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Evidence for an Excitonic Insulator State in Ta2Pd3Te5
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Evidence for an Excitonic Insulator State in Ta2Pd3Te5
Jierui Huang ,1,2,Bei Jiang ,1,2,Jingyu Yao,1,2,Dayu Yan,1,2,Xincheng Lei,1,2,Jiacheng Gao,1,2Zhaopeng Guo,1
Feng Jin,1Yupeng Li,1Zhenyu Yuan,1,2Congcong Chai,1,2Haohao Sheng,1,2Mojun Pan,1,2Famin Chen,1,2Junde Liu,1,2
Shunye Gao,1,2Gexing Qu,1,2Bo Liu,1,2Zhicheng Jiang,3Zhengtai Liu,3Xiaoyan Ma,1,2Shiming Zhou,4Yaobo Huang,3
Chenxia Yun,1Qingming Zhang,1,5Shiliang Li,1,2,6Shifeng Jin,1,2Hong Ding,7,8Jie Shen,1,?Dong Su,1,2,?
Youguo Shi,1,2,6 ,§Zhijun Wang ,1,2,∥and Tian Qian1,?
1Beijing National Laboratory for Condensed Matter Physics and Institute of Physics,
Chinese Academy of Sciences, Beijing 100190, China
2University of Chinese Academy of Sciences, Beijing 100049, China
3Shanghai Synchrotron Radiation Facility, Shanghai Advanced Research Institute,
Chinese Academy of Sciences, Shanghai 201204, China
4Hefei National Research Center for Physical Sciences at the Microscale,
University of Science and Technology of China, Hefei 230026, China
5School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China
6Songshan Lake Materials Laboratory, Dongguan 523808, China
7Tsung-Dao Lee Institute, New Cornerstone Science Laboratory, and School of Physics and Astronomy,
Shanghai Jiao Tong University, Shanghai 201210, China
8Hefei National Laboratory, Hefei 230088, China
(Received 6 December 2022; revised 21 December 2023; accepted 8 February 2024; published 13 March 2024)
The excitonic insulator (EI) is an exotic ground state of narrow-gap semiconductors and semimetals
arising from spontaneous condensation of electron-hole pairs bound by attractive Coulomb interaction.Despite research on EIs dating back to half a century ago, their existence in real materials remains a subject
of ongoing debate. In this study, through systematic experimental and theoretical investigations, we provide
evidence for the existence of an EI ground state in a van der Waals compound Ta
2Pd3Te5. Density-
functional-theory calculations suggest that it is a semimetal with a small band overlap, whereas variousexperiments exhibit an insulating ground state with a clear band gap. Upon incorporating electron-holeCoulomb interaction into our calculations, we obtain an EI phase where the electronic symmetry breakingopens a many-body gap. Angle-resolved photoemission spectroscopy measurements exhibit that the bandgap is closed with a significant change in the dispersions as the number of thermally excited charge carriers
becomes sufficiently large in both equilibrium and nonequilibrium states. Structural measurements reveal a
slight breaking of crystal symmetry with exceptionally small lattice distortion in the insulating state, whichcannot account for the significant gap opening. Therefore, we attribute the insulating ground state with agap opening in Ta
2Pd3Te5to exciton condensation, where the coupling to the symmetry-breaking
electronic state induces a subtle change in the crystal structure.
DOI: 10.1103/PhysRevX.14.011046 Subject Areas: Condensed Matter Physics,
Strongly Correlated Materials
I. INTRODUCTION
In condensed matter systems, many-body interactions
can lead to various exotic quantum phases, such as theMott insulator, unconventional superconductivity, quantum
spin liquid, heavy fermion, and so on. One particularly
intriguing phenomenon is the excitonic insulator (EI)expected to emerge when a semiconductor with a smallband gap or a semimetal with a small band overlap is cooledto sufficiently low temperatures [1–4]. During this process,
bound electron-hole pairs known as excitons spontaneously
form and condensate into a phase-coherent insulating state.
While exciton condensation has been achieved in artificialheterostructures [5–15], the existence of an EI state in real
materials remains a topic of ongoing debate.Theses authors contributed equally to this work.
?Corresponding author: shenjie@iphy.ac.cn
?Corresponding author: dongsu@iphy.ac.cn
§Corresponding author: ygshi@iphy.ac.cn
∥Corresponding author: wzj@iphy.ac.cn
?Corresponding author: tqian@iphy.ac.cn
Published by the American Physical Society under the terms of
theCreative Commons Attribution 4.0 International license.
