continuum slope values measured in Section 4.2.2.

Most of the candidates have relatively low stellar masses in the range
Log(M⋆/M⊙)$=6.8-9.5$. The data cover the redshifted Balmer break for most
galaxies, which helps constrain the older stellar population. Indeed, the best
constraints on the stellar mass, but also the age of the stellar population,
are obtained for galaxies that show an excess in the F444W band indicative of
Balmer break. For example, among the robust candidates, IDs 21623, 26928 and
83338, show a significant Balmer break (Fig. 4) and small uncertainties on
their derived stellar masses. It is also interesting to note that in
comparison to Eazy,BEAGLE attribute more broadband flux to strong emission
lines, which result in lower stellar masses. Strong [Oii]$\lambda\lambda
3726,3729$ and [Neiii]$\lambda 3869$ emission lines can enhance both F410M and
F444W fluxes and mimic a Balmer break. Such strong lines have been observed at
$z\sim 10.6$ for instance in the NIRSpec spectrum of GN-z11 (Bunker et al.,
2023). This explains the difference observed between the Eazy and BEAGLE fits
for a few objects, such as ID 21623. Candidates also show small SFR values,
and young stellar ages between 10 and 100 Myr, confirming previous JWST
results at similar redshifts (Furtak et al., 2021; Topping et al., 2022;
Austin et al., 2023; Whitler et al., 2023). Taken at face value and
considering a constant star formation, their stellar mass would imply older
ages. It is clear that the current SFR derived from our SED fitting is not
representative of the entire star formation history of these candidates.
Intermittent episodes of intense star formation, or simply a higher SFR,
likely occurred in the past in order to build up the estimated stellar mass so
quickly.

####  4.2.1 Mass-Luminosity relation

In addition to the stellar mass derived from the SED fitting, we computed the
absolute rest-frame UV magnitude by combining the observed magnitude in F200W
band and the photometric redshift (column 6 of Table 2). The M⋆-$M_{\rm UV}$
relation provides insights into the stellar mass build up of galaxies and its
evolution with redshift. Figure 7 shows the M⋆-$M_{\rm UV}$ best-fit relation
determined at $z\sim 6$ (blue line; Furtak et al., 2021) and at $z\sim 9$
(black line; Bhatawdekar et al., 2019) using HST and Spitzer observations. The
redshift-evolution of this relation can already be observed. Properties of the
present sample are shown with squares. The red squares indicate the robust
subset of candidates (cf. Table 2). Our results are consistent with a redshift
evolution, where galaxies are on average below the established relations at
lower redshifts. They are also in agreement with other recent JWST constraints
derived by Whitler et al. (2023) represented by purple circles. We note that
for galaxy candidates at $z\gtrsim 11$, the absence of constraints on the
Balmer break tend to underestimate the stellar mass we derive from SED
fitting. Furthermore, the green-shaded region and the red-dashed line are
theoretical predictions at $z=9$ computed from hydrodynamical zoom simulations
(Kannan et al., 2022) and semi-analytical models (Yung et al., 2019). Models
also predict a rapid evolution with redshift, in line with our results.

Figure 7: The stellar mass-luminosity relation for high-redshift galaxies. The
sample of the present study is represented with orange squares. Best-fir
relations derived from observational constraints at $z\sim 6$ are indicated
with the blue-shaded region (Furtak et al., 2021), while results at $z\sim 9$
are indicated with a black line (Bhatawdekar et al., 2019). Theoretical
predictions from semi-analytical models at $z=10$ (Yung et al., 2019) and
hydrodynamical simualtions at $z=9$ are plotted with a red-dashed line and
green-shaded region, respectively.

####  4.2.2 UV Continuum slopes

Next, we explore the UV continuum slope $\beta$, which is widely used to infer
the dust attenuation in high-redshift galaxies. This parameter also encodes
information about the age of the stellar population, where the contribution
from young stars will result in a bluer UV slope. The $\beta$ slope is
measured by fitting a power law of the form
$f_{\lambda}\propto\lambda^{\beta}$ to the rest-frame UV photometric
measurements below 3000 Å in F200W, F277W, F356W bands. We fixed the redshift
to the Eazy best-fit phot$-z$. To estimate the impact of redshift and
photometric uncertainties, we performed a Monte Carlo sampling using a normal
distribution around these fixed parameters in the fitting procedure. The
results are provided in Table 2. Like most of the $z>9$ galaxies recently
uncovered in JWST observations, these candidates show blue UV slopes ranging
from $\beta=-1.8$ to -2.3, which is expected if these candidates have younger
stellar populations with low-durst attenuation and metallicities. Absence of
dust has also been invoked to explain the high number density of high-z
galaxies (Ferrara et al., 2022). We do not find however evidence for extremely
blue slopes like those that were reported in early JWST data (Topping et al.,
2022; Adams et al., 2023). When compared to literature results (see Figure 8),
these candidates show bluer UV slopes at a given luminosity than those
observed in $z\sim 6$ galaxies, for instance (Bouwens et al., 2014) or more
recently from JWST observations (Nanayakkara et al., 2022). They follow the
general trend of $z>9$ galaxies (Austin et al., 2023; Cullen et al., 2023;
Curtis-Lake et al., 2022; Whitler et al., 2023), for which we show only robust
measurements with uncertainties below 0.3 dex. Similarly, the $\beta$-$M_{\rm
UV}$ relation derived from the latest numerical simulations, such FLARES
(Vijayan et al., 2021; Wilkins et al., 2023) and Thesan (Kannan et al., 2022),
show broad agreement with the observed $\beta$ values.

In addition to the dependence with age, the UV slope is also affected by the
nebular continuum, whose contribution is larger at longer wavelengths, which
results in redder $\beta$ values. Albeit with large uncertainties, these
effects, combined with constraints from nebular recombination lines, can be
used to indirectly infer the escape fraction of ionizing continuum $f_{esc}$
in galaxies at the epoch of reionization (e.g., Zackrisson et al., 2017; Plat
et al., 2019; Topping et al., 2022).

