# First Result of Net-Charge Jet-Correlations from STAR

Quan Wang (for the STAR Collaboration<EMAIL_ADDRESS>Department of
Physics, Purdue University, West Lafayette, IN 47907, USA

###### Abstract

We presented results on azimuthal correlation of net-charge with high $p_{T}$
trigger particles. It is found that the net-charge correlation shape is
similar to that of total-charge. On the near-side, the net-charge and total-
charge $p_{T}$ spectra have similar shape and both are harder than the
inclusives. On the away-side, the correlated spectra are not much harder than
the inclusives, and the net-charge/total-charge ratio increases with $p_{T}$
and is similar to the inclusive ratio.

##  1 Introduction

Two novel phenomena have been observed at intermediate transverse momentum
($2<p_{T}<5$GeV/$c$) in heavy-ion collisions at RHIC. First, the azimuthal di-
hadron correlation with a high $p_{T}$ ($p_{T}>3$ GeV/$c$) trigger particle is
significantly broadened on the away-side (double-peak structure) in central
Au+Au collisions relative to p+p collisions bib:broaden . Second, the bayon to
meson ratio is significantly enhanced bib:star bib:ratio . In order to
understand the physics mechanism(s) for these phenomena, we study two-particle
azimuthal correlation of net-charge and compare to that of total-charge. Since
the net-charge is dominated by net-protons, and the total-charge is the sum of
mesons and bayons, the comparison between net-charge and total-charge
azimuthal correlations may help further our understanding of baryon-meson
effects at RHIC.

##  2 Analysis

We obtain the raw azimuthal correlations from positively ($h^{+}$) and
negatively ($h^{-}$) charged hadrons with a charged high $p_{T}$ trigger
particle ($h$). The trigger and associated particle $p_{T}$ ranges are
$3<p_{T}<4$ GeV/$c$ and $1<p_{T}<3$ GeV/$c$, respectively. Both the trigger
and associate particles are restricted to $|\eta|<1$. Tracking efficiency is
corrected for associated particles. The two-particle acceptance effect is
corrected for by the event-mixing technique. The correlations are normalized
per trigger particle. By taking the difference and the sum, we obtain the net-
charge ($h\mbox{-}\Delta Q$) and total-charge ($h\mbox{-}Q$) correlations:

$h\mbox{-}\Delta Q=h\mbox{-}h^{+}-h\mbox{-}h^{-},$ (1)
$h\mbox{-}Q=h\mbox{-}h^{+}+h\mbox{-}h^{-}.$ (2)

We obtain the corresponding backgrounds by using the same technique from
mixed-events and adding in $v_{2}$ modulation, where $v_{2}$ is presently
taken from the charged hadron measurements bib:rpv2 bib:4pv2 . The final
correlation signal is given by

$signal=raw-a*background$ (3)

where $a$ is the normalization factor from Zero Yield At 1 radian (ZYA1)
method. The systematic uncertainty estimate is done according to Ref.
bib:broaden .

Figure 1:  Background subtracted azimuthal correlations of net-charge (data
points) and total-charge (solid histogram) in 12% central Au+Au collisions at
200 GeV. The trigger and associated $p_{T}$ ranges are 3-4 GeV/$c$ and 1-3
GeV/$c$, respectively. Errors shown for the data points are statistical only.
The total-charge result is scaled by 1/15 to compare with the net-charge
result. The dashed histograms show the systematic errors on the total-charge
result, obtained from background subtraction using the modified reaction-plane
$v_{2}$ bib:rpv2  and the 4-particle cumulant $v_{2}$ bib:4pv2 .

##  3 Results and Discussion

Figure 1 shows the background subtracted results. We find the correlation
shapes are similar between total-charge and net-charge. The net-charge
correlation shows a significant away-side broadening (double-peak structure),
similar to previously observed in total-charge bib:broaden . We study the
$p_{T}$ dependence of the correlated yields by dividing the data into four
associated $p_{T}$ bins. In different $p_{T}$ bins, the correlation shapes are
also found to be similar between total-charge and net-charge.

Figure 2:  $p_{T}$ spectra of net-charge (triangles) and total-charge
(squares) correlated with a high $p_{T}$ trigger particle ($3<p_{T}<4$
GeV/$c$) on both near-side (filled symbols) and away-side (open symbols) in
AuAu central collisions at 200 GeV. Errors shown are systematic errors. The
inclusive (round points) $p_{T}$ spectrum is also shown for comparison.

We obtain associated particle $p_{T}$ spectra by integrating over the near-
side ($|\Delta\phi|<1$) and the away-side ($|\Delta\phi|>1$). The obtained
spectra are shown in Fig. 2. For comparison, we also show the inclusive
charged hadron $p_{T}$ spectrum (i.e. without requirement of a high $p_{T}$
trigger particle). We fit the spectra by an exponential function:
$e^{-p_{T}/T}$, where $T$ is the inverse slope parameter. The fit results are
listed in Table 1.

Table 1: Inverse slope parameter $T$ in GeV/$c$ from exponential fit to the $p_{T}$ spectra. Errors are statistical only. | Near-side | Away-side
---|---|---
net-charge | $0.491\pm 0.069$ | $0.378\pm 0.032$
total-charge | $0.459\pm 0.003$ | $0.336\pm 0.002$
inclusive | $0.312\pm 0.001$

As seen from the extracted values of the inverse slope parameter, the shapes
of net-charge and total-charge correlated spectra on near-side are similar,
and they are both harder than the inclusive spectrum. The away-side correlated
net-charge spectrum seems to be harder than the total-charge, and neither is
much harder than the inclusive one.

