# Thin film growth of the Weyl semimetal NbAs

Wilson Yanez  Yu-Sheng Huang  Department of Physics, Pennsylvania State
University, University Park, Pennsylvania 16802, USA  Supriya Ghosh
Department of Chemical Engineering and Materials Science, University of
Minnesota, Minneapolis, Minnesota 55455, USA  Saurav Islam  Emma Steinebronn
Department of Physics, Pennsylvania State University, University Park,
Pennsylvania 16802, USA  Anthony Richardella  Department of Physics,
Pennsylvania State University, University Park, Pennsylvania 16802, USA  K.
Andre Mkhoyan  Department of Chemical Engineering and Materials Science,
University of Minnesota, Minneapolis, Minnesota 55455, USA  Nitin Samarth
<EMAIL_ADDRESS>Department of Physics, Pennsylvania State University,
University Park, Pennsylvania 16802, USA

###### Abstract

We report the synthesis and characterization of thin films of the Weyl
semimetal NbAs grown on GaAs (100) and GaAs (111)B substrates. By choosing the
appropriate substrate, we can stabilize the growth of NbAs in the (001) and
(100) directions. We combine x-ray characterization with high-angle annular
dark field scanning transmission electron microscopy to understand both the
macroscopic and microscopic structure of the NbAs thin films. We show that
these films are textured with domains that are tens of nanometers in size and
that, on a macroscopic scale, are mostly aligned to a single crystalline
direction. Finally, we describe electrical transport measurements that reveal
similar behavior in films grown in both crystalline directions, namely carrier
densities of $\sim 10^{21}-10^{22}$

The TX class (T=Ta/Nb X=As/P) of transition metal monopnictides is a promising
quantum materials platform for studying topological phenomena of contemporary
interest because the bulk band structure corresponds to that of a topological
Weyl semimetal [1, 2, 3, 4]. Broken inversion symmetry in this class of
materials leads to Weyl nodes with different chiralities; when projected onto
the surface of the crystal, these nodes are connected by topological surface
states (Fermi arcs) [1, 2, 5, 4, 6]. Interesting physical phenomena observed
in these canonical Weyl semimetals include the chiral anomaly in charge
transport, transport in the quantum limit under high magnetic fields, phase
transitions between different topological states, strong intrinsic spin Hall
effect, and symmetry-induced non-trivial spin-orbit torque [7, 8, 9, 5, 10].
Most prior studies of this family of topological semimetals have used bulk
single crystal samples; while these are of high structural quality, thin film
samples are more desirable if these Weyl semimetals are to become useful for
technological applications in microelectronics or optoelectronics. This
provides a strong motivation for heterointegration of TX thin films with
materials compatible with semiconductor processing; thin film growth would
also enable the modulation of the band structure by controlling strain in the
crystal [11, 3].

In this study, we develop the synthesis of NbAs thin films on a GaAs substrate
using molecular beam epitaxy (MBE). We show that the growth of NbAs along
different crystalline directions can be stabilized by judicious choice of the
substrate direction. We then use x-ray diffraction to understand the
macroscopic structure of the films, in addition to characterization using
atomic force microscopy and electrical transport measurements. Finally, we use
high-angle annular dark-field scanning transmission electron microscopy
(HAADF-STEM) to show that our films are textured with domains that show a
clear crystal structure and are tens of nanometers in size.

We first discuss the choice of substrate for the growth of NbAs thin films.
NbAs is a transition metal monopnictide that has 12 pairs of Weyl nodes in its
band structure [4, 11, 1]. It is a member of the $\mathrm{I4_{1}md}$ space
group and crystallizes in a body-centered tetragonal structure (Fig. 1(a))
with a lattice constant of $a=0.345$ nm and $c=1.168$ nm [11, 1, 2]. It is
difficult to find an adequate substrate with a lattice constant in this range
[12]. Based on previous reports of MBE growth of this family of semimetals [5,
13, 14, 15], we tried using different III-V semiconductors (GaAs, GaP and
InAs) as our substrates. Among these, the best results were achieved in GaAs
which had a lower lattice mismatch than InAs and, unlike GaP, had the right
surface chemistry to promote NbAs growth. In this paper, we focus on studying
NbAs films grown on GaAs; further information about characterization of NbAs
on other substrates can be found in the supplemental material [16].

Figure 1:  (a) Crystal structure of NbAs. (b) Top view of GaAs (100), NbAs
(001) and NbAs (001) on top of GaAs (100). (c) Top view of GaAs (111)B, NbAs
(100) and NbAs (100) on top of GaAs (111)B. We show the square and hexagonal
symmetry and lattice mismatch between the films and the substrates.

An analysis of the crystal structure of NbAs suggests that the growth of NbAs
(001) can be stabilized by using GaAs (100) as a substrate (Fig. 1(b)): here,
the lattice mismatch is $\mathrm{16\%}$ along the $\langle 110\rangle$ and
$\mathrm{18\%}$ along the $\langle 100\rangle$ GaAs directions. Although this
is a very large lattice mismatch within the context of epitaxial growth, it is
within range to allow NbAs to grow with a $\mathrm{45^{\circ}}$ rotation with
respect to the $\langle 100\rangle$ GaAs direction. NbAs (100) has a similar
relationship with GaAs(111) as a substrate: Fig. 1(c) shows that if we
superimpose both lattices, the NbAs atoms roughly align with the hexagonal
structure of GaAs(111) with a $\mathrm{17\%}$ mismatch on each side.

Figure 2:  RHEED pattern of: (a) GaAs (100) substrate along the
[$\mathrm{\bar{1}10}$], [110] and [010] directions. (b) NbAs (001) thin film
along the same directions as (a), (c) GaAs (111)B substrate along the
[$\mathrm{\bar{1}21}$], [$\mathrm{\bar{1}10}$] and
[$\mathrm{\bar{2}\bar{1}1}$] directions, and (d) NbAs (100) thin film along
the same directions as (c).

We carry out the synthesis of the NbAs films in a VEECO 930 MBE chamber while
monitoring the growth using reflection high energy electron diffraction
(RHEED) at 12 keV (Fig. 2). We desorb the native oxide on an epiready semi-
insulating GaAs substrate and then grow 30 nm of GaAs at a thermocouple
temperature of 720 $\mathrm{{}^{\circ}C}$ using Ga (5N) and As (5N) sources
evaporated from standard effusion cells. The As:Ga beam quivalent pressure
ratio is $\sim 14$ (as measured using an ion gauge). After this, we cool down
the substrate to a thermocouple temperature of 400 $\mathrm{{}^{\circ}C}$ in
the presence of As flux. At this point, we observed a RHEED pattern showing a
$2\times 4$ surface reconstruction for GaAs (100) (Fig. 2(a)) and a C6
symmetry for GaAs (111)B (Fig. 2(c)). We then increase the substrate
temperature to 700-750 $\mathrm{{}^{\circ}C}$ (measured by a thermocouple in
the substrate manipulator) and simultaneously deposit As and Nb (the latter
from a SPECS EBE-4 4 pocket e-beam evaporator), obtaining the RHEED pattern
shown in Figs. 2(b) and 2(d). In the case of NbAs grown on GaAs (100) (Fig.
2(b)), the RHEED pattern is different in the [110] and $\mathrm{[1\bar{1}0]}$
directions. This follows the C2 symmetry of the GaAs substrate in the $2\times
4$ reconstruction. In the case of NbAs grown on GaAs (111)B (Fig. 2(c) and
2(d)), the NbAs RHEED pattern is the same in the GaAs $\mathrm{[1\bar{2}1]}$
and $\mathrm{[2\bar{1}\bar{1}]}$ crystal directions which are
$\mathrm{60^{\circ}}$ apart. This indicates a C6 symmetry in the NbAs thin
film due to twinning during growth.