Figure 8: The UV continuum slope $\beta$ as a function of the UV magnitude.
The present sample is represented by orange squares, while recent JWST results
at similar redshifts are marked with circles (Austin et al., 2023; Cullen et
al., 2023; Whitler et al., 2023) and stars (Curtis-Lake et al., 2022). We also
show theoretical predictions for this relation with a shaded green region
(Kannan et al., 2022) and a gray region (Vijayan et al., 2021), and two brown
curves with (upper curve) and without (lower curve) dust attenuation (Wilkins
et al., 2023). The empirical relation established at $z\sim 6$ by Bouwens et
al. (2014) is represented with the blue line.

##  5 Summary

In this paper, we presented the results of our search for $z>9$ galaxy
candidates in the JWST UNCOVER survey. We used deep NIRCam and NIRISS imaging
from three observing programs UNCOVER (Bezanson et al., 2022), GLASS (Treu et
al., 2022), and a DD program ID 2767, in addition to ancillary HST
observations. We combined dropout selection and photometric redshift estimates
from two independent codes, Eazy and BEAGLE, to identify high-redshift galaxy
candidates. We report the detection of 16 candidates at $9<z<12$ and 3
candidates at $12<z<13$. According to our quality assessment, a total of 7
candidates are deemed robust among this sample. Candidates span a wide dynamic
range in luminosity, from $M_{\rm UV}$ $\sim$ -22 to -17.6 mag. Some of these
sources are among the faintest galaxies discovered at $z>10$, although most of
their magnification factors are still relatively modest, i.e. below $\mu=5$.
Two candidates have spectroscopic confirmation at redshift $z=9.76$ and
$z=9.3$.

In addition to photometric redshift, we ran refined SED fitting with BEAGLE to
constrain the physical properties of the sample, fixing the redshift and
focusing on four parameters: the stellar mass, the stellar age, the star
formation rate averaged over the last 10 Myr, and the attenuation $\tau_{V}$.
We find that galaxies have young ages between 10 and 100 Myr and low star
formation rates from $\sim 0.2$ to $\sim 7$ M⊙ yr-1. These results confirm
previous findings in early JWST observations of $z>9$ galaxies. Most of the
candidates have low stellar masses in the range log(M⋆/M⊙) $\sim$ 6.8-9.5. We
find evidence for a rapid redshift-evolution of the mass-luminosity relation,
in line with recent observational results and theoretical predictions.

We also find that these galaxies have blue UV continuum slopes, between
$\beta=-1.8$ and $\beta=-2.4$, although we do not find extremely blue $\beta$
values as measured in recent $z>10$ studies. The young ages we measure are
consistent with these blue continuum slopes. We also see a redshift-evolution
of the UV slope for a given intrinsic magnitude. The sample aligns with
theoretical predictions and similar observational results for the
$\beta$-$M_{\rm UV}$ relation at $z>9$.

In the near future, JWST will continue to provide increasingly larger samples
of rest-optical observations of galaxies at $z>9$. Combined with follow-up
spectroscopy, these data will help constrain more precisely the physical
properties and star formation histories of these galaxies. In particular,
ultra-deep observations of additional lensing clusters will help us push to
fainter and more representative galaxies at those early epochs.

## Acknowledgements

This work is based on observations obtained with the NASA/ESA/CSA JWST and the
NASA/ESA Hubble Space Telescope (HST), retrieved from the Mikulski Archive for
Space Telescopes (MAST) at the Space Telescope Science Institute (STScI).
STScI is operated by the Association of Universities for Research in
Astronomy, Inc. under NASA contract NAS 5-26555. This work has made use of the
CANDIDE Cluster at the Institut d’Astrophysique de Paris (IAP), made possible
by grants from the PNCG and the region of Île de France through the program
DIM-ACAV+. This work was supported by CNES, focused on the JWST mission. This
work was supported by the Programme National Cosmology and Galaxies (PNCG) of
CNRS/INSU with INP and IN2P3, co-funded by CEA and CNES. P. Dayal acknowledges
support from the NWO grant 016.VIDI.189.162 (“ODIN") and the European
Commission’s and University of Groningen’s CO-FUND Rosalind Franklin program.

## Data Availability

The data underlying this article are publicly available on the Mikulski
Archive for Space Telescopes222https://archive.stsci.edu/ (MAST), under
program ID 2561. Reduced and calibrated mosaics are also available on the
UNCOVER webpage: https://jwst-uncover.github.io/

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# Andreev reflection adjusting in the multi-terminal device with the kink
states

Lin Zhang1,3, Chao Wang∗1,2, Peipei Zhang1, and Yu-Xian Li∗1 1College of
Physics and Hebei Advanced Thin Film Laboratory, Hebei Normal University,
Shijiazhuang 050024, People’s Republic of China
2College of Physics, Shijiazhuang University, Shijiazhuang 050035, People’s
Republic of China
3Shool of Mathematics and Science, Hebei GEO University, Shijiazhuang 050031,
People’s Republic of China

###### Abstract

At the domain wall between two regions with the opposite Chern number, there
should be the one-dimensional chiral states, which are called as the kink
states. The kink states are robust for the lattice deformations. We design a
multi-terminal device with the kink states to study the local Andreev
reflection and the crossed Andreev reflection. In the three-terminal device
the local Andreev reflection can be suppressed completely for either
$\varepsilon_{0}=0.5\Delta_{s}$ and $V_{0}=0.1t$ or
$\varepsilon_{0}=-0.5\Delta_{s}$ and $V_{0}=-0.1t$, where $\varepsilon_{0}$ is
the on-site energy of the graphene terminals and $V_{0}$ is the stagger energy
of the center region. The coefficient of the crossed Andreev reflection can
reach $1$ in the four-terminal device. Besides adjusting the phase difference
between superconductors, the local Andreev reflection and the crossed Andreev
reflection can be controlled by changing the on-site energy and the stagger
energy in the four-terminal device. Our results give some new ideas to design
the quantum device in the future.