Further distribution of this work must maintain attribution to
the author(s) and the published article ’s title, journal citation,
and DOI.PHYSICAL REVIEW X 14,011046 (2024)
2160-3308 =24=14(1) =011046(10) 011046-1 Published by the American Physical SocietySo far, only a few materials have been proposed as
candidates for EIs. Among them, the most intensively
studied ones are 1T-TiSe 2[16–22]and Ta 2NiSe 5[23–29],
in which a band gap is opened around the Fermi level ( EF)
below a critical temperature [21,25] . The gap opening is
accompanied by significant structural changes character-
ized by a charge-density-wave transition with periodiclattice distortion in 1T-TiSe
2[30,31] and an orthorhombic-
to-monoclinic transition with mirror symmetry breakingin Ta
2NiSe 5[32,33] . The coexistence of electronic and
structural instabilities has aroused intense debate on
whether the gap opening originates from exciton conden-sation or lattice distortion. In the former case, excitonsspontaneously form and condense due to electron-hole
coupling, leading to the opening of a many-body gap. In the
EI state, the electronic symmetry breaking induces latticedistortion through electron-lattice coupling [18,20,24,34] .
In the latter case, a structure phase transition is driven byphononic instability. The lattice distortion couples to
electrons, opening a hybridized gap. Density-functional-
theory (DFT) calculations for these two materials reveal thepresence of imaginary phonon frequencies, indicating anunstable crystal structure [35–40]. Despite numerous
efforts over several decades, the origin of the gap opening
remains a subject of significant controversy.
As the symmetry of the electronic state is broken in an EI
state, structural instability inevitably occurs due to electron-lattice coupling, which is inherently present in solid-state
materials. Nevertheless, as a by-product of exciton conden-
sation, lattice distortion can, in principle, be significantlysuppressed. If the effects of structural changes on the bandstructure become sufficiently small, the structural origin ofthe gap opening can be ruled out. In this work, we show that
the van der Waals compound Ta
2Pd3Te5could serve as such
a paradigm of EIs. It exhibits an insulating ground state witha significant band gap derived from an almost zero-gapnormal phase. The insulating state is well reproduced by the
calculations that include electron-hole Coulomb interaction.
The band gap is sensitive to free carrier density, which isincreased by either raising the temperature or laser pumping.The gap opening is accompanied by a slight breaking ofcrystal symmetry with minimal lattice distortion, which has
negligible effects on the band structure. These results suggest
that the insulating ground state in Ta
2Pd3Te5originates from
excitonic instability, with crystal symmetry breaking being aby-product of exciton condensation.
II. INSULATING GROUND STATE
A previous x-ray diffraction (XRD) study reported that
Ta
2Pd3Te5has an orthorhombic crystal structure with space
group Pnma (no. 62) [41]. Each unit cell consists of two
Ta2Pd3Te5monolayers stacked along the aaxis through
van der Waals forces [Fig. 1(a)]. Within each monolayer, Ta
and Pd atoms form one-dimensional (1D) chains along thebaxis, sandwiched by Te atomic layers [41]. Consequently,
the band structure from DFT calculations exhibits a quasi-1D character with strong dispersions along the chain
direction [Fig. 1(c)]. The calculations suggest a semimetallic
band structure, while transport measurements reveal semi-conductorlike behavior over a wide temperature rangewith a metal-insulator transition around 365 K [Fig. 1(d)].
Angle-resolved photoemission spectroscopy (ARPES) dataat 100 K in Fig. 1(e)reveal that the valence bands (VBs) are
1D chain(a) (b)
(d) (e) (f)(100) Suface BZ
Bulk BZ(c)
1101001000 Resistance ()
400 300 200 100 0
Temperature (K)0.248
0.246
0.244
0.242
400 350 300-0.4-0.20.00.20.4 E - EF (eV)
YT Z XS R U X42 meV
5 nm50
40
30
20
10
0dI/dV (a.u.)
-100 0 100
Bias (mV)12 Ka
bc
-0.4-0.20.0E - EF (eV)
-0.2 0.0 0.2
kb(-1)100 Kkbkcka
FIG. 1. (a) Crystal structure of Ta 2Pd3Te5. (b) Bulk Brillouin zone (BZ) and (100) surface BZ. (c) Calculated band structure along
high-symmetry lines by DFT using the MBJ functional. (d) Resistance as a function of the temperature ( R-T) in the b-cplane. The inset
shows a metal-insulator transition around 365 K. (e) Intensity plot of the ARPES data along ?Γ-?Ycollected with hν?6eV at 100 K. For
clarity, the data are divided by the Fermi-Dirac distribution function to visualize the VB bottom above EF. (f) Tunneling differential
conductance spectra at 12 K along the yellow line in the inset. The inset shows a constant-current topographic image of the cleaved (100)surface ( V?100mV, I?100pA). The data are collected in a clean region free from impurities to display the global gap.JIERUI HUANG et al. PHYS. REV . X 14,011046 (2024)
011046-2well below EF, while the conduction bands (CBs) lie
above EF, forming a global band gap. Scanning tun-
neling spectroscopy spectra in Fig. 1(f)exhibit a uniform
“U”-shaped gap in a clean region free from impurities. The
semiconductorlike behavior with a global band gap observed
in experiments contradicts the semimetallic band structurepredicted by DFT calculations.