To characterize our films on a macroscopic scale, we use x-ray diffraction.
First, we perform a coupled $\mathrm{2\theta-\omega}$ scan on NbAs grown on
GaAs (100) (Fig. 3(a)) and detect the presence of diffraction peaks from NbAs
(001). Second, we perform a similar scan on NbAs grown on GaAs (111)B (Fig.
3(b)) and detect the presence of NbAs (100). We emphasize that these different
crystalline planes are not equivalent due to the tetragonal crystal structure
of NbAs (Fig. 1). To quantify the degree of crystallinity in our films, we
perform a rocking curve ($\omega$ scan) around the NbAs peaks and obtain a
full width half maximum (FWHM) of 1.3∘ for NbAs (001) and 2.1∘ for NbAs (100).
To understand the planar structure of our films, we measure a pole figure
around the NbAs $\\{112\\}$ direction. We observe the presence of two
different sets of peaks corresponding to GaAs $K\alpha$ and NbAs $K\beta$
radiation. We find that NbAs (001) stabilizes with a $45^{\circ}$ rotational
offset with respect to the basal plane (Fig. 3(c)). As stated before, this is
due to the lower lattice mismatch in the GaAs $\langle 110\rangle$ direction.
This agrees with previous reports of TaP and NbP grown on a substrate with
cubic crystal structure and high lattice mismatch [14]. The difference in
intensity between the peaks at $0^{\circ}$ and $90^{\circ}$ suggests that
there is a preferred direction of alignment of the domains in the sample,
probably due to the 2 $\times$ 4 GaAs surface reconstruction achieved before
the growth. In Fig. 3(d), we see the presence of 3 dominant GaAs peaks with
the expected C3 symmetry of GaAs in the (111) direction. We also see the
presence of 6 NbAs peaks that are 60∘ apart. This indicates the presence of
domains (twins) that are rotated by 60∘ with respect to each other. Finally,
to understand the structure of the surface of the films, we use atomic force
microscopy (AFM) imaging on these samples. In both surfaces (Figs. 3(e) and
3(f)) we see domains that are tens of nanometers in size. The main difference
between these different surfaces is that in the (001) plane we see the
presence of a rougher surface with domains that show the tetragonal structure
of NbAs while in the (100) direction, we have a smoother surface with a higher
degree of disorder. This qualitatively agrees with the larger FWHM obtained in
the rocking curve in NbAs (100).

Figure 3:  X-ray diffraction $\mathrm{2\theta-\omega}$ scan of NbAs grown on
(a) GaAs (100) and (b) GaAs (111)B. Pole figures around the NbAs $\\{112\\}$
direction for samples grown on (c) GaAs (100) and (d) GaAs (111)B. Atomic
force microscopy image of (e) NbAs (001) and (f) NbAs (100) showing a root
mean square (RMS) surface roughness of 1.4 nm and 0.9 nm respectively.

To understand the microscopic structure of NbAs in the thin film regime, we
use HAADF-STEM imaging and energy-dispersive X-ray spectroscopy (STEM-EDX).
The results shown in the present manuscript correspond to NbAs (001) grown on
GaAs (100). Similar measurements are obtained for NbAs (100)/GaAs (111)B.
Figure 4 (a), shows a cross-section HAADF-STEM image of NbAs on GaAs. The NbAs
layer is polycrystalline with grain sizes in the range of tens of nanometers,
in agreement with the XRD results. The interface between the NbAs and GaAs is
diffuse and shows interdiffusion, likely due to the high temperatures required
to grow NbAs and the large lattice mismatch with GaAs. The relative
concentration of Nb:As and Ga:As is 1:1 in both layers, which confirms the
absence of other phases (Fig. 4 (b) and (c)). There is a self-limited oxide
layer that covers the top $\sim$3 nm of the NbAs film. This is consistent with
our previous studies of other topological semimetals such as TaAs and
$\mathrm{Cd_{3}As_{2}}$ [5, 17].

Figure 4:  (a) HAADF-TEM image of the NbAs (001) thin film on a GaAs
substrate. (b) STEM-EDX elemental maps of Nb, As, Ga and O in the film. (c)
Concentration of the elements in (a) across the NbAs/GaAs interface.

The polycrystalline NbAs layer has domains oriented along the major crystal
directions, in addition to the presence of some grain boundaries and twins
(Fig. 5(a)). Two such examples are shown in Fig. 5 (b) which are commonly
observed in the thin films grown on GaAs. Comparison of the fast Fourier
transforms (FFTs) from the grains to the simulated FFTs confirms the two
grains to be along the (001) and (100) directions respectively (Fig. 5 (c) and
(d)). We note that this is a small subset of several different domains that
were identified in NbAs that had more complex orientations that were harder to
identify. We believe that more complex microscopy techniques that go beyond
the scope of this work (i.e. in plane imaging or statistical analysis of
domain orientation) are needed to fully understand the structure of the
domains in NbAs thin films.

Figure 5:  (a) HAADF-STEM image of NbAs showing polycristalline structure with
multiple grains along different crystal orientations. (b) Common NbAs
orientations observed in grains along with the theoretical model. (c) and (d)
FFT of the NbAs grains highlighted by the purple and orange boxes respectively
along with the simulated FFTs for the (001) and (100) orientations.

In order to characterize the electrical properties of the NbAs thin films, we
fabricated Hall bars using standard photolithography and Ar plasma etching.
The dimensions of the films (length, width and thickness) are $1000$ $\mu$m x
$500$ $\mu$m x 23 nm and $40$ $\mu$m x $10$ $\mu$m x 10 nm respectively. Both
films show similar qualitative and quantitative behavior. The resistivity
($\rho$) vs. temperature ($T$) in both samples shows activated behavior (Fig.
6(a) and (b)), possibly arising from defects, with $\rho\approx
450~{}\mu\Omega$ cm. Hall measurements performed at $T=2$ K show electrons to
be the dominant carrier in both samples (Fig. 6(c) and (d)), with a carrier
density ($n$) $6.5\times 10^{22}$ cm-3 for NbAs (001) and $5\times 10^{21}$
cm-3 in NbAs (100). The Hall mobility is $0.2$ and $2$ cm-2Vs respectively,
while $k_{f}l=2$ and $5$ respectively ($k_{f}$ is the fermi momentum and $l$
is the mean free path), implying highly disordered films. Longitudinal
resistance measurements at $T=2$ K show positive magneto-resistance in both
samples (Fig. 6(c) and (d)). Although $k_{f}l$ is close to the limit for
diffusive transport conditions, as set by the Ioffe-Regel limit
($k_{f}l\approx 1$), we estimated the phase breaking length ($l_{\phi}$) in
both films using the Hikami-Larkin-Nagaoka expression [18] for weak-
antilocalization for high spin-orbit coupled systems:

$\triangle\sigma=\alpha\frac{e^{2}}{\pi
h}\left[\psi\left(\frac{1}{2}+\frac{B_{\phi}}{B}\right)-\ln\left(\frac{B_{\phi}}{B}\right)\right]$
(1)

Here, $B_{\phi}$ is the phase coherence field, and $\alpha$ is a fitting
parameter. We estimate the phase breaking length
($l_{\phi}=\sqrt{\frac{\hbar}{4eB_{\phi}}}$) in both films, to be $50-80$ nm.