##  I Introduction

Topological insulatorMoore2010 (1) has been one of the noticeable advanced
materials due to the novel physical propertiesHasan2010 (2, 3), such as
quantum Hall effectLaughlin1981 (4, 5) and quantum spin Hall effectKane2005a
(6, 7). It is of great significance to study the properties of topological
insulator for developing a new generation of quantum components. Recently, the
quantum anomalous Hall effect has been identified in the three-dimensional
magnetic topological insulatorYu2010 (8, 9, 10, 11), which opens new
possibilities for chiral-edge-state-based devices in zero external magnetic
fieldYasuda2017 (12, 13). The chiral states can also appear at the domain
walls between two regions with the opposite Chern numberLi2017 (14). For
example, the graphene can be gapped by the sublattice symmetry breaking
staggered on-site energy, which is showed in Fig. 1. There are one-dimensional
statesQiao2011 (15, 16, 17, 18), which are referred to as kink states below,
presenting at the boundaries between regions with different quantized Hall
conductances in the graphene nanoribbon.

Figure 1: (Color online) The schematic diagram of the four-terminal device
with the kink states. The terminal 1 and 3 are the graphene ribbons. The width
and the length of the central region are $W=8$ and $L=28$, respectively. The
terminal 2 and 4 are the superconductors. In the center region marked
${}^{\prime}+^{\prime}$(green), the on-site energy is $\varepsilon_{A}=V_{0}$
and $\varepsilon_{B}=-V_{0}$, where $V_{0}$ is called as the stagger energy.
In the region marked ${}^{\prime}-^{\prime}$ (orange),
$\varepsilon_{A}=-V_{0}$ and $\varepsilon_{B}=V_{0}$. The kink states are at
the interface between two regions with the opposite stagger energy.

.

A Majorana fermion, which is its own antiparticle, has the potential for
quantum computing. Over the last two decades it has been realized that
Majorana fermions can emerge at zero-energy modes in topological
superconductorsFu2009 (19, 20, 21). After the chiral Majorana edge modes in
the quantum anomalous Hall insulator-superconductor structure is realized in
the experiment, there are more researches focused on the topological
superconductor deviceXie2009 (23, 24, 25, 26, 27, 28, 29).

At the interface between a superconductor and a normal conductor, an incident
electron from the normal conductor can be reflected as a hole, which is called
Andreev reflection. When the bias voltage is lower than the superconductor
gap, the conductance of the superconductor hybrid device is mainly determined
by the progress of the Andreev reflection. Keeping to the time-reversal
symmetry, the electron and the hole taking part in Andreev reflection come
from the different valleys in the graphene-superconductor deviceBeenakker2006
(30, 31, 32).

In this paper, we calculate the transmission coefficients in a two-terminal
device, where there are lattice deformations around the domain wall. The
transmission coefficients are close to $1$ in the two-terminal device, which
proves the robustness of the kink statesQiao2011 (15, 16, 17). Then we study
the Andreev reflection in the four-terminal device with the topological kink
states showed in Fig. 1. Through calculating the coefficients of the Andreev
reflection in the four-terminal device, we find that the progress of the
crossed Andreev reflection can be controlled by adjusting the on-site energy
and the stagger energy.

The rest of this paper is arranged as follows. In Sec.II, the model
Hamiltonian for the system is presented and the formulas for calculating the
Andreev reflection coefficients are derived. Our main results are shown and
discussed in Sec.III. Finally, a brief conclusion is presented in Sec.IV.

##  II MODEL AND METHOD

The four-terminal device with the kink states is showed in Fig. 1, where the
terminal $1$ and $3$ are the normal graphene ribbons and the terminal $2$ and
$4$ are superconductors. The center region is the colour region. The kink
states are at the interface between the regions with different colour. Along
the x direction and the y direction they are zigzag and armchair,
respectively. The total Hamiltonian of this junction can be represented as

$\ H=H_{C}+H_{G}+H_{S}+H_{T},$ (1)

where$H_{C}$, $H_{G}$, $H_{S}$ and $H_{T}$ are the Hamiltonian of the center
region, the graphene nanoribbons, the superconductor terminals and the
coupling between the center region and the superconductor terminals,
respectively.

In the tight-binding representation, $H_{C}$ and $H_{G}$ are given by

$\displaystyle
H_{C/G}=\sum_{n}\varepsilon_{0}a^{{\dagger}}_{\emph{n}}a_{\emph{n}}-\sum_{<m,n>}[ta_{\emph{n}}^{\dagger}a_{\emph{m}}+H.c.],\qquad$
(2)

where $a_{\emph{n}}^{\dagger}$ and $a_{\emph{n}}$ are the creation operator
and annihilation operators of the $n$th point. $\varepsilon_{0}$ is the on-
site energy in the graphene terminals and the center region. In the center
region, $\varepsilon_{0}=\pm V_{0}$ for the different partition, where $V_{0}$
is the stagger energy of A and B sublattice. The second term in Eq. (2) stands
for the nearest-neighbor hopping Hamiltonian. Considering that the center
region is directly coupled to the superconductor terminals, we use the BCS
Hamiltonian for the superconductor terminals described by a continuum model,

$\displaystyle
H_{S}=\sum_{\textbf{\emph{k}},\sigma}\varepsilon_{\textbf{\emph{k}}}C^{\dagger}_{\textbf{\emph{k}}\sigma}C_{\textbf{\emph{k}}\sigma}+\sum_{\textbf{\emph{k}}}(\Delta
C_{\textbf{\emph{k}}\downarrow}C_{-\textbf{\emph{k}}\uparrow}+\Delta^{*}C^{\dagger}_{-\textbf{\emph{k}}\uparrow}C^{\dagger}_{\textbf{\emph{k}}\downarrow}),\qquad$
(3)

where $\Delta=\Delta_{s}e^{\mathrm{i}\theta}$. Here $\Delta_{s}$ is the
superconductor gap and $\theta$ is the superconductor phase. The coupling
between superconductor terminals and graphene is described by

$\displaystyle
H_{T}=-\sum_{\emph{n},\sigma}\emph{t}_{c}a^{\dagger}_{\emph{n},\sigma}C_{\sigma}(x_{\emph{i}})+H.c.$
(4)

Here $x_{\emph{i}}$ and $n$ represent the positions of the coupling atoms on
the interface of superconductor and the center region, and
$C_{\sigma}(x)=\sum_{\emph{k}_{x}}e^{\mathrm{i}k_{x}x}C_{\textbf{\emph{k}},\sigma}$
is the annihilation operator in real space. Note that $\sigma$ represents the
spin index and $\emph{t}_{c}$ is the coupling strength between graphene and
superconductor terminals.