In a previous study [42], Perdew-Burke-Ernzerhof (PBE)
calculations suggested a semimetallic band structure with aband overlap of 85 meV. Considering the potential under-
estimation of the band gap by PBE, we check the result
using the modified Becke-Johnson (MBJ) functional. TheMBJ band structure in Fig. 1(c) shows a reduced band
overlap of 42 meV, while still maintaining the semimetallic
character (see comparison between PBE and MBJ bandstructures in Fig. S1 in Supplemental Material [43]).
Furthermore, we confirm that the inclusion of spin-orbit
coupling or changes in lattice constants is insufficientto induce a global band gap (Fig. S2 in Supplemental
Material [43]). Since noninteracting DFT calculations fail
to account for the band gap, correlation effects may play acrucial role in the insulating state. We conduct DFT ?U
calculations, where Urepresents on-site Hubbard-like
electron-electron interaction on the Ta 5dand Pd 4d
orbitals. As Uincreases, the band overlap is moderately
reduced (Fig. S3 in Supplemental Material [43]). However,
even with Uincreased to 3 eV, which is already sufficiently
large for 4dand 5delectrons, the semimetallic bandstructure persists, signifying that the on-site Coulomb
interaction cannot account for the insulating state.
Then, we consider electron-hole Coulomb interaction for
the insulating state, since the DFT calculations show a smalloverlap between the valence and conduction bands aroundE
F. For this purpose, we first construct an effective Wannier-
based two-dimensional tight-binding Hamiltonian ( HTB)
extracted from PBE calculations. The noninteracting bandstructure of H
TBis presented in Fig. 2(b).T h eC Bo r i g i n a t e s
from the Ta- dz2orbital, while the VB originates from the
PdA-dxzorbital hybridized with the Te- pxorbital (Fig. S5 in
Supplemental Material [43]). Here, Pd Arepresents the Pd
atoms at the A site [42]. In the absence of electron-hole
interaction, the hybridization between the valence and con-duction bands along Γ-Zis prohibited due to the presence of
mirror symmetry m
bindicated in Fig. 2(a). Subsequently, we
consider the interband density-density term for the electron-hole interaction V. The total Hamiltonian reads as follows:
H?H
TB?VH int;
Hint?X
?Rσσ0X
i?1;2?n5σ? ?R??n5σ? ?R? ?b?/C138niσ0? ?R?
?X
?Rσσ0X
j?3;4?n6σ? ?R??n6σ? ?R? ?b?/C138njσ0? ?R?
?X
?Rσσ0X
i?1;2n7σ? ?R?niσ0? ?R??X
?Rσσ0X
j?3;4n8σ? ?R?njσ0? ?R?;
?1?
(a) (b)
c(y)
b(x)
1
2
3
45
67
8
mb
Ta
TePd(c)
TZ Г Y-0.4-0.20.0E - EF (eV)0.20.4HTB
(d) (f) (e)
E - EF (eV)
-0.4-0.20.0
60504030
hv (eV)
Intensity (a.u.)
60 50 40 30
hν (eV)
-0.4-0.20.0
60504030
hv (eV)E - EF (eV) Intensity (a.u.)
60 50 40 30
hν (eV)
-0.4-0.20.0E - EF (eV)
0.2 -0.2 0.0Г_
Z_
kc (-1)TZ Г Y-0.4-0.20.0E - EF (eV)0.20.4EI
FIG. 2. (a) Schematic illustration of electron-hole Coulomb interaction considered in the theoretical model. Ta, Pd A, and Te atoms with
interacting orbitals are labeled by numbers 1 –8. Red arrows represent the interaction between Ta- dz2and Pd A-dxz, and blue arrows
represent the interaction between Ta- dz2and Te- px, but we assign the same interaction strength Vin the model. (b),(c) Band structures of
the noninteracting Hamiltonian HTB(b) and the EI state (c). The thickness of the red lines scales the Ta- dz2orbital component.