Figure 6:  (a) and (b) Longitudinal resistivity ($\rho_{xx}$) as a function of
temperature in 23 nm thick NbAs (001) and 10 nm thick NbAs (100). (c) and (d)
Longitudinal resistivity ($\rho_{xx}$) and Hall resistivity ($\rho_{yx}$) as a
function of magnetic field in NbAs (001) and (100).

In summary, we report on the synthesis by MBE of Weyl semimetal NbAs thin
films on GaAs substrates, a semiconductor of relavence for optoelectronics. We
show that different NbAs crystalline orientations can be stabilized by
choosing the appropriate substrate orientation. The large lattice mismatch
between GaAs and NbAs, coupled with the high growth temperature needed to
achieve NbAs growth, induces diffusion at the GaAs/NbAs interface. This
hinders the crystallinity of our samples and produces textured films with
domains that are tens of nanometers in size. These domains nonetheless have a
well defined crystal structure that is oriented in different crystalline
directions. Despite the large lattice mismatch, the surface chemistry of GaAs
seems to be a decisive factor for effectively nucleating NbAs growth. There is
some apparent inconsistency between the textured nature of our films shown in
STEM and the clear peaks corresponding to a single crystalline orientation
shown in the X-ray diffraction data. We reconcile both measurements by
proposing the existence of a preferred crystalline orientation of these
domains that can only be seen on a macroscopic scale. More detailed microscopy
studies that include statistical analysis and in plane imaging, are required
to confirm this hypothesis. We observe that the films naturally oxidize when
taken out of vacuum. This effect makes it difficult to access the electronic
states of NbAs using surface sensitive techniques like angle resolved
photoemission spectroscopy or scanning tunneling spectroscopy that involve the
out-of-vacuum transfer of samples between different vacuum chambers. This
suggests caution when trying to probe topological surface states in this
family of Weyl semimetals in samples with an oxidized surface. Finally, we
expect that further experimental improvements will allow us to increase the
degree of crystallinity in NbAs films so that we are able to explore a broader
range of physics in this family of well-established Weyl semimetals.

The principal support for this project was provided by SMART, one of seven
centers of nCORE, a Semiconductor Research Corporation program, sponsored by
the National Institute of Standards and Technology (NIST). This supported the
synthesis and standard characterization of NbAs films (WY, YH, NS) and their
characterization using STEM (SG, AM). Additional support for materials
synthesis and characterization was provided by the Penn State Two-Dimensional
Crystal Consortium-Materials Innovation Platform (2DCC-MIP) under NSF Grant
No. DMR-2039351 (SI, ES, AR, NS). Parts of this work were carried out in the
Characterization Facility, University of Minnesota, which receives partial
support from the NSF through the MRSEC (Award Number DMR-2011401) and the NNCI
(Award Number ECCS-2025124) programs. SG acknowledges support from a Doctoral
Dissertation Fellowship received from the Graduate School at the University of
Minnesota. This work utilizes low-temperature transport facilities provided by
the Penn State Materials Research Science and Engineering Center under award
NSF-DMR 2011839.

## References

  * Xu  _et al._ [2015a] S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, S.-M. Huang, H. Zheng, J. Ma, D. S. Sanchez, B. Wang, A. Bansil, F. Chou, P. P. Shibayev, H. Lin, S. Jia, and M. Z. Hasan, Discovery of a Weyl fermion semimetal and topological Fermi arcs, Science 349, 613 (2015a).
  * Lv  _et al._ [2015] B. Q. Lv, H. M. Weng, B. B. Fu, X. P. Wang, H. Miao, J. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, Z. Fang, X. Dai, T. Qian, and H. Ding, Experimental discovery of Weyl semimetal $\mathrm{TaAs}$, Phys. Rev. X 5, 031013 (2015).
  * Xu  _et al._ [2016] S.-Y. Xu, I. Belopolski, D. S. Sanchez, M. Neupane, G. Chang, K. Yaji, Z. Yuan, C. Zhang, K. Kuroda, G. Bian, C. Guo, H. Lu, T.-R. Chang, N. Alidoust, H. Zheng, C.-C. Lee, S.-M. Huang, C.-H. Hsu, H.-T. Jeng, A. Bansil, T. Neupert, F. Komori, T. Kondo, S. Shin, H. Lin, S. Jia, and M. Z. Hasan, Spin polarization and texture of the Fermi arcs in the Weyl fermion semimetal $\mathrm{TaAs}$, Phys. Rev. Lett. 116, 096801 (2016).
  * Huang  _et al._ [2015] S.-M. Huang, S.-Y. Xu, I. Belopolski, C.-C. Lee, G. Chang, B. Wang, N. Alidoust, G. Bian, M. Neupane, C. Zhang, S. Jia, A. Bansil, H. Lin, and M. Z. Hasan, A Weyl fermion semimetal with surface Fermi arcs in the transition metal monopnictide $\mathrm{TaAs}$ class, Nature Communications 6, 7373 (2015).
  * Yanez  _et al._ [2022] W. Yanez, Y. Ou, R. Xiao, S. Ghosh, J. Dwivedi, E. Steinebronn, A. Richardella, K. A. Mkhoyan, and N. Samarth, Giant dampinglike-torque efficiency in naturally oxidized polycrystalline $\mathrm{Ta}\mathrm{As}$ thin films, Phys. Rev. Appl. 18, 054004 (2022).
  * Yuan  _et al._ [2018] X. Yuan, Z. Yan, C. Song, M. Zhang, Z. Li, C. Zhang, Y. Liu, W. Wang, M. Zhao, Z. Lin, T. Xie, J. Ludwig, Y. Jiang, X. Zhang, C. Shang, Z. Ye, J. Wang, F. Chen, Z. Xia, D. Smirnov, X. Chen, Z. Wang, H. Yan, and F. Xiu, Chiral landau levels in Weyl semimetal $\mathrm{NbAs}$ with multiple topological carriers, Nature Communications 9, 1854 (2018).
  * Yuan  _et al._ [2020] X. Yuan, C. Zhang, Y. Zhang, Z. Yan, T. Lyu, M. Zhang, Z. Li, C. Song, M. Zhao, P. Leng, M. Ozerov, X. Chen, N. Wang, Y. Shi, H. Yan, and F. Xiu, The discovery of dynamic chiral anomaly in a Weyl semimetal $\mathrm{NbAs}$, Nature Communications 11, 1259 (2020).
  * Kealhofer  _et al._ [2020] D. A. Kealhofer, L. Galletti, T. Schumann, A. Suslov, and S. Stemmer, Topological insulator state and collapse of the quantum hall effect in a three-dimensional dirac semimetal heterojunction, Phys. Rev. X 10, 011050 (2020).
  * Ramshaw  _et al._ [2018] B. J. Ramshaw, K. A. Modic, A. Shekhter, Y. Zhang, E.-A. Kim, P. J. W. Moll, M. D. Bachmann, M. K. Chan, J. B. Betts, F. Balakirev, A. Migliori, N. J. Ghimire, E. D. Bauer, F. Ronning, and R. D. McDonald, Quantum limit transport and destruction of the Weyl nodes in $\mathrm{TaAs}$, Nature Communications 9, 2217 (2018).
  * Sun  _et al._ [2016] Y. Sun, Y. Zhang, C. Felser, and B. Yan, Strong intrinsic spin hall effect in the $\mathrm{TaAs}$ family of Weyl semimetals, Phys. Rev. Lett. 117, 146403 (2016).
  * Xu  _et al._ [2015b] S.-Y. Xu, N. Alidoust, I. Belopolski, Z. Yuan, G. Bian, T.-R. Chang, H. Zheng, V. N. Strocov, D. S. Sanchez, G. Chang, C. Zhang, D. Mou, Y. Wu, L. Huang, C.-C. Lee, S.-M. Huang, B. Wang, A. Bansil, H.-T. Jeng, T. Neupert, A. Kaminski, H. Lin, S. Jia, and M. Zahid Hasan, Discovery of a Weyl fermion state with Fermi arcs in niobium arsenide, Nature Physics 11, 748 (2015b).
  * Vurgaftman  _et al._ [2001] I. Vurgaftman, J. R. Meyer, and L. R. Ram-Mohan, Band parameters for $\mathrm{III}$-$\mathrm{V}$ compound semiconductors and their alloys, J. Appl. Phys. 89, 5815 (2001).
  * Sadowski  _et al._ [2022] J. Sadowski, J. Z. Domagała, W. Zajkowska, S. Kret, B. Seredyński, M. Gryglas-Borysiewicz, Z. Ogorzałek, R. Bożek, and W. Pacuski, Structural properties of $\mathrm{TaAs}$ Weyl semimetal thin films grown by molecular beam epitaxy on $\mathrm{GaAs}$ (001) substrates, Crystal Growth & Design 22, 6039 (2022), https://doi.org/10.1021/acs.cgd.2c00669 .
  * Bedoya-Pinto  _et al._ [2020] A. Bedoya-Pinto, A. K. Pandeya, D. Liu, H. Deniz, K. Chang, H. Tan, H. Han, J. Jena, I. Kostanovskiy, and S. S. P. Parkin, Realization of epitaxial $\mathrm{NbP}$ and $\mathrm{TaP}$ Weyl semimetal thin films, ACS Nano 14, 4405 (2020).
  * Nelson  _et al._ [2023] J. N. Nelson, A. D. Rice, R. Kurleto, A. Shackelford, Z. Sierzega, C.-S. Jiang, A. G. Norman, M. E. Holtz, J. S. Mangum, I. A. Leahy, K. N. Heinselman, H. Ness, M. Van Schilfgaarde, D. S. Dessau, and K. Alberi, Thin film taas: developing a platform for weyl semimetal devices (2023).
  * sup [2023] See supplemental material at: INSERT_URL_HERE (2023).
  * Yanez  _et al._ [2021] W. Yanez, Y. Ou, R. Xiao, J. Koo, J. T. Held, S. Ghosh, J. Rable, T. Pillsbury, E. G. Delgado, K. Yang, J. Chamorro, A. J. Grutter, P. Quarterman, A. Richardella, A. Sengupta, T. McQueen, J. A. Borchers, K. A. Mkhoyan, B. Yan, and N. Samarth, Spin and charge interconversion in Dirac-semimetal thin films, Phys. Rev. Appl. 16, 054031 (2021).
  * Hikami  _et al._ [1980] S. Hikami, A. I. Larkin, and Y. Nagaoka, Spin-Orbit Interaction and Magnetoresistance in the Two Dimensional Random System, Progress of Theoretical Physics 63, 707 (1980).
  * MacNeill  _et al._ [2017] D. MacNeill, G. M. Stiehl, M. H. D. Guimaraes, R. A. Buhrman, J. Park, and D. C. Ralph, Control of spin–orbit torques through crystal symmetry in $\mathrm{WTe_{2}}$/ferromagnet bilayers, Nature Physics 13, 300 (2017).