We now turn to analyze the process that an incident electron from the graphene
terminal is reflected into a hole with a Cooper pair emerging in the
superconductor terminal. Using nonequilibrium Green’s function method, we can
calculate the retarded and advanced Green’s function
$G^{r}(E)=[G^{a}]^{\dagger}=1/(EI-
H_{C}-\sum_{\alpha}\mathbf{\Sigma}^{r}_{\alpha})$, where $H_{C}$ is the
Hamiltonian of the center region in the Nambu representation and $I$ is the
unit matrix with the same dimension as $H_{C}$.
$\mathbf{\Sigma}_{\alpha}^{r}=t_{c}g_{\alpha}^{r}(E)t_{c}$ is the retarded
self-energy due to the coupling to the terminal $\alpha$, where
$g_{\alpha}^{r}(E)$ is the surface Green’s function of the terminal $\alpha$.
We can numerically calculate the surface Green’s function of the graphene
terminals. For superconductor terminals, the surface Green’s functionXie2009
(23, 27, 25) in real space is

$\displaystyle
g_{\alpha,ij}^{r}(E)=i\pi\rho\beta(E)J_{0}[k_{f}(x_{i}-x_{j})]\left(\begin{array}[]{cc}1&\Delta/E\\\
\Delta^{*}/E&1\\\ \end{array}\right),\qquad$ (7)

where $\alpha=2,4$ and $\rho$ is the density of normal electron states.
$J_{0}[k_{f}(x_{i}-x_{j})]$ is the Bessel function of the first kind with the
Fermi wavevector $k_{f}$. $\beta(E)=-iE/\sqrt{\Delta_{s}^{2}-E^{2}}$ for
$|E|<\Delta_{s}$ and $\beta(E)=|E|/\sqrt{E^{2}-\Delta_{s}^{2}}$ for
$|E|>\Delta_{s}$.

The Andreev reflection coefficients for the incident electron coming from the
graphene terminal $1$ can be obtainedXie2009 (23) by

$\displaystyle
T_{A,11}(E)=\mathrm{Tr}\\{\Gamma_{1,\uparrow\uparrow}G^{r}_{\uparrow\downarrow}\Gamma_{1,\downarrow\downarrow}G^{a}_{\downarrow\uparrow}\\},$
$\displaystyle
T_{A,13}(E)=\mathrm{Tr}\\{\Gamma_{1,\uparrow\uparrow}G^{r}_{\uparrow\downarrow}\Gamma_{3,\downarrow\downarrow}G^{a}_{\downarrow\uparrow}\\},$
(8)

where the subscripts $\uparrow\uparrow$, $\downarrow\downarrow$,
$\uparrow\downarrow$ and $\downarrow\uparrow$ represent the 11, 22, 12 and 21
matrix elements, respectively, in the Nambu representation. The linewidth
function $\Gamma_{\alpha}$ is defined with the aid of self-energy as
$\Gamma_{\alpha}=i[\mathbf{\Sigma}_{\alpha}^{r}-(\mathbf{\Sigma}_{\alpha}^{r})^{{\dagger}}]$.
$T_{A,11}$ and $T_{A,13}$ represent the coefficients of the local Andreev
reflection and the crossed Andreev reflection, respectively. Because the
Andreev reflection from an electron to a hole is equivalent to that from a
hole to an electron under particle-hole symmetry, in this work we only
consider the Andreev reflection, where an incident electron is reflected as a
hole.

##  III NUMERICAL RESULTS AND ANALYSIS

In numerical calculations, we set the nearest-neighbour hopping energy
$t=2.75eV$. The length of the nearest-neighbor C-C bond is set to be
$a_{0}=0.142$ $\mathrm{nm}$ as in a real graphene sample. The superconductor
gap is set to be $\Delta_{s}=0.02t$ and the Fermi wavevector $k_{f}=10$
$\mathrm{nm^{-1}}$. For the convenience of discussing the influence of the
kink states on Andreev reflection, The Fermi energy $E_{\textit{f}}$ is set to
be zeros in our calculations for the convenient.

Figure 2: (Color online) The local density of states distribution for modes
incident from the terminal $1$. All of the terminals are the graphene
nanoribbons. The width and the length of the central region are $W=80$ and
$L=120$, respectively.

Fig. 2 shows the local density of states contribution of scattering states
injected from the terminal $1$ when the four terminals connected with the
center region are the graphene nanoribbon. From Fig. 2, we can see that in the
center region the electrons can only travel along the interface between two
regions with the opposite value of stagger energy.It is clear that when the
electrons injected from terminal $1$, they can only travel along the kink
states into the terminal $2$ and the terminal $4$. The propagation to terminal
$3$ is forbidden. It shows that an electronic beam splitter is created by this
design. At the intersection point propagation in the forward direction from
the terminal $1$ to the terminal $3$ is forbidden because of the reversed
pseudospin in the direction of propagation along the $x$ directionQiao2011
(15), which is explained in the energy band below.

Figure 3: (Color online) $T_{A}$ vs the incident energy $\varepsilon$ in the
three-terminal device. The on-site energy of the garphene terminal is
$\varepsilon_{0}=0.5\Delta_{s}$ in (a) and (b) and
$\varepsilon_{0}=-0.5\Delta_{s}$ in (c) and (d). The stagger energy is
$V_{0}=0.1t=50\Delta_{s}$ in (a) and (c) and $V_{0}=-0.1t=-50\Delta_{s}$ in
(b) and (d). The width and the length of the central region are $W=80$ and
$L=120$, respectively.