(d) Intensity plot of the ARPES data along ?Γ-?Zcollected with hν?40eV at 10 K. (e) hνdependence of the spectral intensities at two
constant energies indicated by the dashed lines in the inset. Inset: intensity plot of the ARPES data at ?Γwith varying hν. The spectral
intensities are normalized by photon flux. (f) Same as (e), but collected at ?Z.EVIDENCE FOR AN EXCITONIC INSULATOR STATE … PHYS. REV . X 14,011046 (2024)
011046-3where the Ta- dz2,P d A-dxz, and Te- pxorbitals are labeled
by numbers 1 –4, 5–6, and 7 –8, respectively, as indicated in
Fig.2(a).σandσ0denote the spin degrees of freedom. We
employ the Hartree-Fock approximation to treat the Coulombinteraction. In the self-consistent process, we exclude theHartree terms, as they are already considered in DFT
calculations.
The mean-field band structure with V?1.1eV in
Fig. 2(c) exhibits a gap opening at E
Fwith a sizable
hybridization. The hybridization indicates that the mb
symmetry of the electronic state is broken due to the
interband interaction, even though crystal symmetry ispreserved, which is the hallmark of excitonic instability.
Here, we define an order parameter ?δof the form
?δ??δ
15;δ25;δ36;δ46?;
δi5?hc?
ic5i?hc?
ic5?? ?b?i;
δj6?hc?
jc6i?hc?
jc6?? ?b?i: ?2?
We drop the spin index as we focus on the spin-singlet case.
The four δmnare in general independent. The detailed
calculations show that the inversion symmetry and allmirror symmetries are broken in the EI state, leading to
a nonzero order parameter of ?δ?δ
0??1;?1;?1;?1?.
To verify the band hybridization of the EI state, we
perform photon-energy- ( hν) dependent ARPES measure-
ments to determine the orbital components of the VBs.
For transition-metal compounds, when hνis tuned to the
binding energies of porbitals, the spectral intensities of the
VBs originating from dorbitals are suppressed due to p-d
antiresonance [44,45] . The hν-dependent data at ?Γin
Fig. 2(e) exhibit significant suppression around 34 and
43 eV, corresponding to the binding energies of theTa5p
3=2and 5p1=2orbitals, respectively (Fig. S6 in
Supplemental Material [43]). At ?Z, in addition to the
suppression around 34 and 43 eV, the data in Fig. 2(f)
show kinks around 50 and 55 eV , corresponding to the
binding energies of the Pd 4p3=2and 4p1=2orbitals,
respectively (Fig. S6 in Supplemental Material [43]).
These results demonstrate the presence of a considerableTa5dorbital component in the highest VB, signifying a
strong interband hybridization due to the breaking of m
b.
III. BAND GAP CONTROLLED
BY CARRIER DENSITY
EIs exhibit a semiconductorlike band structure with a
band gap at EF, where thermal excitation leads to an increase
in the number of free carriers with increasing temperature.The higher carrier density effectively screens the electron-hole Coulomb interaction, diminishing the stability of
excitons. As a result, the gap size of an EI gradually
decreases as the temperature increases [20,21,25] .H a l l
resistance measurements on Ta
2Pd3Te5reveal a substantialincrease in carrier density with increasing temperature above
30 K (Fig. S10 in Supplemental Material [43]). We perform
temperature-dependent ARPES experiments to investigatethe evolution of the band structure with the temperature. TheARPES data in Figs. 3(a)and3(b)show that the VBs lie well
below E
Fat low temperatures, while the CBs above EF
become visible when thermally occupied above 100 K. Both
valence and conduction bands shift in energy with the
temperature [Fig. 3(c)]. They gradually approach with
increasing temperature [Fig. 3(d)], resulting in a substantial
reduction in the gap size from 55 meV at 75 K to 5 meV at
300 K [Fig. 3(e)]. Furthermore, the dispersions around ?Γ
change from parabolic to linear when the temperaturereaches 300 K. These results reveal a significant renormal-
ization in the low-energy state with the temperature.
The temperature dependence of the gap size is further
validated by transport data. The R-Tcurve in Fig. 1(d)
exhibits semiconductorlike behavior below 365 K. In semi-conductors, the thermal activation of carriers follows the
relation ρ?ρ
0exp???EA=2kBT?/C138,w h e r e ρ0is a constant
with the dimension of resistance, and EArepresents the
activation energy of carriers, reflecting the magnitude of
the band gap. By fitting the R-Tcurve with the formula
EA??2kBT2??lnρ=?T?,w eo b t a i n EAas a function of
the temperature [Fig. 3(e)]. Above 100 K, EAmonotonically
decreases with increasing temperature, and its magnitude
closely aligns with the gap size extracted from the ARPESdata, indicating that the thermal activation model effectivelydescribes the evolution of the band gap above 100 K.