# Scheme for a 50 TeV muon accumulator

O.R. Blanco-García<EMAIL_ADDRESS>INFN-LNF, Via E. Fermi 40, 00044
Frascati, Rome, Italy

###### Abstract

Submitted as input for discussions on a possible low emittance muon
accumulator at 50 TeV.

I present a scheme to obtain high quality positive and negative muon beams in
terms of low emittance, high charge and high energy using an accumulator at 50
TeV (or tens of TeV) filled with a train of low charge and low emittance muon
bunches to be injected in top-up mode on a single bunch circulating in a
storage/collider ring at the same energy, where damping from synchrotron
radiation merges the bunches with minimal emittance degradation.

##  I Introduction

The construction of a 100 TeV proton–proton collider (FCC–hh) is currently
under study to continue expanding the energy frontier exploration in high
energy physics fcchh . Two proton beams, at 50 TeV each, circulate inside two
intercepting rings.

In this context, it is also worth studying in parallel the possibility of a
muon–muon collider in the tens of TeV scale because of the advantages in the
kinematics analysis of point-like particle collisions given by leptons and
possible access to physics beyond the standard model muoncolliders ;
Zimmermann .

The main difficulty in the realization of a muon collider lies in the limited
time (before muons decay) to obtain a highly populated, small emittance and
high energy bunch for high luminosity collisions boscolo1808 .

I would like to present, as input for further discussion, a scheme to produce
high quality muon beams (in terms of high charge, high energy and low
emittance) obtained from a muon accumulator at 50 TeV filled with a low
emittance multi-bunch train to be injected in top-up mode into a single bunch
of a main storage/collider ring.

Given the intermediate mass of the muon at rest, i.e. 207 times the electron
mass and about 1/9 of the proton mass, a muon bunch at 50 TeV in the FCC–hh
collider ring would experience total energy loss from synchrotron radiation in
a relative small amount of time, which is comparable to one beam life time
$\tau$ and very close to one second. This energy loss can be recovered with
radio frequency (RF) cavities in the accelerator that in combination produce a
damping effect, well known in electron and positron rings damp . Therefore,
damping should be visible for muons at 50 TeV in a 100 km ring like the FCC–hh
design.

Profiting from damping in a high energy main ring, we can consider the known
method of operation called top-up injection in electron storage rings topup .
It consists in the increase of the bunch population by injecting a small
additional amount of particles on top of the existing ones in the main ring.
In electron rings, particles perform decaying oscillations in the phase space
over a time interval of few units of $\tau$ after which they finally reach an
equilibrium. The most convenient type of injection for our muon
collider/storage ring seems to be on-axis longitudinal injection that consist
in the injection of new particles with an offset in time and/or energy with
respect to the synchronous bunch. It has the advantage to be twice faster than
the transverse damping due to the partition numbers of a typical storage ring.

It might be possible that muons show longitudinal damping even at 25 TeV in a
ring with a circumference adapted to the reduced life time of muons, thus,
lowering the requirements on fast acceleration in previous stages. However,
for the moment we leave this as a possibility for further study and
concentrate in the 50 TeV scheme to obtain a high intensity bunch at high
energy starting from a low charge 22 GeV small emittance muon train given by
$e^{+}e^{-}$ annihilation of a positron bunch train into fixed targets,
studied by the Low EMittance Muon Accelerator (LEMMA) NIM ;
Antonelli:IPAC16-TUPMY001 ; Boscolo:IPAC17-WEOBA3 ; MaricaIPAC2019 ;
eplusringopt  team.

The scheme presented in this article could increase the charge of a single
muon bunch while preserving or mitigating the growth of the muon beam
emittance profiting from synchrotron radiation in the main storage/collider
ring.

##  II Scheme

The scheme is shown in Fig. 1. It consist in four stages : a positron source,
a positron to muon conversion and transport line, a chain of low muon current
fast acceleration rings, and finally a muon accumulator ramping from few TeV
to the desired energy (7 to 50 TeV in the scheme). I will describe the stages
in the following.

###  II.1 Positron source

LEMMA has put forward the idea of a low emittance muon source where muons are
produced as secondaries from $e^{+}e^{-}$ annihilation of a high energy
positron beam, above the energy threshold at 43.7 GeV for muon pair
production, impinging on a fixed target.

It is convenient to set the positron beam energy to 44 GeV because the energy
spread of the produced muon beam will match the acceptance of the next stage.
Further details are discussed in Subsection II.2.