It is certified that how the electrons travel along the kink states in the
four-terminal device in Fig. 2. Next we want to know the influences of the
kink states on the Andreev reflection. The superconductor gap is set to be
$\Delta_{s}=0.02t$, which is more less than the stagger energy $|V_{0}|=0.1t$,
so that only kink states take part in the progress of Andreev reflection.
Firstly, we study a three-terminal superconductor device, where only one
superconductor terminal $2$ or $4$ is retained in the four-terminal device,
which is showed in Fig. 1. The coefficients of the local Andreev reflection
$T_{A,11}$ and the crossed Andreev reflection $T_{A,13}$ varying with the
incident energy $\varepsilon$ in the three-terminal device are presented in
Fig. 3.

In Fig. 3 (a), when $\varepsilon_{0}=0.5\Delta_{s}$ and $V_{0}=0.1t$, the
coefficient of local Andreev reflection is $T_{A,11}=0$, so the local Andreev
reflection is suppressed. The coefficient of the crossed Andreev reflection is
zero for $-1.5\Delta_{s}<\varepsilon<0.5\Delta_{s}$. When the incident energy
increases to $\varepsilon=0.5\Delta_{s}$, $T_{A,13}$ changes from $0$ to $0.8$
quickly, then oscillates with $\varepsilon$ increasing. $T_{A,13}$ reaches the
peak value about $0.9$ when $\varepsilon$ increases to $0.85\Delta_{s}$. With
$\varepsilon$ increasing more than $0.9\Delta_{s}$, $T_{A,13}$ decreases
quickly. Fixing the on-site energy $\varepsilon_{0}=0.5\Delta_{s}$ and
adjusting the stagger energy to $V_{0}=-0.1t$ in Fig. 3 (b), we can see that
there is the local Andreev reflection arising for
$-0.5\Delta_{s}<\varepsilon<0.5\Delta_{s}$. $T_{A,11}$ is symmetrical about
the point $\varepsilon=0$ and reaches the peak value $0.8$ at the points of
$|\varepsilon|=0.25\Delta_{s}$. $T_{A,13}$ is zero for
$-0.5\Delta_{s}<\varepsilon<1.5\Delta_{s}$. When the incident energy decreases
from $-0.5\Delta_{s}$, $T_{A,13}$ increases to the peak value $1.0$ quickly
and oscillates with $\varepsilon$ decreasing. $T_{A,13}$ reaches the second
highest peak value about $0.85$ at $\varepsilon=-1.0\Delta_{s}$, then
decreases quickly with $\varepsilon$ decreasing less than $-1.0\Delta_{s}$.
When the stagger energy is set to be $V_{0}=1.0t$ and the on-site energy is
$-0.5\Delta_{s}$, the curves in Fig. 3 (c) are the same as the mirror image of
that in Fig. 3 (b). Setting $V_{0}=-1.0t$ and
$\varepsilon_{0}=-0.5\Delta_{s}$, we find that the local Andreev reflection is
suppressed again and the curve of $T_{A,13}$ in Fig. 3 (d) is the same as the
mirror image of that in Fig. 3 (a).

In Fig. 3, $\varepsilon=|\varepsilon_{0}|$ are a critical points between
$T_{A,11}$ and $T_{A,13}$. In Fig. 3 (a) and (d) the local Andreev reflection
is suppressed and the crossed Andreev reflection takes place for
$\varepsilon>|\varepsilon_{0}|$ in Fig. 3 (a) and
$\varepsilon<-|\varepsilon_{0}|$ in Fig. 3 (d). In Fig. 3 (b) and (c),
$T_{A,11}$ is nonzero for $\varepsilon<|\varepsilon_{0}|$. $T_{A,13}$ is zeros
for $\varepsilon>-|\varepsilon_{0}|$ and $\varepsilon<|\varepsilon_{0}|$ in
Fig. 3 (b) and (c), respectively. When the sign of the on-site energy
$\varepsilon_{0}$ and the stagger energy $V_{0}$ are set to be same, the local
Andreev reflection is suppressed. To sum up, the progress of Andreev
reflection can be controlled by adjusting the on-site energy and the stagger
energy in the device with kink states.

Figure 4: (Color online) The coefficients of the local Andreev reflection
$T_{A,11}$ and the crossed Andreev reflection $T_{A,13}$ vs the incident
energy $E$ in the four-terminal graphene-superconductor junction. The phase
difference between two superconductor terminals is $\triangle\phi=0$ in (a)
and (b) and $\triangle\phi=\pi$ in (c) and (d).

Then when we set the on-site energy $\varepsilon_{0}=0.5\Delta_{s}$, the
coefficients of Andreev reflection in the four-terminal device are showed in
Fig. 4 for $V_{0}=\pm 0.1t$. In the previous works, Andreev reflection can be
adjusted by the phase difference of the superconductor terminals
$\triangle\phi$ in the four-terminal devicecheng2009 (33, 34). The local
Andreev reflection is suppressed when $\triangle\phi=\pi$, conversely, the
crossed Andreev reflection is suppressed when $\triangle\phi=0$. In Fig. 4 (b)
and (c), it is clear that the crossed Andreev reflection $T_{A,13}$ is
suppressed for $\triangle\phi=0$ and the local Andreev reflection $T_{A,11}$
is suppressed for $\triangle\phi=\pi$. These results are in accord with the
previous workcheng2009 (33, 35). It is important to note that in Fig. 4 (a)
for $V_{0}=0.1t$ $T_{A,11}$ is always zero when $\triangle\phi=0$, which is
different from the results of the previous works. That is to say when
$\triangle\phi=0$ the local Andreev reflection can be suppressed by adjusting
the stagger energy. In Fig. 4 (d), for $\varepsilon_{0}=\pm 0.5\Delta_{s}$,
when $V_{0}=0.1t$, $T_{A,13}$ keeps zero for $\varepsilon<|\varepsilon_{0}|$;
on the contrary, when $V_{0}=-0.1t$, $T_{A,13}$ keeps zero for
$\varepsilon>-|\varepsilon_{0}|$.