In contrast, E
Adecreases dramatically below 100 K. This
behavior can be attributed to the presence of in-gap states,
which contribute finite intensities near EFto the low-
temperature ARPES spectra (Fig. S9 in SupplementalMaterial [43]). The in-gap states could originate from
impurities with a finite spatial extension of the wave
function, as observed in the Si-doped semiconductorβ-Ga
2O3[46,47] . Based on this assumption, we estimate
the spatial extension of the impurity wave function to be
about 16 ? by fitting the momentum distribution curve atE
F(Fig. S11 in Supplemental Material [43]). Scanning-
tunneling-microscopy (STM) measurements confirm the
presence of impurities in some regions on sample surfaces,
and their spatial extensions are consistent with the valueestimated from the ARPES data (Fig. S12 in Supplemental
Material [43]). Carrier hopping between nearby impurities
would have a significant impact on transport behavior atlow temperatures, leading to an obvious deviation from
the thermal activation model as well as a rapid upturn in
carrier density below 30 K (Fig. S10 in SupplementalMaterial [43]. With increasing temperature, the contribu-
tion of thermally excited intrinsic carriers gradually rises,
eventually becoming dominant above 100 K.
In addition to heating in the equilibrium state, in pump-
probe ARPES experiments, pump laser pulses can sub-
stantially raise the transient electronic temperature [48,49] ,JIERUI HUANG et al. PHYS. REV . X 14,011046 (2024)
011046-4thereby increasing the number of thermally excited carriers
in the nonequilibrium state (Fig. S14 in Supplemental
Material [43]). Hence, we investigate the effect of laser
pumping on the insulating state of Ta 2Pd3Te5with pump-
p r o b eA R P E S .T oo b s e r v et h ee v o l u t i o no ft h eC B sm o r e
clearly and reduce the thermal effect (Fig. S13 in
Supplemental Material [43]), the pump-probe ARPES
experiments are conducted at 150 K. The ARPES data inFigs. 4(a)and4(b)exhibit a clear band gap in the equilibrium
state without laser pumping. The gap gradually diminishes
with an increase in pump fluence and is closed at a fluence
of0.17mJ=cm
2. We compare band dispersions at pump
fluences of 0 and 0.25mJ=cm2in Fig. 4(c). The dispersions
around ?Γchange from curved to linear, resulting in a gap
closing, while those away from ?Γare almost unchanged.
Our ARPES results demonstrate that the band gap is
closed with a significant change in the dispersions around
?Γ, when the number of carriers becomes sufficiently large
through thermal excitation in both equilibrium and non-
equilibrium states, as illustrated in Fig. 4(d). These findings
are well consistent with the expectation for EIs.
IV. STRUCTURAL INSTABILITY
In an EI state, structural instability is expected to occur
due to finite electron-lattice coupling. Hence, we conduct
a systematic investigation to clarify whether structuralinstability exists in Ta 2Pd3Te5. The calculated phonon
spectra in Fig. 5(a) reveal the absence of imaginary
frequencies, indicating that the Pnma crystal structure is
stable with no tendency toward spontaneous symmetrybreaking. This result is in contrast to the calculations for theEI candidates 1T-TiSe
2[35–37]and Ta 2NiSe 5[38–40].
The single-crystal XRD data at 300 and 50 K can be wellrefined with space group Pnma [Fig. 5(b)], in agreement
with the previous report [41]. The Raman spectra exhibit
continuous temperature-dependent behavior for all phononmodes without any splitting or emergence of new modesbelow 450 K (Fig. S15 in Supplemental Material [43]). The
specific heat data in Fig. 5(c) do not show any anomaly
associated with a structure phase transition. These resultspoint to a stable crystal structure without a structural phasetransition. We note that an electronically driven EI phasetransition cannot be ruled out in the specific heat data, sincethe contribution of electronic heat capacity is negligible athigh temperatures.