The positron bunch population has been fixed to $5\times 10^{11}$, which is a
relatively high charge in order to produce as many muons as possible given the
small probability of muon pair production, also further discussed in
Subsection II.2.

I fix the positron source requirement to a train of 1000 bunches in order to
increase the muon population by a factor 1000 when combining all separate muon
bunches into one, and also to be compatible with the positron source
requirement studied in simone ; MaricaIPAC2019 ; alesini2019positron .

The required positron rate has been estimated to be about $1.5\times
10^{18}e^{+}$/s given a separation of 100 m among neighboring bunches. Notice
that the positron bunch separation will be the same muon bunch separation in
the train inside the muon accumulator ring.

The transverse emittance and beam size is set to be 7 $\pi$ nm and 60 $\mu$m
respectively to match the input parameters of the positron to muon conversion
stage, discussed in Subsection II.2.

The energy spread and bunch length are 0.1% and 3 mm respectively, taken from
previous studies of a 6 or 27 km positron ring simone .

Finally, I remark that all numbers have been used to clarify and discuss an
initial scheme and they could change as required.

###  II.2 Positron to muon conversion

The purpose of the positron to muon conversion stage is to produce a low
charge and low emittance muon bunch per positron bunch passage.

The three particles species ($e^{+}$ at 44 GeV, and $\mu^{+}\mu^{-}$ or simply
$\mu$ pairs at 22 GeV) are transported to the final end of the transport line
without significative emittance growth of the muon beam, and a small
deterioration of positron bunch in terms of emittance and particle population.

A detailed description of materials and accelerator optics studies dedicated
to this stage can be found in blancoprab2020 .

In this article I have chosen to use a line consisting of 25 liquid Lithium
(LLi) targets of 1% of a radiation length $X_{0}$ connected by a series of
quadrupoles for a total length of 323 m. This design is able to produce
$0.6\times 10^{-6}$ muon pairs per impinging positron, which is factor 10
above a single thin target of 1%$X_{0}$ and also distributes the target power
deposition.

Using the parameters of the positron source shown in Subsection II.1, we will
obtain a bunch population of $3\times 10^{5}$ muon pairs at 22 GeV per
positron bunch, with an energy spread of $\pm 5$% in a flat distribution, and
with a very small transverse emittance of about 25 $\pi$ nm (equivalent to 5
$\pi$ $\mu$m normalized emittance).

The longitudinal emittance will be product of the bunch length of the incoming
positron beam by the energy spread from the kinematics of the collision,
therefore 3$\times$1 $\pi$ mm GeV (3 mm $\times$ $0.05\times$22 GeV).

For a 22 GeV muon beam the length of the transport line is very short and no
significative muon losses are expected.

Each one of the 1000 positron bunches will pass one at the time and produce
muon pairs that are transported to the acceleration stage. The remaining
positrons in the bunch could be spilled or redirected to the previous stage.

###  II.3 Low Muon Current Fast Acceleration

Fortunately in the LEMMA scheme the kinematics of the collision boosts the
lifetime by a factor 208 with respect to that of muons at rest, giving an
initial time-frame of 0.46 ms of lifetime to accelerate the beam.

Muons are already relativistic and therefore I expect acceleration would
influence minimally the timing among bunches at different energies.

The positive and negative muon beams at 22 GeV will have to be separated and
passed through a chain of fast accelerating cavities with the highest possible
gradient. I have done an estimation of 500 m of RF cavities at 20 MV/m in
order to gain 10 GeV per passage. Although this number could appear high, it
is required in order to reduce the number of muon losses due to decay along
the acceleration chain. Even higher gradients would be beneficial.

There is no definitive structure for the acceleration chain. I have considered
three stages as an initial proposal :

  1. 1.

from 22 to 200 GeV, which is a factor ten in energy gain obtained in ten
passages over an RF configuration providing 20 GeV per passage, or twenty
turns over an RF configuration at 10 GeV per turn;

  2. 2.

from 200 GeV to 1 TeV, which is a factor five in energy gain obtained over
approximately 100 turns in a dedicated ring;

  3. 3.

from 1 TeV to 7 TeV, which is a factor seven in energy gain obtained over more
than 500 turns.

The exact configuration of these acceleration stages needs to be further
studied, but, I would like to avoid ramping magnets because of the short
lifetime of the muon beam when compared to technological ramping capabilities.
Better said, I would prefer to avoid ramping magnets in the KHz range.

Several proposals point to technology based in multi-pass Energy Recovery
Linacs (ERL) cbeta  and/or Fixed Field Alternating Gradient (FFA) trbojevic ;
lagrange  ring designs, in particular, vertical FFA (vFFA) brooks  to profit
from the zero momentum compaction factor and large energy acceptance that
could accelerate the beam without the dilution of the longitudinal emittance.

Due to the total number of cycles in the acceleration chain, it is expected to
produce a significative muon population loss that has been estimated to be
half of the initial bunch, leaving 1.5$\times 10^{5}$ muons per bunch.

###  II.4 Accumulator Ring

The last section is the Accumulator Ring. It is included last in the scheme
because further acceleration in the TeV scale of single muon bunches would
require several kilometers of RF cavities and it would be preferable to use a
single ring. The ramping frequency is expected to be in the order of few
hundreds of Hz, which is a factor 10 above the muon beam life time of 140 ms
at 7 TeV that grows up to one second at 50 TeV.

The muon life time of 140 ms at 7 TeV also allows for enough time to allocate
1000 individual bunches into separated buckets inside the accumulator with
negligible losses due to decay.

Once the muon bunch train is in the accumulator, it can be ramped from low to
high energy (7 TeV to 50 TeV in the scheme). Then, it could be possible to
extract one by one the individual low charge bunches into a single bunch
provided the synchronization of the two machines. The most simple case that I
can foresee is to have a small difference in circumferences between the
accumulator and the main storage/collider ring in order to make coincide once
cycle of the bunch in the storage/collider ring with a different bucket of the
accumulator every time.

We could expect muon losses due to decay given the large number of passages to
accelerate (ramp up) the muon beam train. I have estimated a reduction of the
individual bunch to 1.0$\times 10^{5}$ muons.

Injecting a thousand of these bunches into a storage/collider ring will bring
the final bunch charge to about $10^{8}$ muons with a normalized transverse
emittance close to 5 $\pi$ $\mu$m, and bunch length and energy spread
dependent on the realization of the acceleration stages.

##  III Conclusion

I have presented a scheme to produce a high quality muon beam in terms of high
particle population, low emittance and energy of 50 TeV (or tens of TeV),
using an accumulator ring at the same energy to ramp a low charge, low
emittance and low energy train of muon bunches to be injected in top-up mode
into a main storage/collider ring.

This scheme uses a positron source and a short transport line to produce muon
pairs as secondaries from $e^{+}e^{-}$ annihilation of a high energy positron
beam on fixed targets.

Muon pairs are produced at 22 GeV and accelerated in a chain of Fixed Field
Accelerator Gradient (FFA) rings or alternatively Energy Recovery Linacs
(ERL). The number of acceleration stages has been set to three considering the
possibility to gain a factor 10 in energy per stage, and the availability of
radio-frequency cavities to provide at least 10 GeV per passage to the muon
beam.

I believe several of the parameters here mentioned (e.g. the RF cavity
gradient and the positron to muon conversion efficiency) can be pushed by a
factor two or 4, or maybe more, so that the final possible outcome of further
studies of this scheme could be very positive.

##  IV Acknowledgments

This work has been financially supported by the Istituto Nazionale di Fisica
Nucleare (INFN), Italy, Commissione Scientifica Nazionale 5, Ricerca
Tecnologica – Bando n. 20069, 2019.