Figure 5: (Color online) $T_{A}$ vs the incident energy $\varepsilon$ in the
four-terminal device. The phase difference between superconductors is
$\triangle\phi=\pi$.

After that, the on-site energy is set to be zero. In Fig. 5, as the incident
energy changing the coefficients of the crossed Andreev reflection $T_{A,13}$
in the four-terminal device are showed for the on-site energy
$\varepsilon_{0}=0$ with $\triangle\phi=\pi$. When $V_{0}=0.1t$, the
coefficient is zero for the incident energy $\varepsilon<0$. Increasing the
incident energy, the coefficient changes from $0$ to $0.2$ rapidly. When
$\varepsilon$ comes up to $0.5\Delta_{s}$, the coefficient reaches the peak.
Continuing increasing $\varepsilon$, the coefficient decreases gradually. When
$V_{0}=-0.1t$, $T_{A,13}$ is zero for $\varepsilon>0$ and reaches the peak at
$\varepsilon=-0.5\Delta_{s}$. The peak value of the coefficients can reach $1$
at $\varepsilon=|0.5\Delta_{s}|$, namely all of the reflected hole can
transport into terminal $3$ in this device in some conditions. To explain this
case we plot the energy band structures of the terminal and the center region
in Fig. 6.

Fig. 6 (a) and (b) are the energy band structures of the terminal $1$ and $3$
with $\varepsilon_{0}=\pm 0.5\Delta_{s}=\pm 0.01t$. Fig. 6 (c) and (d) are the
energy bands of the center region with opposite stagger energy, respectively.
In Fig. 7 (a), the point A and B are in the conduction band. The point A is in
the valley $K$ and represents the state of outgoing. The point B is in the
valley $K^{\prime}$ and represents the state of incoming. In Fig. 6 (b), the
point C and D are in valence band. The point C in the valley K represents the
state of incoming and the point D in valley $K^{\prime}$ represents the state
of outgoing. Similarly, in Fig. 6 (c) and (d) the point O and R (P and Q)
represent the state of incoming (outgoing), which belong to the valley $K$ and
$K^{\prime}$, respectively.

When the incident electrons from terminal $1$ travel into the center region,
which come from the point $B$ in the conduction band, they can transport into
the point $O$ or the point $R$ due to the conservation of the momentum. Beside
the conservation of the momentum, the travel of the electron must make the
pseudospin invariant. So the transport from the point $B$ to the point $O$ is
forbidden and the incident electrons from the point $B$ can only travel into
the point $R$. In other words, for the low-potential regions, when the
incident electrons coming from the valley $K$ (the conduction band) or
$K^{\prime}$ (the valence band) travel into the center region, they should
travel into the same valley in the band of center region with the kink states,
otherwise, propagation is forbidden. It can explain why the propagation is
forbidden in Fig. 2. In Fig. 5, when the incident energy
$\varepsilon>\varepsilon_{0}$, the electrons come from the point $B$ in the
conduction band. So the incident electrons can only travel into point R for
$V_{0}=0.1t$ and the propagation of the electrons is forbidden for
$\varepsilon<\varepsilon_{0}$ in this case.

Figure 6: (Color online) (a) and (b) are the band structures of the graphene
terminals with different $E_{\textit{f}}$. (c) and (d) are the band structures
of center region with different stagger energy $V_{0}$ in the x direction. The
lines in blue represent the kink states.

There is another question to answer. When $\varepsilon_{0}=0$ the local
Andreev reflection is suppressed and $T_{A,11}$ is zeros for $\Delta\phi=\pi$
which is beneficial for the crossed Andreev reflection in the four-terminal
device. However, we find that for $\Delta\phi=0$, which is beneficial for the
local Andreev reflection, the coefficient $T_{A,11}$ is always zeros when
$\varepsilon_{0}=0$. The figure is not showed in the paper.

What is the reason of this case? From Fig. 2, we know that the incident
electrons with $\varepsilon$ travel along the kink states to the interfaces
between the center region and the superconductors. The reflected holes with
$-\varepsilon$ must travel along the kink states, too. From our discussions,
we know that due to the conservation of the momentum and the pseudospin,
propagation of the incident electrons can be forbidden in some conditions. The
same reason applies to propagation of the reflected holes. For example, when
$\varepsilon_{0}=0$, the incident electrons from the valley $K$ can travel
into the center region along the zigzag kink states for
$\varepsilon>\varepsilon_{0}$ and $V_{0}=0.1t$. As the incident electrons flow
into the superconductor along the armchair kink states, the reflected holes
with $-\varepsilon$ travel back to the center region along the armchair kink
states. At the intersection, along the zigzag kink states the reflected holes
flowing in the $-x$ direction belongs to the valley $K^{\prime}$ and can not
flow into the terminal $1$. So the reflected holes flowing in the $x$
direction, which belong to the valley $K$, can only travel into the terminal
$3$.

Figure 7: (Color online) The transmission coefficients vs the incident energy
$E$ in the two-terminal junction with zigzag ribbon under the lattice
deformation. The width and the length of the central region are $W=80$ and
$L=60$, respectively.

The lattice deformations around the interface are common in the real device.
There is a question how the lattice deformations influence the kink states.
The two-terminal device with the kink states is showed in the inset of Fig. 7.
Considering the deformations of the lattices near the interface, we calculate
the transmission coefficients for $V_{0}=\pm 0.1t$ to answer the question. The
transmission coefficient is
$T=\mathrm{Tr}\\{\Gamma_{L}G^{r}\Gamma_{R}G^{a}\\}$, where $L$ and $R$
represents the terminal $1$ and $2$ in the two-terminal device, respectively.
We set the deformation of the lattice to be a random value in the range of
$[0,0.2a]$. The processes of the calculation are cycled for $500$ times and
the average values are showed in Fig. 7. Due to the lattice deformation, there
should be scattering effect at the interface, the transport coefficients are a
little less than $1$ for the stagger energy $V_{0}=0.1t$ or $V_{0}=-0.1t$.
From the Fig. 7, we can see that the influence of the lattice deformation on
transport is very slight, the minimum value of the transport coefficients is
about $0.998$, which is very close to $1$. The kink states are robust, so it
is a good choice for designing quantum devices.