While no structural phase transition is identified, trans-
mission-electron-microscopy (TEM) measurements reveal
the existence of crystal symmetry breaking in the insulatingstate. For space group Pnma , the ( h00) and ( 00l) diffrac-
tion spots, where handlare odd numbers, are forbidden
due to the presence of glide symmetries ?m
cand ?ma. The
electron-diffraction patterns oriented along the [100] direc-tion are displayed in Fig. 5(d). To demonstrate the subtle
(a)
(c)10 K 50 K 100 K 150 K 200 K 250 K 300 K
-0.2-0.10.00.1E - EF (eV)
-0.2 0.0 0.2
kb(-1)
-0.2-0.10.00.1E - EF (eV)
-0.2 0.0 0.2
kb(-1)
-0.2 0.0 0.2
kb(-1)
-0.2 0.0 0.2
kb(-1)
-0.2 0.0 0.2
kb(-1)
-0.2 0.0 0.2
kb(-1)
-0.2 0.0 0.2
kb(-1)(b)
-0.2
-40-20020
300 200 100 0
Temperature (K) CB
VBE - EF (meV)60
40
20
0Gap size (meV)
300 200 100 0
Temperature (K)ARPES
Transport(d) (e)
10 K 100 K
200 K 300 K
-0.10.0
-0.2 0.0 0.2E - EF (eV)
kb(-1)
FIG. 3. (a) Intensity plots of the ARPES data along ?Γ-?Ycollected with hν?6eV at different temperatures. For clarity, the data are
divided by the Fermi-Dirac distribution function to visualize the VB bottom above EF. (b) Intensity plots of the second derivative of the
ARPES data in (a). (c) Band dispersions extracted by tracking peak positions in the intensity plots in (b). (d) Energy positions of VB topand CB bottom as a function of the temperature. (e) Temperature dependence of the gap size determined from the results in (d) and E
A
obtained by fitting the R-Tcurve with the formula EA??2kBT2??lnρ=?T?.EVIDENCE FOR AN EXCITONIC INSULATOR STATE … PHYS. REV . X 14,011046 (2024)
011046-5changes with the temperature in these patterns, we high-
light the base of the line profiles along the [001] direction inFig.5(e). Only the primary spots with an even number of l
are observed at 368 K, confirming that ?m
ais preserved.
Remarkably, the ( 00l) forbidden spots become visible at
300 and 100 K. Similar behavior is observed for the ( h00)
forbidden spots (Fig. S16 in Supplemental Material [43]).
The emergence of the ( h00) and ( 00l) forbidden spots
upon cooling indicates that both ?mcand ?maare broken. The
simulated electron-diffraction patterns for Pnma and its
orthorhombic subgroups indicate that both ( h00) and ( 00l)forbidden spots appear only in space group P212121
(Fig. S17 in Supplemental Material [43]), in which both
?mcand ?maare broken.
The crystal symmetry breaking occurs near the metal-
insulator transition with a gap opening, signifying a close
relationship between electronic and structural instabilities
in Ta 2Pd3Te5. In the EI candidates 1T-TiSe 2and Ta 2NiSe 5,
the concurrence of electronic and structural instabilities
has aroused intense debate on the origin of the gap opening
[39,40,50 –55]. While crystal symmetry breaking allows
the opening of a hybridized gap between the valence and
368 K
(002)
(020)
5 nm-1
100 K368 K
4 3 2 1 0Intensity (a.u.)
1/d (nm-1)300 K
100 K
300 K3
2
1
0Frequency (THz)
YT Z XS RU X200
100
0C (J/K mol)
400 200 0
T (K)(a) (b)
(d)(c)
(e)Observed Intensity (a.u.)
Calculated Intensity (a.u.)106
104
102
106104102 300 K
50 K
FIG. 5. (a) Calculated phonon dispersions of Ta 2Pd3Te5along high-symmetry lines by DFT using the generalized-gradient-
approximation functional. (b) Comparison between the observed XRD intensities from all Bragg peaks measured at 300 and 50 K andthe calculated intensities with space group Pnma . (c) Specific heat as a function of the temperature. (d) Electron-diffraction patterns
oriented with respect to the [100] direction at 368, 300, and 100 K. (e) Line profiles along the [001] direction extracted from the regionsin the rectangles in (d).
-0.10.00.1E - EF (eV)0 mJ/cm20.08 mJ/cm20.13 mJ/cm20.17 mJ/cm20.25 mJ/cm20.35 mJ/cm2
-0.10.00.1E - EF (eV)
-0.2 0.0 0.2
kb (-1)
-0.2 0.0 0.2
kb (-1)
-0.2 0.0 0.2
kb (-1)
-0.2 0.0 0.2
kb (-1)
-0.2 0.0 0.2
kb (-1)
-0.2 0.0 0.2
kb (-1)-0.2 0.0 0.2-0.10.00.1E - EF (eV)
kb (-1)0.25 mJ/cm2
0 mJ/cm2
VB CB
EI
Normal stateEnergy
Carrier densityGap close(a)
(b)(c)
(d)
FIG. 4. (a) Intensity plots of the ARPES data along ?Γ-?Ycollected with different pump fluences. All nonequilibrium data are collected
at a time delay of 0 ps. (b) Intensity plots of the second derivative of the ARPES data in (a). (c) Band dispersions extracted by tracking
peak positions in the intensity plots in (b) at pump fluences of 0 and 0.25mJ=cm2. (d) Schematic diagram depicting the transition from
an EI to normal state with increasing carrier density.JIERUI HUANG et al. PHYS. REV . X 14,011046 (2024)
011046-6conduction bands, the gap size depends on the magnitude of
lattice distortion. By comparing the refinement results of the
XRD data at 50 K with Pnma andP212121,w ec o n f i r m
that the lattice distortion is exceptionally small in thesymmetry-breaking phase (Tables S1 –S3 in Supplemental
Material [43]). To assess the impact of crystal symmetry
breaking on the band structure, we calculate the bandstructure of P2
12121with the refined lattice parameters.