Figure 3:  Ratios of correlated yields of net-charge over total-charge on
away-side (squares) and near-side (triangles) in 12% central Au+Au collisions
at 200 GeV. The trigger $p_{T}$ range is from 3-4 GeV/$c$. Vertical bars are
statistical errors. Horizontal bars are the $p_{T}$ bin size. The curve shows
the inclusive ratio of
$\frac{p-\overline{p}}{\pi^{+}+\pi^{-}+p+\overline{p}}$, where the shaded area
is statitical uncertainty (the data at $p_{T}<$2.5 GeV/$c$ are from TOF
measurement, and the $p_{T}>$2.5 GeV/$c$ data are from TPC measurement)
bib:star .

The inclusive bayon to meson ratio is strongly enhanced at intermediate
$p_{T}$ as mentioned earlier. We want to study the bayon/meson ratio of the
correlated hadrons with high $p_{T}$ trigger particles. We take the ratio of
the $p_{T}$ spectra on near- and away-side separately. The obtained results
are shown in Fig. 3, and compared with the inclusive ratio. The ratio of the
correlated net-charge to total-charge yields on away-side is larger than that
on the near-side. The away-side ratio is similar to the inclusive ratio, with
an average difference of $0.34\sigma$. The near-side ratio seems smaller than
the inclusive ratio with an average difference of $0.80\sigma$.

Figure 3 shows that the near-side ratio is independent of $p_{T}$. A fit of
the near-side ratio to a constant yields $0.037\pm 0.005(stat.)$, with a
$\chi^{2}/ndf=1.7/3$. This is to be compared to the inclusive ratio of
$0.050\pm 0.001$. On the other hand, the away-side ratio appears to increase
with $p_{T}$, similar to the inclusives. A constant fit yields $0.055\pm
0.004(stat.)$, with a significantly larger $\chi^{2}/ndf=5.4/3$.

##  4 Summary

We have presented results on azimuthal correlation of net-charge with high
$p_{T}$ trigger particles. The net-charge correlation shape is found to be
similar to that of total-charge. We studied the associate $p_{T}$ spectra of
correlated net-charge, and the net-charge to total-charge ratio. On the near-
side, net-charge and total-charge spectra have similar shape; the net-
charge/total-charge ratio is constant over $p_{T}$. However, they are both
harder than the inclusives, suggesting jet nature for the correlated
particles. On the away-side, the correlated spectra are not much harder than
the inclusives, suggesting partial equilibration of the correlated hadrons
with the medium. The net-charge/total-charge ratio increases with $p_{T}$ and
is similar to inclusives.

## References

  * (1) J. Adams _et al._ , STAR Collaboration, Phys. Rev. Lett. 95, 152301 (2005).
  * (2) B.I. Abelev _et al._ , STAR collaboration, Phys. Rev. Lett. 97, 152301 (2006).
  * (3) B.I. Abelev _et al._ , STAR collaboration, Phys. Lett. B 655, 104 (2007).
  * (4) J. Adams et al. STAR Collaboration, Phys. Rev. C 72, 014904 (2005).
  * (5) C. Adler et al. STAR Collaboration, Phys. Rev. C 66, 034904 (2002).


# Bandwidth-tuning from insulating Mott quantum spin liquid to Fermi liquid
via chemical substitution in $\kappa$-[(BEDT-TTF)1-x(BEDT-STF)x]2Cu2(CN)3

Y. Saito  1\. Physikalisches Institut, Universität Stuttgart, 70569 Stuttgart,
Germany  Department of Physics, Graduate School of Science, Hokkaido
University, Sapporo 060-0810, Japan  R. Rösslhuber  1\. Physikalisches
Institut, Universität Stuttgart, 70569 Stuttgart, Germany  A. Löhle  1\.
Physikalisches Institut, Universität Stuttgart, 70569 Stuttgart, Germany  M.
Sanz Alonso  1\. Physikalisches Institut, Universität Stuttgart, 70569
Stuttgart, Germany  M. Wenzel  1\. Physikalisches Institut, Universität
Stuttgart, 70569 Stuttgart, Germany  A. Kawamoto  Department of Physics,
Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan  A.
Pustogow  1\. Physikalisches Institut, Universität Stuttgart, 70569 Stuttgart,
Germany  M. Dressel  1\. Physikalisches Institut, Universität Stuttgart, 70569
Stuttgart, Germany

###### Abstract

The electronic properties of molecular conductors can be readily varied via
physical or chemical pressure as it increases the bandwidth $W$; this enables
crossing the Mott insulator-to-metal phase transition by reducing electronic
correlations $U/W$. Here we introduce an alternative path by increasing the
molecular orbitals when partially replacing sulfur by selenium in the
constituting bis-(ethylenedithio)-tetrathiafulvalene (BEDT-TTF) molecules of
the title compound. We characterize the tuning of the insulating quantum spin
liquid state via a Mott transition to the metallic Fermi-liquid state by
transport, dielectric, and optical measurements. At this first-order phase
transition, metallic regions coexist in the insulating matrix leading to
pronounced percolative effects most obvious in a strong enhancement of the
dielectric constant at low temperatures.