##  IV CONCLUSIONS

We study the influence of the lattice deformations on the kink states in a
two-terminal device. Through our research, we certify that the lattice
deformations could weaken the electron transport along the kink states, but
the influence is very small. So the kink states are robustness under the
lattice deformations.

In the three-terminal device, we find that through adjusting the on-site
energy and the stagger energy, for example $\varepsilon_{0}=0.5\Delta_{s}$ and
$V_{0}=1.0t$, the local Andreev reflection can be completely suppressed. In
the four-terminal device, due to the conservation of the momentum and the
pseudospin, both the local Andreev reflection and the crossed Andreev
reflection can be suppressed when $\triangle\phi=0$ and $V_{0}=0.1t$. This
results show us that the progress of Andreev reflection can be controlled by
adjusting the on-site energy $\varepsilon_{0}$ and the stagger energy $V_{0}$
in the multi-terminal device with the kink states. It should give us some new
ideas on the research and development of the quantum device.

###### Acknowledgements.

This work was supported by the National Natural Science Foundation of China
(Grant Nos. 11874139, 11474085), the Natural Science Foundation of Hebei
(Grant Nos. A2017205108, A2019205190), the youth talent support program of
Hebei education department (Grant No. BJ2014038), the Outstanding Youth
Foundation of HBTU (Grant No. L2016J01), the science program of Shijiazhuang
(Grant No. 201790741), the youth talent support program of Hebei Province, and
Doctoral Research Foundation of Shijiazhuang College (Grant No. 20BS017).

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1

# Commonsense Knowledge Base Construction
in the Age of Big Data

Simon Razniewski111Max Planck Institute for Informatics, Saarbrücken.
<EMAIL_ADDRESS>
###### Abstract

Compiling commonsense knowledge is traditionally an AI topic approached by
manual labor. Recent advances in web data processing have enabled automated
approaches. In this demonstration we will showcase three systems for automated
commonsense knowledge base construction, highlighting each time one aspect of
specific interest to the data management community. (i) We use Quasimodo to
illustrate knowledge extraction systems engineering, (ii) Dice to illustrate
the role that schema constraints play in cleaning fuzzy commonsense knowledge,
and (iii) Ascent to illustrate the relevance of conceptual modelling. The
demos are available online at https://quasimodo.r2.enst.fr, https://dice.mpi-
inf.mpg.de and ascent.mpi-inf.mpg.de.

###### keywords:

Commonsense knowledge Web information extraction Data cleaning

##  1 Motivation

Knowledge and reasoning about general-world concepts are major challenges in
AI. In recent years, these tasks are supported by a growing number of
knowledge repositories, so-called commonsense knowledge bases (CSKBs), that
store statements like lions live in groups, or painters use pencils. CSKBs
share similarities with longer-established encyclopedic KBs (e.g., DBpedia,
Yago, Wikidata) - wide scope, pragmatic construction, triple-centric data
models, incompleteness and reliance on the open-world assumption, yet also
differ notably in terms of semantic and construction complexity [LFL+19,
WDRS21].
In terms of semantic complexity, commonsense assertions generalize across sets
of instances, which makes it more complex to qualify their truth (e.g., lions
attack humans \- does that actually apply to most lions, in most places, most
of the time?). In contrast, instance-centric encyclopedic knowledge in most
cases goes well with a binary truth notion (e.g., Angela Merkel is either born
in Hamburg, or not).
In terms of construction complexity, CSKBs typically have to deal with a
myriad of corroborating and conflicting candidate assertions, and cannot rely
on a fixed set of relations that alleviates consolidation. For example, texts
may state that cats are solitary, and that cats are loners (corroborating
assertions), but also that lions live in packs (conflicting, given that lions
are big cats).

CSKB construction has recently been revived at a global level [SLA+18, THLB19,
ISZ21, ZKSR20], and receives growing interest also in the German data
management community [JBCC19, OZHH20, HSW+20, LFD21].

In this demonstration session we showcase three systems for CSKB construction,
Quasimodo [RRP+19, RR20], Dice [CRW20a, CRW20] and Ascent [NRW21], which are
part of a long-term research agenda on commonsense at the
MPII.222https://www.mpi-inf.mpg.de/departments/databases-and-information-
systems/research/yago-naga/commonsense Each system highlights one particular
aspect of CSKB construction with high relevance to the data management
community:

  1. 1.

Quasimodo: Knowledge extraction systems engineering: Quasimodo is a multi-
source CSKB construction system, exemplarily highlighting the important stages
of CSKB construction, from source identification to extraction, normalization,
validation signal gathering and supervised consolidation.

  2. 2.

Dice: Soft schema constraints for CSK cleaning: In databases, schema
constraints are typically clear-cut rules that are strictly enforced. Although
strict rules are not applicable to CSK, in Dice we show how soft schema
constraints can be utilized to clean noisy CSKB assertions within an
approximate and joint reasoning framework.

  3. 3.

Ascent: Conceptual modelling for CSK: Most CSKBs adopt a simple triple-based
data model, thus gaining maximum flexibility, at the price of limits on
expressivity. With Ascent we show how conceptual modelling can help to capture
important relations among commonsence concepts, as well as qualifications for
CSK triples.

##  2 Systems Description

Quasimodo is a CSKB construction framework designed to extract salient
assertions, that is, assertions that would spontaneously come to the mind of
humans. To achieve this, Quasimodo taps into search engine query logs via
auto-completion suggestions as a non-standard input source. However, frequent
queries – which are the ones that are visible through auto-completion – are
often about sensational and untypical issues. Therefore, Quasimodo combine a
recall-oriented candidate gathering phase with two subsequent phases for
cleaning, refining, and ranking assertions. Pipeline runs can be inspected in
the demonstration system, where one can see in detail how source text give
rise to extraction candidates, how these are validated against corroboration
sources, and how assertions are ranked and utilized in use cases. Uniquely, it
is the first automated CSKB construction system focusing on salient
assertions.

