Coulomb attraction between electrons and holes in a narrow-gap semiconductor or a semimetal is predicted to lead to an elusive phase of matter dubbed 'excitonic insulator'. However, direct observation of such electronic instability remains extremely rare. Here, we report the observation of incipient divergence in the static excitonic susceptibility of the candidate material Ta2NiSe5 using Raman spectroscopy. Critical fluctuations of the excitonic order parameter give rise to quasi-elastic scattering of B2g symmetry, whose intensity grows inversely with temperature toward the Weiss temperature of Tw ~241 K, which is arrested by a structural phase transition driven by an acoustic phonon of the same symmetry at Tc =325 K. Concurrently, a B2g optical phonon becomes heavily damped to the extent that its trace is almost invisible around Tc, which manifests a strong electron-phonon coupling that has obscured the identification of the low-temperature phase as an excitonic insulator for more than a decade. Our result unambiguously reveals the electronic origin of the phase transition.
Using linear response theory with the dynamical mean-field approximation we investigate the particle-hole instabilities of the two-band Hubbard model in the vicinity of the spin-state transition. Besides the previously reported high-spin--low-spin order we find an instability towards triplet excitonic condensate. We discuss the strong and weak coupling limits of the model, in particular, a connection to the spinful hard-core bosons with a nearest-neighbor interaction. Possible realization in LaCoO3 at intermediate temperatures is briefly discussed.
The origin of the second order phase transition at 328K in Ta$_2$NiSe$_5$, a prominent candidate for direct gap excitonic insulator, remains under fervent debate. The driving force for the transition can be revealed by identification of the soft mode's origin that may be deducted from polarization resolved Raman scattering experiments. Such studies were recently reported in [arXiv:2007.07344 (2020)], [arXiv:2102.07912 (2021)], [arXiv:2007.01723 (2020)] and [arXiv:2007.08212 (2020)]. In this Comment, it is shown that the parameters derived in a recent arXiv by Kwangrae Kim et. al. [arXiv:2007.0…
We report the pressure-dependent optical reflectivity spectra of a strongly correlated insulator, samarium monosulfide (SmS), in the far- and middle-infrared regions to investigate the origin of the pressure-induced phase transition from the black phase to the golden phase. The energy gap becomes narrow with increasing pressure in the black phase. A valence transition from Sm2+ in the black phase to mainly Sm3+ in the golden phase accompanied by spectral change from insulator to metal were observed at the transition pressure of 0.65 GPa. The black-to-golden phase transition occurs when the ene…
Recent advances in the study of nodal Weyl fermions (WFs), quasi-relativistic massless particles, constitute a novel realm of quantum many-body phenomena. The Coulomb interaction in such systems, having a zero density of states at the Fermi level, is of particular interest, since in contrast to conventional correlated metals, its long-ranged component is unscreened. Here, through nuclear-magnetic-resonance (NMR) measurements, we unveil the exotic spin correlations of two-dimensional WFs in an organic material, causing a divergent increase of the Korringa ratio by a factor of 1000 upon cooling,…
The electron-electron Coulomb interaction in Dirac-Weyl semimetals harbours a novel paradigm of correlation effects that hybridizes diverse realms of solid-state physics with their relativistic counterpart. Driving spontaneous mass acquisition, the excitonic condensate of strongly-interacting massless Dirac fermions is one such example whose exact nature remains debated. Here, by focussing on the two-dimensional tilted Dirac cones in the organic salt $α$-(BEDT-TTF)$_2$I$_3$, we show that the excitonic instability is controlled by a small chemicalpotential shift and an in-plane magnetic field. …
We use a functional renormalization group (fRG) approach to investigate potential interaction-induced instabilities in a two-dimensional model for the Dirac nodal-line materials ZrSiS and ZrSiSe employing model parameters derived from {\it ab initio} calculations. Our results confirm that the excitonic instability recently found in random-phase approximation for ZrSiS is indeed the leading instability. In the simplest modeling, spin- and charge-excitonic states are degenerate. Beyond this, we show that the fRG analysis produces an energy scale for the onset of the instability in good agreement…
Electron correlation effects are studied in ZrSiS using a combination of first-principles and model approaches. We show that basic electronic properties of ZrSiS can be described within a two-dimensional lattice model of two nested square lattices. High degree of electron-hole symmetry characteristic for ZrSiS is one of the key features of this model. Having determined model parameters from first-principles calculations, we then explicitly take electron-electron interactions into account and show that at moderately low temperatures ZrSiS exhibits excitonic instability, leading to the formation…
We investigate the excitonic instability in the theory of Dirac fermions in graphene with long-range Coulomb interaction. We analyze the electron-hole vertex relevant for exciton condensation in the ladder approximation, showing that it blows up at a critical value of the interaction strength α= e^2/4πv_F sensitive to further many-body corrections. Under static screening of the interaction, we find that taking into account electron self-energy corrections increases the critical coupling to α_c \approx 2.09, for a number N = 4 of two-component Dirac fermions. We show that the dynamical screenin…
We analyze the Coulomb interacting problem in undoped graphene layers by using an excitonic variational ansatz. By minimizing the energy, we derive a gap equation which reproduces and extends known results. We show that a full treatment of the exchange term, which includes the renormalization of the Fermi velocity, tends to suppress the phase transition by increasing the critical coupling at which the excitonic instability takes place.