###### pacs:

71.30.+h, 78.30.Jw 74.70.Kn, 77.22.-d, 64.60.ah, 78.30.-j,

##  I Introduction

The fundamental nature of the Mott insulator-metal transition remains subject
of controversy and debate. Early theories Mott (1990); Georges  _et al._
(1996); Vollhardt (2012) favored a robust first-order scenario but apart from
hysteresis effects it has proven difficult to identify conclusive experimental
evidence for the expected phase-coexistence region Imada  _et al._ (1998);
Lefebvre  _et al._ (2000); Limelette  _et al._ (2003a, b); Kagawa  _et al._
(2004); Kurosaki  _et al._ (2005). Alternative viewpoints envision a more
continuous crossover at finite temperature featuring aspects of quantum
criticality Senthil (2008); Vučičević  _et al._ (2013); Furukawa  _et al._
(2015, 2018). Recently, quantum spin liquids were recognized as the materials
best suited for studying the pristine Mott state in absence of magnetic order
Pustogow  _et al._ (2018), and its low-temperature transition to a Fermi
liquid Furukawa  _et al._ (2018).

Since most molecular solids are rather soft, their electronic properties can
readily be tuned by relatively low hydrostatic pressure Ishiguro  _et al._
(1998); *ToyotaBook; *LebedBook; *MoriBook; Yasuzuka and Murata (2009).
Nevertheless, many experiments become cumbersome, inaccurate or even
impossible when confined to pressure cells; hence alternative methods are
desirable. In the case of charge-transfer salts, reducing the size of the
anions acts like chemical pressure that brings the organic donor molecules
closer together. This approach is frequently applied to quasi-one-dimensional
TMTTF or quasi-two-dimensional BEDT-TTF salts Yamada and Sugimoto (2004);
Ishiguro  _et al._ (1998); *ToyotaBook; *LebedBook; *MoriBook. Already in the
1970s it was realized by Bechgaard and others that replacing sulfur by
selenium in the fulvalene-type central unit TTF increases the orbital overlap
of adjacent molecules and thus the bandwidth; eventually leading to
superconductivity in (TMTSF)2PF6 Jérome  _et al._ (1980).

Here we apply this approach to quasi-two-dimensional BEDT-TTF salts, where we
replace two out of the four inner sulfur atoms by selenium as depicted in Fig.
1(a), resulting in BEDT-STF 111In contrast to the so-called BETS molecule
(BEDT-TSF, bis-ethylene-dithio-tetraselenafulvalene) which contains four
slenium in the fulvalene unit. H. Kobayashi, H. Cui, and A. Kobayashi, Chem.
Rev. 104, 5265 (2004). . While $\kappa$-(BEDT-TTF)2Cu2(CN)3 is a Mott
insulator, known as a quantum spin liquid, $\kappa$-(BEDT-STF)2Cu2(CN)3 is a
good conductor in the entire temperature regime. Performing the substitution
on the donor molecules ensures that the polymeric anion network and the
crystal symmetry remain unaffected, which is crucial for the highly frustrated
compounds. This way we can cross the Mott transition from a paramagnetic
insulator – that is a quantum spin liquid – to a paramagnetic metal, without
any indications of magnetic order down to lowest temperatures.

Figure 1: (a) Organic donor molecules bis-(ethylenedithio)-tetrathiafulvalene,
called BEDT-TTF and bis-(ethylenedithio)-diseleniumdithiafulvalene,
abbreviated BEDT-STF. In the latter case two sulfur atoms of the inner rings
are replaced by selenium. (b) The crystal structure contains dimers of the
donor molecules forming layers in the $bc$-plane which are separated by the
Cu2(CN)3 anion sheets. (c) The dimers are arranged in a triangular pattern
with transfer integrals $t^{\prime}/t=0.83$ close to complete frustration. The
STF-substitution leads to a spatially random extension of the transfer
integrals due to the larger molecular orbitals.

In the present study we focus on the electronic properties and investigate the
coexistence regime at the first-order phase transition by transport, optical
and dielectric methods. We observe a divergency in the permittivity as the
hallmark of a percolative transition; in other words, we prove the insulator-
metal phase coexistence below the critical endpoint $T_{\rm crit}\approx
15$-20 K.

##  II Experimental Details

Single crystals of $\kappa$-[(BEDT-TTF)1-x(BEDT-
STF)x]$\rm{}_{2}\\-Cu_{2}(CN)_{3}$ with various stoichiometry ($x=0$, 0.04,
0.1, 0.12, 0.16, 0.19, 0.21, 0.25, 0.28, 0.44, 0.78 and 1) were prepared by
standard electrochemical oxidation Geiser  _et al._ (1991). Both BEDT-TTF and
BEDT-STF were synthesized at Hokkaido University in Sapporo, where also the
crystal growth is carried out. For the alloying series, the amount of donor
molecules was preselected; for each batch the actual substitution value $x$
was determined a posteriori by energy-dispersive x-ray spectroscopy: using
$\kappa$-(BEDT-TTF)2Cu2(CN)3 as a reference we compared the intensity of S
atoms to that of Se atoms Saito  _et al._ (2018).