The band structure remains almost unchanged due to the
minimal lattice distortion (Fig. S18 in Supplemental
Material [43]). Therefore, the slight breaking of crystal
symmetry cannot account for the significant gap opening.Given the stable crystal structure and the negligible effects of
crystal symmetry breaking on the band structure, we rule out
the possibility that the gap opening in Ta
2Pd3Te5is induced
by a structural change resulting from phononic instability.
In contrast, the gap opening w ith crystal symmetry break-
ing can be well explained within the framework of EIs. Thehigh-temperature normal phase exhibits an almost zero-gapband structure with linear dis persions. The electron-hole
Coulomb interaction is weakly screened due to the quasi-
1D structure with a vanishing density of states at E
F.T h e
electronic state becomes unstable against exciton condensa-tion. Excitons are trapped to lattice sites and form a static
charge transfer from the Pd 4d=Te5pto Ta 5dorbital,
breaking the symmetry of the electronic state. This allows thehybridization between the valence and conduction bands,resulting in the opening of a many-body gap. Meanwhile, the
electronic symmetry breaking induces local lattice distortion
through electron-lattice coupling, causing a breaking ofcrystal symmetry. The small lattice distortion suggests a weakcoupling between electron and lattice degrees of freedom.
V. OUTLOOK
We reveal that Ta
2Pd3Te5exhibits an EI ground state
emerging from an almost zero-gap normal phase. As theVB top and CB bottom are located at the same momentum
point Γin the BZ (Fig. S4 in Supplemental Material [43],
the excitons carry zero momentum. The zero-momentumexcitons couple to the q?0phonon mode, resulting in
crystal symmetry breaking that does not change the period in
the lattice. It is well known that BCS-type exciton con-
densation occurs in a semimetal, while BEC-type excitoncondensation occurs in a semiconductor. Our results showthat the normal phase features an almost zero-gap band
structure, making Ta
2Pd3Te5a promising platform for
investigating many-body phenomena in the BCS-BECcrossover region. Because of the quasi-1D van der Waalsstructure, this material can be easily mechanically exfoliated
into large flakes with long straight edges along the 1D chains
[56]. The chemical potential can be conveniently tuned by
applying gate voltages to thin flakes, which is favorable forfurther studies of the EI state. Consistently, the firstprinci-
ples calculations with many-body perturbation theory pre-
dict an EI state in the Ta
2Pd3Te5monolayer [57].Furthermore, the abnormal band order indicates that
Ta2Pd3Te5is an unconventional material with a mismatch
between charge centers and atomic positions [58,59] ,l e a d i n g
to the emergence of quasi-1D edge states with typical
Luttinger liquid behavior within the excitonic gap [56].
VI. METHOD
A. Sample growth
Single crystals of Ta 2Pd3Te5were synthesized by the self-
flux method. Starting materials of Ta (powder, 99.999%),
Pd (bar, 99.9999%), and Te (lump, 99.9999%) weremixed in an Ar-filled glove box at a molar radio ofTa∶Pd∶Te?2∶4.5∶7.5. The mixture was placed in an
alumina crucible, which was then sealed in an evacuated
quartz tube. The tube was heated to 950°C over ten hours
and dwelt for two days. Then, the tube was slowly cooleddown to 800° Ca tar a t eo f 0.5°C=h. Finally, the extra flux
was removed by centrifuging at 800°C. After centrifuging,
the black and shiny single crystals of Ta
2Pd3Te5were
picked out from the remnants in the crucible.
B. ARPES experiments
Laser-based ARPES experiments were conducted at the
Institute of Physics, Chinese Academy of Sciences [60]. The
equilibrium ARPES data were collected with hν?6eV. In
nonequilibrium ARPES experiments, the samples werepumped by an ultrafast laser pulse ( hν?2.4eV) with a
pulse duration of 250 fs and a repetition rate of 800 kHz. An
ultraviolet probe laser pulse ( hν?7.2eV) subsequently
photoemitted electrons. The overall time and energy reso-lutions were set to 500 fs and 18 meV, respectively.
Synchrotron ARPES experiments were conducted at the
03U beam line [61] and the “Dreamline ”beam line at the
Shanghai Synchrotron Radiation Facility.