Figure 1: Production and acceleration scheme of a low emittance muon beam for
a 50 TeV collider.

## References

  * [1] A. Abada, M. Abbrescia, S.S. AbdusSalam, _et al._ “FCC-hh: The Hadron Collider”, Eur. Phys. J. Spec. Top. 228, 775-1107 (2019) https://doi.org/10.1140/epjst/e2019-900087-0
  * [2] J.P. Delahaye _et al._ , “Muon Colliders”, Input to the European Particle Physics Strategy Update, January 18, 2019. arXiv:1901.06150v1 https://arxiv.org/abs/1901.06150
  * [3] F. Zimmermann. MOPMF065, Proceedings on IPAC18, Vancouver, BC, Canada (2018) https://accelconf.web.cern.ch/IPAC2018/papers/mopmf065.pdf
  * [4] M. Boscolo, J.P. Delahaye, M. Palmer. “The future prospects of muon colliders and neutrino factories”. arXiv:1808.01858v2 https://arxiv.org/abs/1808.01858
  * [5] S. Turner. “Fifth General Accelerator Physics Course”. The CERN Accelerator School, University of Jyvaskyla, Finland, September 7–18, 1992. CERN Yellow Proceedings Volume 1/1994. CERN 94-01. http://dx.doi.org/10.5170/CERN-1994-001
  * [6] B. Holzer. “Beam Injection, Extraction and Transfer”. The CERN Accelerator School, Erice, Italy, March 10–19, 2017. CERN Yellow Reports: School Proceedings Volume 5/2018. CERN-2018-008-SP. http://dx.doi.org/10.23730/CYRSP-2018-005
  * [7] M. Antonelli, M. Boscolo, R. Di Nardo and P. Raimondi, “Novel proposal for a low emittance muon beam using positron beam on target,” Nucl. Instrum. Meth. A 807 (2016) 101 https://doi.org/10.1016/j.nima.2015.10.097
  * [8] M. Antonelli _et al._ , “Very Low Emittance Muon Beam using Positron Beam on Target”, in _Proc. 7th Int. Particle Accelerator Conf. (IPAC’16)_ , Busan, Korea, May 2016, pp. 1536–1538. doi:10.18429/JACoW-IPAC2016-TUPMY001
  * [9] M. Boscolo _et al._ , “Studies of a Scheme for Low Emittance Muon Beam Production From Positrons on Target”, in _Proc. 8th Int. Particle Accelerator Conf. (IPAC’17)_ , Copenhagen, Denmark, May 2017, pp. 2486–2489. doi:10.18429/JACoW-IPAC2017-WEOBA3
  * [10] M. Boscolo, _e_ t. al. “Low emittance muon accelerator studies with production from positrons on target”, Phys. Rev. Accel. Beams 21, 061005 (2018), DOI: https://doi.org/10.1103/PhysRevAccelBeams.21.061005
  * [11] M. Biagini, _e_ t. al., “Positron Driven Muon Source for a Muon Collider: Recent Developments”, presented at the 10th International Particle Accelerator Conf. (IPAC’19), Melbourne, Australia, May. 2019, paper MOZZPLS2. https://accelconf.web.cern.ch/IPAC2019/papers/mozzpls2.pdf
  * [12] D. Alesini, _e_ t. al., “Positron driven muon source for a muon collider”, 2019, arxiv 1905.05747. https://arxiv.org/abs/1905.05747
  * [13] S. Liuzzo. “Lemma e+ ring”. Presentation at the Low Emittance Muon Collider Workshop, Padova, Italy. July 1-3, 2018. https://indico.cern.ch/event/719240/
  * [14] O.R. Blanco-Garcia and A. Ciarma. “Nanometric muon beam emittance from e+ annihilation on multiple thin targets.” Phys. Rev. Accel. Beams Accepted for publication, August 31, 2020.
  * [15] A. Bartnik, N. Banerjee, D. Burke, _e_ t al. “CBETA: First Multipass Superconducting Linear Accelerator with Energy Recovery.” Phys. Rev. Lett. 125 044803 (2020) https://link.aps.org/doi/10.1103/PhysRevLett.125.044803
  * [16] D. Trbojevic et al. FFAG lattice for muon acceleration with distributed RF, Proceedings of the 2003 Particle Accelerator Conference. https://accelconf.web.cern.ch/p03/PAPERS/TPPG003.PDF
  * [17] J. B. Lagrange. THPMB053 et al. NUSTORM FFAG decay ring. Proceedings of IPAC2016, Busan, Korea. https://accelconf.web.cern.ch/IPAC2016/papers/thpmb053.pdf
  * [18] S. Brooks. Vertical orbit excursion fixed field alternating gradient accelerators. Physical Review Special Topics – Accelerators and Beams 16, 084001 (2013) https://journals.aps.org/prab/abstract/10.1103/PhysRevSTAB.16.084001


# Cortical Mirror-System Activation During Real-Life Game Playing:
An Intracranial Electroencephalography (EEG) Study

Markus Kern<EMAIL_ADDRESS>
BrainLinks-BrainTools Cluster of Excellence, University of Freiburg, Germany
Johanna Ruescher<EMAIL_ADDRESS>
Faculty of Biology – University of Freiburg
79104, Freiburg, Germany Andreas Schulze-Bonhage (schulze-bonhage@uniklinik-
freiburg.de)
Epilepsy Center, Department of Neurosurgery, Medical Center — University of
Freiburg,
79106, Freiburg, Germany Tonio Ball<EMAIL_ADDRESS>
Medical AI Lab, University Medical Center Freiburg
79106, Freiburg, Germany

## Abstract

Analogous to the mirror neuron system repeatedly described in monkeys as a
possible substrate for imitation learning and/or action understanding, a
neuronal execution/observation matching system (OEMS) is assumed in humans,
but little is known to what extent this system is activated in non-
experimental, real-life conditions. In the present case study, we investigated
brain activity of this system during natural, non-experimental motor behavior
as it occurred during playing of the board game ”Malefiz”. We compared
spectral modulations of the high-gamma band related to ipsilateral reaching
movement execution and observation of the same kind of movement using
electrocorticography (ECoG) in one participant. Spatially coincident activity
during both conditions execution and observation was recorded at electrode
contacts over the premotor/primary motor cortex. The topography and amplitude
of the high-gamma modulations related to both, movement observation and
execution were clearly spatially correlated over several fronto-parietal brain
areas. Thus, our findings indicate that a network of cortical areas
contributes to the human OEMS, beyond primary/premotor cortex including
Broca’s area and the temporo-parieto-occipital junction area, in real-life
conditions.

Keywords: mirror system; ECoG; non-experimental; real life

## Introduction

Mirror neurons that respond both to (visually or auditory) movement
observation and execution, have first been described in monkeys in area F5 of
the ventral premotor cortex Pellegrino . (1992); Rizzolatti, Fadiga, Matelli .
(1996), in the inferior parietal cortex (IPC) Fogassi . (2005) and the
intraparietal sulcus (IPS) Keysers (2009). The analogous observation-execution
matching system (OEMS) in humans, which is suggested to play a crucial role in
imitation learning Iacoboni Wilson (2006) and/or action understanding
Rizzolatti, Fadiga, Gallese Fogassi (1996), is assumed to be more widely
distributed over the human cortex than in monkeys Buccino . (2001); Keysers
Gazzola (2010). Indications of Human brain activity associated with the OEMS
were observed in several cortical areas including the superior temporal sulcus
(STS) Rizzolatti, Fadiga, Matelli . (1996), Broca´s area (BR) Gazzola Keysers
(2009); Iacoboni . (1999); Rizzolatti, Fadiga, Matelli . (1996), the IPC
Gazzola Keysers (2009); Newman-Norlund . (2007), the dorsal premotor cortex
Gazzola Keysers (2009), the ventral premotor cortex (vPM) Buccino . (2001);
Dinstein . (2007); Filimon . (2015), the supplementary motor area (SMA)
Gazzola Keysers (2009); Hamzei . (2003); Iacoboni . (1999), the superior
parietal cortex (SPC) Gazzola Keysers (2009); Iacoboni . (1999), as well as
the primary and secondary somatosensory cortex (S1/S2) Gazzola Keysers (2009).