Table 1: Room-temperature values of the unit cell parameters of $\kappa$-(BEDT-TTF)2Cu2(CN)3 and $\kappa$-(BEDT-STF)2Cu2(CN)3 assuming space groups P21/c and P$\bar{1}$ for the analysis of the x-ray scattering results. Data for the former compound are taken from Refs. Pinterić  _et al._ , 2014 and Foury-Leylekian  _et al._ , 2018.  |  $\kappa$-(BEDT-TTF)2Cu2(CN)3 |  $\kappa$-(BEDT-STF)2Cu2(CN)3
---|---|---
| P21/c | P$\bar{1}$ | P21/c | P$\bar{1}$
$a$ | 16.0920(4) Å | 16.1221(10) Å | 16.2965(8) Å | 16.5625(8) Å
$b$ | 8.5813(2) Å | 8.591(6) Å | 8.6082(5) Å | 8.6292(3) Å
$c$ | 13.3904(4) Å | 13.412(8) Å | 13.3985(6) Å | 13.4025(5) Å
$\alpha$ | 90∘ | 89.99(2)∘ | 90∘ | 90.00∘
$\beta$ | 113.381(3)∘ | 113.43(2)∘ | 113.1300(16)∘ | 115.0115(14)∘
$\gamma$ | 90∘ | 90.01(2)∘ | 90∘ | 90.00∘
$V$ | 1697.25 Å3 | 1704.46 Å3 | 1728.5 Å3 | 1735.87 Å3
$Z$ | 2 | 2 | 2 | 2

The structure consists of $bc$ layers of strongly dimerized BEDT-TTF or BEDT-
STF molecules, with each dimer oriented approximately perpendicular to its
nearest neighbors (Fig. 1). Overall it is assumed that the compounds
crystallize in monoclinic and centrosymmetric P21/c space group. Based on an
x-ray study of the parent compound Foury-Leylekian et al. recently suggested a
triclinic symmetry P$\bar{1}$ with two non-equivalent dimers in the unit cell
Foury-Leylekian  _et al._ (2018), however, the charge imbalance among the
sites is extremely weak. Upon sulfur substitution the unit cell volume
slightly increases (less than $2\,\%$) in a linear fashion without any change
in symmetry. In Tab. 1 we list the unit cell parameters for the limiting
cases, assuming both, P21/c and P$\bar{1}$ space group symmetry.

Electrical transport was measured parallel to the $c$-axis from room
temperature down to $T=1.8$ K by standard four-probe technique. For this, thin
gold wires were attached by carbon paste. Furthermore, we measured the complex
electrical impedance as a function of temperature and frequency in order to
obtain the dielectric permittivity $\hat{\varepsilon}=\varepsilon_{1}+{\rm
i}\varepsilon_{2}$. Here, gold wires were attached to opposite crystal
surfaces and the data recorded by an impedance analyzer in the frequency range
from 40 Hz to 10 MHz covering temperatures down to $T=5$ K. The applied ac
voltage was set to 0.5 V, making sure that we operate in the Ohmic regime.

The optical properties of several single crystals have been studied by
reflectivity measurements using standard Fourier-transform spectroscopy from
the far-infrared up to the near-infrared range Dressel and Drichko (2004). The
light was polarized along the two principal optical axes, i.e. $E\parallel b$
and $E\parallel c$, on as-grown surfaces. Besides regular in-plane
experiments, we also probed the polarization perpendicular to the conducting
planes, a direction which couples to the most charge-sensitive infrared-active
intramolecular vibrational mode $\nu_{27}(b_{1u})$. The sample was cooled down
to $T=10$ K by a helium-cooled optical cryostat. In addition, the high-
frequency properties (up to 35 000 cm-1) were determined by spectroscopic
ellipsometry at ambient condition. The optical conductivity was calculated via
Kramer-Kronig analysis using a constant reflectivity extrapolation at low
frequencies and temperatures for the Mott insulators, while a Hagen-Rubens
behavior was assumed for elevated temperatures and substitions $x>0.12$ where
metallic properties prevail Elsässer  _et al._ (2012); Sedlmeier  _et al._
(2012).

##  III DC Transport

Fig. 2 displays the $c$-axis dc resistivity $\rho(T)$ as a function of
temperature for all samples in our substitution series from $x=0$ to 1. The
room-temperature values increase from approximately $0.03~{}\Omega$cm for
$x=1$ to around $0.5~{}\Omega$cm for $x=0$. For $x=0.12$ and higher the
systems turns metallic at low temperatures; the temperature range of metallic
conductivity increases for larger substitution and exceeds $T=300$ K for
$x\geq 0.44$. The maximum in $\rho(T)$ defines the Brinkman-Rice temperature
$T_{\rm BR}$ that increases upon alloying. For very low temperatures, the
metallic properties are clearly characterized by a $\rho(T)\propto T^{2}$
behavior that is the hallmark of electron-electron interaction. A detailed
analysis of the Fermi-liquid properties will be provided elsewhere Pustogow
_et al._ (2020).

Figure 2: Temperature dependence of the dc resistivity of $\kappa$-[(BEDT-
TTF)1-x(BEDT-STF)x]$\rm{}_{2}\\-Cu_{2}(CN)_{3}$ for various substitution
values $x$ as indicated spanning the full range from the insulating $x=0$ to
the metallic side. The data are measured along the highly conducting $c$-axis
and normalized to the respective room temperature value for better comparison.