C. STM experiments
STM experiments were conducted in a low-temperature
ultrahigh-vacuum STM system, Unisoku USM-1300.Topographic images were acquired in the constant-currentmode with a tungsten tip. Before the measurements, STM tips
were heated by e-beam and calibrated on a clean Ag surface.
The scanning settings of all the topographies were under abias voltage of 100 mV and a setpoint of 100 pA unlessspecifically mentioned. Differential conductance spectra were
acquired by a standard lock-in technique at a reference
frequency of 973 Hz unless specifically mentioned.
D. TEM experiments
The specimens oriented with respect to the [100]
direction were thinned by the conventional mechanical
exfoliation method, while those oriented with respect to the
[001] direction were prepared by the conventional focused-ion-beam (Helios 600i) lift-out method. After that, theEVIDENCE FOR AN EXCITONIC INSULATOR STATE … PHYS. REV . X 14,011046 (2024)
011046-7specimens were transferred to a Cu grid for ED charac-
terization, which were collected using a TEM (JEOL
JEM-F200). The cryo-TEM holder (Gatan) with heatingcontroller was used to maintain the specimen temperatureat 100, 300, and 368 K. The diffraction patterns at each
temperature were collected using an operating voltage of
200 kV at a camera length of 400 mm.
E. X-ray diffraction experiments
A specimen of Ta
2Pd3Te5with dimensions of 0.017×
0.038×0.089mm3was used for the x-ray crystallographic
analysis on the Bruker D8 Venture with the Mo K αradiation
(λ?0.710 73 ?. The frames were integrated with the
Bruker SAINT software package using a narrow-frame
algorithm. The data were corrected for absorption effectsusing the MultiScan method (
SADABS ). Data collection, cell
refinement, and data reduction were performed using the
Bruker APEX 4program. The refinement was carried out
using SHELX programs within the Olex2-1.5-alpha software
package [62]. The crystal structure was successfully solved
using the intrinsic phasing method with SHELXT [63] and
refined with SHELXL [64]against the F2data, incorporating
anisotropic displacement parameters for all atoms.
F. DFT calculations
First-principles calculations were conducted within the
framework of DFT using the projector-augmented-wavemethod [65,66] , as implemented in Vienna ab initio
simulation package [67,68] . The PBE generalized-
gradient-approximation exchange-correlation functional [69]
was used. In the self-consistent process, 4×16×4k-point
sampling grids were used, and the cutoff energy for plane-
wave expansion was 500 eV. Since PBE band calculations
usually underestimate the band gap, we introduced the MBJexchange potential [70,71] to improve this underestimation.
The maximally localized Wannier functions were constructed
by using the
WANNIER 90package [72].
Note added in proof. A similar study in Ref. [73] also
provides evidence for an excitonic state in Ta 2Pd3Te5.
ACKNOWLEDGMENTS
We thank Xi Dai, Xinzheng Li, Hongming Weng,
Xuetao Zhu, and Peng Zhang for useful discussions.We thank Zhicheng Rao, Anqi Wang, Huan Wang,
Xuezhi Chen, Bingjie Chen, Xiaofan Shi, Xingchen
Guo, Zhe Zheng, Mingzhe Hu, Yao Meng, HongxiongLiu, Xiafan Xu, and Jin Ding for technical assistance. This
work was supported by the Ministry of Science and
Technology of China (Grants No. 2022YFA1403800,No. 2022YFA1402704, and No. 2022YFA1403400),the National Natural Science Foundation of
China (Grants No. U1832202, No. U22A6005,
No. U2032204, No. 12188101, No. 92065203,No. 12174430, No. 12274186, No. 11888101,
No. 12104491, No. 11774419, and No. 52272268),
the Chinese Academy of Sciences (GrantsNo. XDB33000000, No. XDB28000000 and No. GJTD-
2020-01), the Beijing Natural Science Foundation (Grant
No. JQ23022), the Beijing Nova Program (GrantNo. Z211100002121144), the New Cornerstone ScienceFoundation (Grant No. 23H010801236), the Innovation
Program for Quantum Science and Technology (Grant
No. 2021ZD0302700), the Shanghai Committee ofScience and Technology (Grant No. 23JC1403300), the
China Postdoctoral Science Foundation funded project
(Grant No. 2021M703461), the Shanghai MunicipalScience and Technology Major Project, the Synergetic
Extreme Condition User Facility, and the Centre for
Materials Genome. Q. M. Z. acknowledges the support fromUsers with Excellence Program of Hefei Science Centre and
High Magnetic Field Facility, CAS. S. Y . G. was supported by
the China Scholarship Council (Grant No. 202104910090)and the Sino Swiss Science and Technology Cooperation(Grant No. CN-EG-03-012021).
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