However, while these experimental studies clearly show the existence of an
OEMS in the human brain, it is not clear whether the same kind of overlapping
brain activities are also present during non-experimental, real-life
conditions. Since striking differences in the firing behavior of cortical
cells of the monkey brain were observed during natural movements compared to
the instructed ones during experimental conditions Harrison Murphy (2014), the
investigation of human brain activity in real-life conditions is of interest.

Thus, in the present study we collected ECOG data during natural movement
execution and observation, i.e., while the patient was engaged in the board
game “Malefiz” with her life partner. This particular situation was chosen for
due to the following reasons: i) the high degree of uniformity of arm
movements in the observation and execution condition, ii) in the playing
situation, the visitor was sitting close enough to the patients’ bed to be
filmed by the digital video recorded for medical reasons, capturing only the
direct vicinity of the hospital bed and iii) the patients’ attention during
observation trials was specifically concentrated on the movements/actions of
her game partner.

Figure 1: Game situation analyzed in this study. a) Movement execution
condition b) Movement observation condition (both video frames anonymized).

## Methods

Data from a female, left handed 41 year-old patient were used, who was
suffering from pharmacological resistant epilepsy and had a subdural 8*8
platinum electrode grid implanted over the left fronto-parietal cortex for
pre-surgical evaluation. The patient agreed by informed consent to scientific
usage of the recorded data and the study was approved by the local ethics
committee. ECoG was recorded with a sampling rate of 1024 Hz. Monopolar
electrical stimulation was conducted by physicians of the University Hospital
Freiburg using an INOMED NS 60 stimulator (INOMED, Germany) (Fig. 2a). Details
about the stimulation procedure are described in Ruescher . (2013). Anatomical
assignment of electrodes to functional brain areas have been performed using
the hierarchic anatomical assignment approach described in Pistohl . (2012).

We analyzed the ECoG data recorded while the patient played the game “Malefiz”
with her life partner. In this game, both partners performed similar reaching
movements to move their tokens on the game board. Due to handedness (left) and
hemisphere of implantation (left), we analyzed ipsilateral reaching movements
of the patient in the execution condition, consisting of 120 trials (Fig.1a).
In the observation condition, we analyzed 87 trials of the left (14 trials)
and right (73 trials) arm of the patient’s visitor (Fig.1b). Both persons were
monitored by digital video recorded for medical reasons with a 25-Hz sampling
rate and 640x480 pixels resolution. Trials were pre-selected by visual
inspection of video recordings and confirmed by the analysis of the EMG
recordings of the right and left deltoid muscles of the patient.

Event-related spectral power was calculated using a multi-taper spectral
analysis method Percival Walden (2006) with time windows of 200 ms, 20-ms time
steps and 5 Slepian tapers. Since event-related HG power is proposed to be a
suitable marker of local brain activity Crone . (1998), we analyzed
modulations of HG band power relative to the power in baseline trials (resting
condition, no movement execution or observation of movement, 21 trials).

The significance of HG power modulations was calculated using a paired two-
sided Wilcoxon’s sign test. P-values were corrected by using the false
discovery rate (FDR) approach Benjamini . (2001) with a q-level of $10^{-9}$.
For a comparison of the overall fronto-parietal brain activity captured by
grid electrodes during both conditions, we calculated Spearman’s rank-based
correlations coefficient for HG power related between the execution and
observation condition over the 64 grid electrode contacts.

## Results

Both the execution and observation condition showed widespread high gamma (HG)
band modulations in frontal and parietal regions (Fig. 2b,c). For the
execution condition (Fig. 2b), significant increases of HG power were found
over S1, PM, and IPC, while significant HG power decreases were found at two
electrodes above the central sulcus and in the ventral S1. In the observation
condition (Fig. 2c), significant HG power increases were found in PM, temporo-
parieto-occipital junction area (TPO), dorsal S1 and BR.

On the single electrode level, significant responses overlapped in dorsal
premotor cortex in a region showing hand motor responses during electrical
stimulation mapping (Fig. 2a). Comparison of HG response topographies recorded
over the whole electrode grid revealed significant positive correlations with
r=0.71 and $p<10^{-6}$ (Fig. 2d).

## Discussion

In the present case study, we investigated the human OEMS by analyzing HG
modulations in ECoG recordings of a female epilepsy patient while she was
playing a board game with her partner. We found a significant increase of HG
power at electrodes over PM during ipsilateral reaching movements as well as
during the observation of unilateral reaching movements of the partner. This
coincidental activity in PM is in line with results of recent fMRI studies
investigating the OEMS Gazzola Keysers (2009).

Overlapping activity was also recorded over Broca’s Area, the temporo-parietö-
occipital (TPO) junction area and dorsal S1, but did not reach significance in
the execution condition. This might partially be ascribed to the laterality of
movement execution, since a movement-related increase in HG power is rather
weak in the ipsilateral hemisphere compared to the contralateral side.
However, BR and S1 have also been associated to the OEMS in previous studies
Gazzola Keysers (2009); Iacoboni . (1999); Rizzolatti, Fadiga, Matelli .
(1996).

Figure 2: Electrical stimulation mapping (ESM) and high gamma (HG) mapping
results. a) Left panel: position of 8*8 subdurally implanted electrode grid of
the patient visualized on a standard brain; right panel: anatomical assignment
of the electrode contacts and responses during ESM. Prefrontal cortex: PF,
Broca’s area: BR, premotor cortex: PM, primary somatosensory cortex: S1,
inferior parietal cortex: IPC, superior parietal cortex: SPC. Solid blue line:
central sulcus (CS), solid green line: lateral sulcus (LS), dashed black
lines: probabilistically defined borders within frontal cortex, dashed white
line: probabilistically defined border between the anterior and posterior
parietal cortex. Electrode contacts marked by black dots were not tested or
did not elicit responses during ESM. b) Topography of reaching-execution-
related relative power changes in the HG band. Electrodes where significant
(sign test, $p<10^{-9}$, FRD corrected) power changes were recorded, are
marked as black dots. c) Topography of reaching-observation-related relative
power changes (color bar) in high-gamma band. Conventions as in b) d) The
logarithmic relative HG band power values (black stars) of reaching
observation and execution in the time window 0-500ms displayed in (b,c) are
plotted against each other. Blue line: regression line. Correlation
coefficients and p-values after Spearman´s correlation are displayed in the
plot.

However, BR and S1 have also been associated to the OEMS in previous studies
Gazzola Keysers (2009); Iacoboni . (1999); Rizzolatti, Fadiga, Matelli .
(1996). TPO has been found to be active during action observation Hamzei .
(2003) and might thus play a role in the OEMS, too.

Additionally, we found significant coincident activity in S1, PM, prefrontal
cortex and BR in another epilepsy patient not included in this study, related
to contralateral finger movement execution (for more details, see P1 in Ball .
(2008)), compared to the observation of her partner manipulating a Rubik’s
cube.