For $x=0.1$ and 0.12 we identify traces of superconductivity in $\rho(T)$ that
is suppressed by a strong magnetic field ($B=5$ T). Measurements of the
magnetic susceptibility $\chi(T)$ confirm a superconducting transition
temperature $T_{c}\approx 2.8$ K. A more detailed characterization of the
superconducting state will be subject of a separate publication.

##  IV Optical Properties

The in-plane optical conductivity $\sigma_{1}(\omega)$ of $\kappa$-[(BEDT-
TTF)1-x(BEDT-STF)x]$\rm{}_{2}\\-Cu_{2}(CN)_{3}$ is displayed in Fig. 3 for
crystals of varying substitution $0\leq x\leq 1$. The data are measured for
the in-plane directions $E\parallel b$ and $E\parallel c$ from room
temperatures down to $T=5$ K. The properties are rather similar for both
polarizations indicating electronically isotropic behavior within the
$bc$-plane.

For BEDT-STF substitutions $x<0.1$, the compounds remain insulating at all
temperatures; but no Mott gap develops upon cooling. On the contrary, similar
to the pristine crystals Kézsmárki  _et al._ (2006); Elsässer  _et al._
(2012); Pustogow  _et al._ (2018), a pronounced in-gap absorption is present
that becomes enhanced as or $T$ is reduced or $x$ increases. In these cases we
enter the coexistence regime of metallic and insulating regions expected for
first-order phase transitions: the rising metallic fraction increasingly
contributes to the optical properties. Eventually the alloys exhibit a Drude-
like contribution to the optical conductivity, indicating the metallic
properties in accord with the dc results presented in Fig. 2. An extended
Drude analysis of the optical conductivity be presented elsewhere Pustogow
_et al._ (2020), where the frequency dependence of the scattering rate
$1/\tau$ and effective mass is extracted and the dependence on the
substitutional value $x$ is discussed. According to the $\rho(T)\propto T^{2}$
behavior in the resistivity, we can identify a
$1/\tau(\omega)\propto\omega^{2}$ dependence at the lowest temperatures.

Figure 3: Frequency dependent conductivity of $\kappa$-[(BEDT-TTF)1-x(BEDT-
STF)x]$\rm{}_{2}\\-Cu_{2}(CN)_{3}$ for several substitution values $x=0.04$,
0.12, 0.28, and $x=1$ recorded for the two polarizations within the plane
(left column $E\parallel b$; right column $E\parallel c$) at different
temperatures as indicated.

In Fig. 3 we also see that the mid-infrared peak consists of two
contributions: inter-dimer excitations and transitions between the lower and
the upper Hubbard bands, which almost coincide when probed along the $c$-axis.
This has been observed in most $\kappa$-phase BEDT-TTF compounds and confirmed
by ab-initio calculations Faltermeier  _et al._ (2007); *Merino08; *Dumm09;
*Dressel09; Elsässer  _et al._ (2012); Ferber  _et al._ (2014). Following the
approach taken in Ref. Pustogow  _et al._ , 2018, we focus on the low-
temperature spectra ($T=5$ K, $E\parallel c$) where we assign the maximum of
the mid-infrared peak to the transitions between the lower and the upper
Hubbard band separated by $U$. The width of the conductivity band in
$\sigma_{1}(\omega)$ corresponds to twice the electronic bandwidth $W$, as
illustrated in the inset of Fig. 4 222Due to the metallic contribution at low
frequencies, we determined the bandwidth as $1/2$ of the full width of the
Mott-Hubbard band after subtracting a Drude fit for the compounds with
metallic ground state. In particular, the band edge at the high-frequency tail
$\omega_{\rm high}$ was defined from a linear cut-off; continuing
$\sigma_{1}(\omega_{\rm high})$ to the low-frequency tail yields $\omega_{\rm
low}$. Using these assignments, $2W$ corresponds simply to $\omega_{\rm
high}-\omega_{\rm low}$. As a matter of course, the resulting Mott-Hubbard
band parameters of CuCN are slightly different than in Ref. Pustogow  _et al._
, 2018. Also $U$ was extracted after subtracting a low-frequency Drude fit,
the frequency-dependent background of which slightly shifts the maximum of
$\sigma_{1}(\omega)$ to higher energy compared to the raw data..

The extracted absolute values of $U$ and $W$ are plotted in the main frame as
a function of STF-substitution $x$. We observe an increase of the electronic
repulsion $U$ corresponding to the larger intra-dimer overlap $t_{d}$ as
orbitals extend; even more pronounced is the rise of the bandwidth $W$,
resulting from the increase of the transfer integrals $t$ and $t^{\prime}$
between adjacent dimers. The effect of correlations is measured by the ratio
$U/W$, which is also plotted in Fig. 4, corresponding to the right scale.
Obviously, the metallic compound $\kappa$-(BEDT-STF)2Cu2(CN)3 is much less
correlated compared to the Mott insulator $\kappa$-(BEDT-TTF)2Cu2(CN)3. The
variation, however, is far from linear: a dramatic drop of $U/W$ is found for
$x<0.2$, while for larger $x$ the ratio saturates around $U/W\approx 1.02$
333The apparent leveling off of $U/W$ around a value near unity can be also a
result of the method applied to determine the bandwidth. If the Hubbard bands
strongly overlap, the simple scheme depicted in the inset of Fig. 4 may
underestimate $W$.. Overall, from these optical experiments the Mott
insulator-to-metal transition can be located around $x\approx 0.1$ in
agreement with the dc resistivity.