Dice: Database constraints like foreign keys, or value type restrictions, or
regex checks are instrumental for ensuring data quality, yet not suited for
the open nature of CSK. The Dice framework therefore uses relaxed soft
constraints, such as that assertion of taxonomic parents should typically also
apply to children, or that textually similar assertions more likely have a
similar truth value, to consolidate noisy candidate sets of CSK assertions.
Specifically, Dice encodes 17 kinds of these constraints, encodes statement
scoring into a weighted MaxSAT problem, and uses approximate solutions found
via linear programming in order to efficiently consolidate very large
candidate sets. The demo system allows inspecting the underlying taxonomies,
the grounded constraint system, and the resulting scores of assertions.
Uniquely, it is the first CSKB consolidation system that jointly consolidates
candidate assertions.

Ascent introduces a data model where CSK assertions are refined by qualitative
facets, thus allowing a finer-grained qualification of assertion truth. It
relies on a combination of judicious automated web querying to collect source
texts, and dependency-parsing-based extraction that obtains not only S-P-O-
triples, but also qualifications such as TIME, LOCATION or CAUSE. To deal with
noise and redundancy, in a consolidation phase, assertions are iteratively
grouped and semantically organized by an efficient combination of fast
word2vec similarity, and classification based on a fine-tuned RoBERTa language
model. It is one of the first systems to go beyond the pure triple-based data
model for CSK.

##  3 Demonstration Experience

Extraction systems engineering (Demo: https://quasimodo.r2.enst.fr)
Demo attendees will be guided step-by-step through the system design of the
Quasimodo CSKB construction pipeline. Each component will be exemplified with
sample concepts, and we will critically review strengths and limitations of
the implemented approach. Furthermore, attendees will be shown how the
resulting knowledge can be utilized in two use cases, question answering, and
the game of Taboo .

Soft constraints for data cleaning (Demo: https://dice.mpi-inf.mpg.de)
Attendees will be shown the web-extracted taxonomy used for building the
constraint systems, as well as the constraint templates. They can then inspect
resulting constraint systems for individual subjects, and how changes in input
weights affect output scores. Furthermore, attendees will be introduced to the
multidimensional scoring mechanism of Dice, and its advantages and challenges
compared with existing unidimensional scoring mechanisms.

Conceptual modelling for CSK (Demo: https://ascent.mpi-inf.mpg.de)
Attendees will be first introduced to the shortcomings of existing CSKBs in
terms of their organisation of subjects and assertions, using the generic
example of elephant trunk, which is out of dictionary for existing CSKBs,
while trunk alone is confused with trunks of different animals, as well as
even car trunks. Attendees will then be shown how Ascent retains trunk and
similar concepts as dedicated aspects of elephant, as well as how it retains
taxonomic as well as state- and activity-based subgroups like Indian elephant,
baby elephant, foraging elephant. Attendees will be shown how the attached
assertions differ substantially, as well as how qualitative assertions of
time, location or degree refine generic triples. Finally, attendees will be
shown the role that state-of-the-art pretrained language models play in the
statement consolidation.

## Acknowledgment

I am grateful to the principal authors of the respective demo systems, Julien
Romero, Yohan Chalier and Tuan-Phong Nguyen, as well as to all other
collaborators.

## References

  * [CRW20] Yohan Chalier, Simon Razniewski and Gerhard Weikum  “Dice: A Joint Reasoning Framework for Multi-Faceted Commonsense Knowledge”  In _ISWC system demonstrations_ , 2020
  * [CRW20a] Yohan Chalier, Simon Razniewski and Gerhard Weikum  “Joint Reasoning for Multi-Faceted Commonsense Knowledge”  In _AKBC_ , 2020
  * [HSW+20] S. Heindorf et al.  “CauseNet: Towards a Causality Graph Extracted from the Web”  In _CIKM_ , 2020
  * [ISZ21] Filip Ilievski, Pedro Szekely and Bin Zhang  “CSKG: The CommonSense Knowledge Graph”  In _ESWC_ , 2021
  * [JBCC19] Soufian Jebbara, Valerio Basile, Elena Cabrio and Philipp Cimiano  “Extracting common sense knowledge via triple ranking using supervised and unsupervised distributional models”  In _Semantic Web Journal_ , 2019
  * [LFD21] Viktor Losing, Lydia Fischer and Joerg Deigmoeller  “Extraction of Common-Sense Relations from Procedural Task Instructions using BERT”  In _Global Wordnet Conference_ , 2021
  * [LFL+19] Yuliang Li et al.  “Subjective databases”  In _VLDB_ , 2019
  * [NRW21] Tuan-Phong Nguyen, Simon Razniewski and Gerhard Weikum  “Advanced Semantics for Commonsense Knowledge Extraction”  In _WWW_ , 2021
  * [OZHH20] Janna Omeliyanenko, Albin Zehe, Lena Hettinger and Andreas Hotho  “LM4KG: Improving Common Sense Knowledge Graphs with Language Models”  In _ISWC_ , 2020
  * [RR20] Julien Romero and Simon Razniewski  “Inside Quasimodo: Exploring Construction and Usage of Commonsense Knowledge”  In _CIKM system demonstrations_ , 2020
  * [RRP+19] Julien Romero et al.  “Commonsense Properties from Query Logs and Question Answering Forums”  In _CIKM_ , 2019
  * [SLA+18] Maarten Sap et al.  “Atomic: An atlas of machine commonsense for if-then reasoning”  In _AAAI_ , 2018
  * [THLB19] Alon Talmor, Jonathan Herzig, Nicholas Lourie and Jonathan Berant  “CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge”  In _NAACL_ , 2019
  * [WDRS21] Gerhard Weikum, Luna Dong, Simon Razniewski and Fabian Suchanek  “Machine Knowledge: Creation and Curation of Comprehensive Knowledge Bases”  In _Foundations and Trends in Databases_ , 2021
  * [ZKSR20] Hongming Zhang, Daniel Khashabi, Yangqiu Song and Dan Roth  “TransOMCS: From Linguistic Graphs to Commonsense Knowledge”  In _IJCAI_ , 2020