Taken together, these findings support the suggestion, that the coincident
activity we recorded over PM, BR, TPO and S1 during real-life conditions may
be ascribed to the human OEMS. Interestingly, when comparing HG power at every
channel of the fronto-parietal electrode grid, we found strong correlations
between HG band modulations related to both conditions. First of all, this
finding confirms the idea of multiple brain areas contributing to the human
OEMS. Furthermore, the similarity of recorded signals during movement
observation and execution might also be of interest for future research in the
area of brain-computer interfaces, where it is crucial to reliably
differentiate between these two conditions.

## Acknowledgments

We would like to thank Simon Contzen for his help in preparing this
manuscript. This study was (partly) funded by the WISPER Project, Baden-
Württemberg Stiftung.

## References

  * Ball . (2008) ball_movement_2008Ball, T., Demandt, E., Mutschler, I., Neitzel, E., Mehring, C., Vogt, K.Schulze-Bonhage, A.  200806\.  Movement related activity in the high gamma range of the human EEG Movement related activity in the high gamma range of the human EEG.  NeuroImage412302–310.
  * Benjamini . (2001) benjamini_controlling_2001Benjamini, Y., Drai, D., Elmer, G., Kafkafi, N. Golani, I.  200111\.  Controlling the false discovery rate in behavior genetics research Controlling the false discovery rate in behavior genetics research.  Behavioural Brain Research1251-2279–284.
  * Buccino . (2001) buccino_action_2001Buccino, G., Binkofski, F., Fink, GR., Fadiga, L., Fogassi, L., Gallese, V.Freund, HJ.  200101\.  Action observation activates premotor and parietal areas in a somatotopic manner: an fMRI study Action observation activates premotor and parietal areas in a somatotopic manner: an fMRI study.  European Journal of Neuroscience132400–404.
  * Crone . (1998) crone_functional_1998Crone, NE., Miglioretti, DL., Gordon, B. Lesser, RP.  199812\.  Functional mapping of human sensorimotor cortex with electrocorticographic spectral analysis. II. Event-related synchronization in the gamma band. Functional mapping of human sensorimotor cortex with electrocorticographic spectral analysis. II. Event-related synchronization in the gamma band.  Brain121122301 –2315.
  * Dinstein . (2007) dinstein_brain_2007Dinstein, I., Hasson, U., Rubin, N. Heeger, DJ.  200709\.  Brain Areas Selective for Both Observed and Executed Movements Brain Areas Selective for Both Observed and Executed Movements.  Journal of Neurophysiology9831415–1427.
  * Filimon . (2015) filimon_observed_2015Filimon, F., Rieth, CA., Sereno, MI. Cottrell, GW.  201509\.  Observed, Executed, and Imagined Action Representations can be Decoded From Ventral and Dorsal Areas Observed, Executed, and Imagined Action Representations can be Decoded From Ventral and Dorsal Areas.  Cerebral Cortex2593144–3158.
  * Fogassi . (2005) fogassi_parietal_2005Fogassi, L., Ferrari, PF., Gesierich, B., Rozzi, S., Chersi, F. Rizzolatti, G.  200504\.  Parietal Lobe: From Action Organization to Intention Understanding Parietal Lobe: From Action Organization to Intention Understanding.  Science3085722662–667.
  * Gazzola Keysers (2009) gazzola_observation_2009Gazzola, V. Keysers, C.  200906\.  The Observation and Execution of Actions Share Motor and Somatosensory Voxels in all Tested Subjects: Single-Subject Analyses of Unsmoothed fMRI Data The Observation and Execution of Actions Share Motor and Somatosensory Voxels in all Tested Subjects: Single-Subject Analyses of Unsmoothed fMRI Data.  Cerebral Cortex1961239–1255.
  * Hamzei . (2003) hamzei_human_2003Hamzei, F., Rijntjes, M., Dettmers, C., Glauche, V., Weiller, C. Büchel, C.  200307\.  The human action recognition system and its relationship to Broca’s area: an fMRI study The human action recognition system and its relationship to Broca’s area: an fMRI study.  NeuroImage193637–644.
  * Harrison Murphy (2014) harrison_motor_2014Harrison, TC. Murphy, TH.  201402\.  Motor maps and the cortical control of movement Motor maps and the cortical control of movement.  Current Opinion in Neurobiology2488–94.
  * Iacoboni Wilson (2006) iacoboni_beyond_2006Iacoboni, M. Wilson, SM.  2006\.  Beyond a Single Area: Motor Control and Language Within a Neural Architecture Encompassing Broca’s Area Beyond a Single Area: Motor Control and Language Within a Neural Architecture Encompassing Broca’s Area.  Cortex424503–506.
  * Iacoboni . (1999) iacoboni_cortical_1999Iacoboni, M., Woods, RP., Brass, M., Bekkering, H., Mazziotta, JC. Rizzolatti, G.  199912\.  Cortical Mechanisms of Human Imitation Cortical Mechanisms of Human Imitation.  Science28654492526–2528.
  * Keysers (2009) keysers_mirror_2009Keysers, C.  200911\.  Mirror neurons Mirror neurons.  Current biology: CB1921R971–973.
  * Keysers Gazzola (2010) keysers_social_2010Keysers, C. Gazzola, V.  201004\.  Social Neuroscience: Mirror Neurons Recorded in Humans Social Neuroscience: Mirror Neurons Recorded in Humans.  Current Biology208R353–R354.
  * Newman-Norlund . (2007) newman-norlund_mirror_2007Newman-Norlund, RD., Schie, HTv., Zuijlen, AMJv. Bekkering, H.  200707\.  The mirror neuron system is more active during complementary compared with imitative action The mirror neuron system is more active during complementary compared with imitative action.  Nature Neuroscience107817–818.
  * Pellegrino . (1992) pellegrino_understanding_1992Pellegrino, Gd., Fadiga, L., Fogassi, L., Gallese, V. Rizzolatti, G.  199210\.  Understanding motor events: a neurophysiological study Understanding motor events: a neurophysiological study.  Experimental Brain Research911176–180.
  * Percival Walden (2006) percival_wavelet_2006Percival, DB. Walden, AT.  2006\.  Wavelet Methods for Time Series Analysis Wavelet Methods for Time Series Analysis.  Cambridge University Press.
  * Pistohl . (2012) pistohl_decoding_2012Pistohl, T., Schulze-Bonhage, A., Aertsen, A., Mehring, C. Ball, T.  201201\.  Decoding natural grasp types from human ECoG Decoding natural grasp types from human ECoG.  NeuroImage591248–260.
  * Rizzolatti, Fadiga, Gallese Fogassi (1996) rizzolatti_premotor_1996Rizzolatti, G., Fadiga, L., Gallese, V. Fogassi, L.  199603\.  Premotor cortex and the recognition of motor actions Premotor cortex and the recognition of motor actions.  Cognitive Brain Research32131–141.
  * Rizzolatti, Fadiga, Matelli . (1996) rizzolatti_localization_1996Rizzolatti, G., Fadiga, L., Matelli, M., Bettinardi, V., Paulesu, E., Perani, D. Fazio, F.  199609\.  Localization of grasp representations in humans by PET: 1. Observation versus execution Localization of grasp representations in humans by PET: 1. Observation versus execution.  Experimental Brain Research1112246–252.
  * Ruescher . (2013) ruescher_somatotopic_2013Ruescher, J., Iljina, O., Altenmüller, DM., Aertsen, A., Schulze-Bonhage, A. Ball, T.  201311\.  Somatotopic mapping of natural upper- and lower-extremity movements and speech production with high gamma electrocorticography Somatotopic mapping of natural upper- and lower-extremity movements and speech production with high gamma electrocorticography.  NeuroImage81164–177.