Figure 4: Dependence of the Coulomb interaction $U$ (full black squares) and
bandwidth $W$ (solid blue dots) on the substitution $x$ in $\kappa$-[(BEDT-
TTF)1-x(BEDT-STF)x]$\rm{}_{2}\\-Cu_{2}(CN)_{3}$ as determined from low-
temperature optical conductivity. The inset explains the determination of $U$
from the mid-infrared maximum in $\sigma_{1}(\omega)$ and $W$ from the half-
width at half maximum. The effective correlation strength is given by the
ratio $U/W$ (open red diamonds) and also plotted, corresponding to the right-
hand scale. The three sketches above illustrate how the substitution $x$
gradually tunes $\kappa$-(BEDT-TTF)2Cu2(CN)3 to $\kappa$-(BEDT-STF)2Cu2(CN)3;
the lines of increasing thickness indicate the enhancement of transfer
integrals $t$ (solid blue), $t^{\prime}$ (dashed blue) and $t_{d}$ (dotted
black).

##  V Vibrational Spectroscopy

By now, it is well established that most of the dimerized BEDT-TTF salts, such
as $\kappa$-(BEDT-TTF)2Cu[N(CN)2]Cl, $\kappa$-(BEDT-TTF)2Cu2(CN)3, or
$\kappa$-(BEDT-TTF)2Ag2(CN)3 do not possess sizeable charge disproportionation
within the dimers Sedlmeier  _et al._ (2012); Pinterić  _et al._ (2016); Tomić
and Dressel (2015), with a few exceptions, like $\kappa$-(BEDT-TTF)2Hg(SCN)2Cl
Drichko  _et al._ (2014); *Lohle16; *Ivek17. Raman and infrared spectroscopies
are the best suited tools to locally probe the charge per molecule by
inspecting the intramolecular vibrations that are known to be extremely
sensitive to the amount of charge residing on the molecule Dressel and Drichko
(2004); Yamamoto  _et al._ (2005); Girlando (2011); *Girlando12. Here we
addressed the question whether charge imbalance occurs when sulfur is replaced
by selenium in the alloys $\kappa$-[(BEDT-TTF)1-x(BEDT-
STF)x]$\rm{}_{2}\\-Cu_{2}(CN)_{3}$.

To that end we recorded the optical properties perpendicular to the planes. In
Fig. 5 the out-of-plane conductivity of $\kappa$-(BEDT-TTF)2Cu2(CN)3 is
compared to $\kappa$-(BEDT-STF)2Cu2(CN)3 in the finger-print spectral region
where the most charge-sensitive molecular vibrations of the central C=C occur.

Figure 5: Optical conductivity of $\kappa$-(BEDT-TTF)2Cu2(CN)3 and
$\kappa$-(BEDT-STF)2Cu2(CN)3 recorded for the out-of-plane polarization
$E\parallel a$. The curves for the different temperatures are displaced for
clarity reasons. The strong C=C vibrational mode $\nu_{27}(B_{1u})$ around
1460 cm-1 sharpens upon cooling but does not exhibit any severe modifications
or splitting, as expected if strong charge disproportionation would occur. The
data for $\kappa$-(BEDT-TTF)2Cu2(CN)3 were previously discussed in Ref.
Sedlmeier  _et al._ , 2012.

The dominant mode $\nu_{27}(B_{1u})$ alters only slightly upon STF-
substitution. If we focus on the limiting cases $x=0$ and $x=1$, we see that
both compounds exhibit basically the same temperature dependence: a typical
sharpening and slight hardening upon cooling. This behavior is explained by
the fact that the sufur/selenium atoms in the pentagonal inner ring are
basically not involved in these modes. It can best be seen from the
vibrational analysis and animations of Ref. Dressel  _et al._ , 2016 that
these vibrations are well confined to the C=C bonds. Most important, since we
do not observe any pronounced mode splitting in the $\kappa$-[(BEDT-
TTF)1-x(BEDT-STF)x]$\rm{}_{2}\\-Cu_{2}(CN)_{3}$ series, we conclude the
absence of any significant charge imbalance among the donor molecules.

##  VI Dielectric Properties

From the Kramers-Kronig analysis of the measured reflectivity spectra we
obtain the complex dielectric constant $\hat{\varepsilon}(\omega,T,x)$ as a
function of frequency, temperature and substitution. Fig. 6 shows the real
part $\varepsilon_{1}(\omega)$ for the different $\kappa$-[(BEDT-TTF)1-x(BEDT-
STF)x]$\rm{}_{2}\\-Cu_{2}(CN)_{3}$ crystals recorded at $T=5$ K. In the Mott
insulating state ($x\leq 0.1$), the permittivity is basically frequency-
independent and acquires a small, positive value. As $x$ increases, the quasi-
static $\varepsilon_{1}(\omega\rightarrow 0)$ first increases before it
rapidly drops to large negative values. After crossing the Mott insulator-to-
metal transition the system becomes conductive: the strong screening of the
coherent quasiparticle drives $\varepsilon_{1}$ negative. A similar
observation was reported for the Mott transition of VO2, where the low-
frequency permittivity diverges as a function of temperature. Near-field
optical microscopy revealed that this behavior stems from the phase
coexistence of metallic puddles in an insulating matrix Qazilbash  _et al._
(2007). In general, the divergency of the dielectric permittivity
$\varepsilon_{1}(x)$ is a hallmark of percolative phase transitions in
microemulsions Grannan  _et al._ (1981); van Dijk  _et al._ (1986); Clarkson
and Smedley (1988); *Clarkson88b; Alexandrov  _et al._ (1999), composites
Pecharromán and Moya (2000); *Pecharroman01; Nan  _et al._ (2010) or
percolating metal films Berthier  _et al._ (1997); Hövel  _et al._ (2010);
*Hovel11; De Zuani  _et al._ (2014); *deZuani16.

Figure 6: Despite continuously increasing low-frequency conductivity, in the
low-frequency limit the dielectric permittivity $\varepsilon_{1}(x)$ exhibits
a peak around the Mott transition, reminiscent of a percolative-type
coexistence of metallic and insulating regions. The left panel displays the
real part of the dielectric permittivity $\varepsilon_{1}(x)$ as obtained from
far-infrared reflectivity measurements for $E\parallel c$ at $T=5$ K for
$\kappa$-[(BEDT-TTF)1-x(BEDT-STF)x]$\rm{}_{2}\\-Cu_{2}(CN)_{3}$ with various
substitutions $x$ as indicated. To better follow the substitutional
dependence, panel (b) displays the dielectric permittivity taken at
$\omega/2\pi c=100$ cm-1 indicated by the dashed line in panel (a).

Since audio- and radio-frequency experiments are more suitable for exploring
the dielectric behavior at the insulator-metal transition, we have conducted
dielectric experiments down to 40 Hz. Fig. 7 summarizes the dielectric
response of $\kappa$-(BEDT-TTF)2Cu2(CN)3 and how it is affected by moving
across the Mott insulator-to-metal transition via STF-substitution. We plot
the real part of the permittivity $\varepsilon_{1}$ as a function of
temperature $T$ for selected frequencies $f$ and substitutions $x$, as
indicated. The pronounced peak dominating the temperature dependence of
$\varepsilon_{1}(T)$ was discovered by Abdel-Jawad et al. Abdel-Jawad  _et
al._ (2010) and subsequently confirmed by other groups Pinterić  _et al._
(2014, 2015); Tomić and Dressel (2015); Sasaki  _et al._ (2015); Rösslhuber
_et al._ (2019). When probed at $f=7.5$ kHz, the maximum is observed around
$T=30$ K in the case of $\kappa$-(BEDT-TTF)2Cu2(CN)3 [Fig. 7(a)]; with a
slight sample-to-sample dependence, in agreement with previous reports. The
peak shifts to higher temperatures as the frequency increases; at the same
time, however, it gets less pronounced. This behavior resembles the well-known
phenomenology of relaxor ferroelectrics Cross (2008).

Figure 7: Temperature-dependent dielectric permittivity of $\kappa$-[(BEDT-
TTF)1-x(BEDT-STF)x]$\rm{}_{2}\\-Cu_{2}(CN)_{3}$ for substitutional values
$x=0$, 0.04, 0.10, 0.12, 0.16 and 0.25 measured at several frequencies. Note
the different ordinates used in the various panels. (a) The pure crystal
exhibits a relaxor-type ferroelectric feature below $T=50$ K, which becomes
more pronounced and shifts to lower $T$ as frequency gets smaller. (b,c) As
$x$ is increased to 0.1, $\varepsilon_{1}(T)$ rises strongly and the peak
appears at lower temperatures. (d-e) Eventually the permittivity reaches
values of $10^{5}$ due to the coexistence of spatially separated metallic and
insulating regions. The response is strongly frequency dependent. (f) Upon
percolation around $x=0.2$, the dielectric constant is negative, giving
evidence for the metallic behavior that continues for all higher substitutions
up to $x=1$.

Already the minimal substitution of $x=0.04$ and 0.1 enhances the dielectric
permittivity significantly with the maximum $\varepsilon_{1}(f=7.5~{}{\rm
kHz})\approx 50$ and 80. This strong increase of $\varepsilon_{1}(T)$ and
concomitant shift of the peak to lower temperatures when we approach the
insulator-metal transition is in full accord with our pressure-dependent
dielectric studies Rösslhuber  _et al._ (2019) where an extensive and detailed
analysis is given. As we approach the phase transition further ($x=0.12$ and
0.16), the dielectric constant drastically diverges, reaching values up to
$10^{5}$ in the static low-temperature limit. A divergency in
$\varepsilon_{1}(x)$ is the fingerprint of a percolative phase transition
where metallic regions form in an insulating matrix Mott (1990); Kirkpatrick
(1973); Efros and Shklovskii (1976). When crossing the percolation threshold,
the system acts like a metal, characterized by a negative dielectric
permittivity, $\varepsilon_{1}<0$. With rising $x$ the sign change of the
dielectric constant traces the Brinckman-Rice temperature, as it was
identified by the maximum in $\rho(T)$ (Fig. 2) Pustogow  _et al._ (2020).
These results confirm the observations we extracted from the optical response
in Fig. 6.

Figure 8: Dielectric properties of $\kappa$-[(BEDT-TTF)1-x(BEDT-
STF)x]$\rm{}_{2}\\-Cu_{2}(CN)_{3}$ in dependence of the substitution level
$x$, recorded perpendicular to the $bc$-plane at a fixed frequency $f=100$ kHz
at different temperatures as indicated. Note the logarithmic scales. (a) The
permittivity $\varepsilon_{1}(x)$ forms a pronounced maximum followed by a
rapid drop to negative values, corresponding to right scale. (b) The
conductivity $\sigma_{1}(x)$ exhibits a step-like increase at $x=0.12$,
indicating the Mott transition. The observed behavior matches the signature of
a percolating system. At the insulator-to-metal transition, the nucleation and
growth of metallic puddles sets in, which are spatially separated in an
insulating matrix. Upon increasing $x$, the metallic filling fraction grows
until the metallic state is completely established at $x=0.25$. With rising
temperature the features diminish in amplitude or step size, respectively,
consistent with the change from the first-order insulator-metal transition to
the crossover region at elevated temperatures.

For better comparison, we plot $\varepsilon_{1}(x)$ and $\sigma_{1}(x)$ for
the complete series $\kappa$-[(BEDT-TTF)1-x(BEDT-
STF)x]$\rm{}_{2}\\-Cu_{2}(CN)_{3}$ in Fig. 8 measured at various temperatures
$T$. Raising the STF-content results in a strong enhancement of the dielectric
constant up to $10^{3}$, whereas for $x=0.25$ a drop to large negative values
of the order of $\varepsilon_{1}(x)\approx-10^{3}$ is observed. Concurrently,
$\sigma_{1}(x)$ increases by several orders of magnitude: the rapid rise at
$x\approx 0.12$ indicates the crossing of the phase boundary into the metallic
regime.

##  VII Discussion and Summary

In a complementary study Rösslhuber  _et al._ (2019) the dielectric properties
of $\kappa$-(BEDT-TTF)2Cu2(CN)3 have been measured as a function of
hydrostatic pressure. This is an alternative way to shift the Mott insulator
through the first-order phase transition until the Fermi-liquid state is
reached above $p\approx 1$ kbar. The behavior obtained by the pressure-
dependent investigations is in full accord with the dielectric response
observed here in the substitutional series; both can be well described by
dynamical mean-field theory on the single-band Hubbard model when combined
with percolation theory Pustogow  _et al._ (2019).

Figure 9: Contour plot of the dielectric permittivity $\varepsilon_{1}$
recorded at $f=380$ kHz as a function of temperature and STF-substitution $x$.
We observe a strong increase of $\varepsilon_{1}$ up to 2500, centered around
$x=0.15$-0.2 and below $T\approx 15$-20 K, close to the first-order Mott
transition. We ascribe this to phase coexistence around the first-order Mott
transition hosting spatially separated metallic and insulating regions, in
agreement with state-of-the-art dynamical-mean-field-theory Vučičević  _et
al._ (2013); Pustogow  _et al._ (2019). See text for more details.

The fact that both approaches reach very much the same results provides firm
evidence for a percolative Mott transition. Substituting BEDT-STF molecules
increases the intra- and interdimer transfer integrals on a local scale, but
this effect is smeared out. Local strain does not alter the crystal symmetry;
the substitution results in a slightly larger unit cell as seen from Tab. 1.
Since the organic molecules are rather large, diffusion within the crystal is
prohibited, ruling out the formation of BEDT-STF clusters or domains of
extended size beyond the stochastic occurrence. As depicted in Fig. 4, STF-
substitution only results in a gradual decrease of effective correlation
strength $U/W$.

Our findings are summarized in Fig. 9 where the dielectric permittivity
$\varepsilon_{1}$ is plotted as a function of temperature and STF-substitution
$x$ producing a contour plot that constitutes the corresponding phase diagram.
We conclude that the discovery of the enormous divergency in the low-
temperature quasi-static dielectric permittivity $\varepsilon_{1}(x)$ proves
metallic regions coexisting with the insulating matrix. The reduction of
electronic interactions $U/W$ due to increasing $x$ leads to a spatial phase
separation that is confined to temperatures below the critical endpoint
$T_{\rm crit}\approx 15$-20 K. With rising metallic fraction, the resistivity
decreases, as can be well understood by effective medium models Choy (2015).
At large substitutions, metallic fluctuations dominate the electronic
response. This range is well distinct by the negative and very large
permittivity; its boundary trails the Brinkman-Rice temperature for the onset
of metallic conductivity. The complete electrodynamical properties of this
correlated electron system including the percolative aspect of the first-order
Mott transition can be reproduced by the hybrid approach of dynamical mean-
field theory amended with percolation theory Pustogow  _et al._ (2019).
Finally we would like to point out that the novel path of tuning the effective
correlations by increasing the molecular orbitals when partially replacing
BEDT-TTF by the selenium-containing BEDT-STF molecules can be applied to other
charge-transfer salts as well, providing an interesting alternative to
chemical and physical pressure.

## Acknowledgements

We acknowledge continuous discussions with V. Dobrosavljević and Y. Tan. We
thank N. Kircher for participating in some experiments and Y. Takahashi for
performing x-ray diffraction; G. Untereiner put an enormous efforts into
sample preparation. The project was supported by the Deutsche
Forschungsgemeinschaft (DFG) via DR228/39-3.

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