By a combination of Hartree-Fock simulations, exact diagonalization, and perturbative calculations, we investigate the ground-state properties of disorder-free circular quantum dots formed in a graphene monolayer. Taking the reference chemical potential at the Dirac point, we study N \leq 15 interacting particles, where the fine structure constant α parametrizes the Coulomb interaction. We explore three different theoretical concepts: (i) Sucher's positive projection ("no-pair") approach, (ii) a more general Hamiltonian conserving both N and the number of additional electron-hole pairs, and (i…
We study the different phases in the Quantum Electrodynamics of 3D Dirac semimetals depending on the number $N$ of Dirac fermions, using renormalization group methods and the self-consistent resolution of the Schwinger-Dyson equation. We find that, for $N < 4$, a phase with dynamical generation of mass prevails at sufficiently strong coupling, sharing the same physics of the excitonic instability in 2D Dirac semimetals. For $N \geq 4$, we show that the phase diagram has instead a line of critical points characterized by the suppression of the quasiparticle weight at low energies, making the sy…
We study the electronic phase diagram of the excitonic insulator candidates Ta$_2$Ni(Se$_{1-x}$S$_x$)$_5$ [x=0, ... ,1] using Raman spectroscopy. Critical excitonic fluctuations are observed, that diminish with $x$ and ultimately shift to high energies, characteristic of a quantum phase transition. Nonetheless, a symmetry-breaking transition at finite temperatures is detected for all $x$, exposing a cooperating lattice instability that takes over for large $x$. Our study reveals a failed excitonic quantum phase transition, masked by a preemptive structural order.
We study the excitonic phase and low-energy excitation spectra of perovskite cobalt oxides. Constructing the five-orbital Hubbard model defined on the three-dimensional cubic lattice for the $3d$ bands of Pr$_{0.5}$Ca$_{0.5}$CoO$_3$, we calculate the excitonic susceptibility in the normal state in the random-phase approximation (RPA) to show the presence of the instability toward excitonic condensation. Based on the excitonic ground state with a magnetic multipole obtained in the mean-field approximation, we calculate the dynamical susceptibility of the excitonic phase in the RPA and find that…
Based on the SO(2)-invariant slave-boson scheme, the static charge, orbital, and excitonic susceptibilities in the extended Falicov-Kimball model are calculated. Analyzing the phase without long-range order we find instabilities towards charge order, orbital order, and the excitonic insulator (EI) phase. The instability towards the EI is in agreement with the saddle-point phase diagram. We also evaluate the dynamic excitonic susceptibility, which allows the investigation of uncondensed excitons. We find qualitatively different features of the exciton dispersion at the semimetal-EI and at the s…
Three-dimensional gapless semiconductors with quadratic band touching, such as HgTe, $α$-Sn, or Pr$_2$Ir$_2$O$_7$ are believed to display a non-Fermi-liquid ground state due to long-range electron-electron interaction. We argue that this state is inherently unstable towards spontaneous formation of a (topological) excitonic insulator. The instability can be parameterized by a critical fermion number $N_c$. For $N < N_c$ the rotational symmetry is spontaneously broken, the system develops a gap in the spectrum, and features a finite nematic order parameter. To leading order in the 1/N expansion…
Excitonic insulators are insulating states formed by the coherent condensation of electron and hole pairs into BCS-like states. Isotropic spatial wave functions are commonly considered for excitonic condensates since the attractive interaction among the electrons and the holes in semiconductors usually leads to $s$-wave excitons. Here, we propose a new type of excitonic insulator that exhibits order parameter with $p+ip$ symmetry and is characterized by a chiral Chern number $C_\textrm{c}=1/2$. This state displays the parity anomaly, which results in two novel topological properties: fractiona…
We consider the excitonic insulator state (often associated with electronic ferroelectricity), which arises on the phase diagram of an extended spinless Falicov--Kimball model (FKM) at half-filling. Within the Hartree--Fock approach, we calculate the spectrum of low-energy collective excitations in this state up to second order in the narrow-band hopping and/or hybridisation. This allows to probe the mean-field stability of the excitonic insulator. The latter is found to be unstable when the case of the pure FKM (no hybridisation with a fully localised band) is approached. The instability is d…
The influence of phonons on the formation of the excitonic insulator has hardly been analyzed so far. Recent experiments on $\rm Ta_2NiSe_5$, 1$T$-$\rm TiSe_2$, and $\rm TmSe_{0.45}Te_{0.55}$, being candidates for realizing the excitonic-insulator state, suggest, however, that the underlying lattice plays a significant role. Employing the Kadanoff-Baym approach we address this issue theoretically. We show that owing to the electron-phonon coupling a static lattice distortion may arise at the excitonic instability. Most importantly such a distortion will destroy the acoustic phase mode being pr…
Magnetic frustration can lead to peculiar magnetic orderings that break a discrete symmetry of the lattice in addition to the fundamental magnetic symmetries (i.e., spin rotation invariance and time-reversal symmetry). In this work, we focus on frustrated quantum magnets and study the nature of the quantum phase transition between a paramagnet and a magnetically ordered state with broken threefold ($Z_3$) crystal rotation symmetry. We predict the transition to happen in two stages, giving rise to an intermediate nematic phase in which rotation symmetry is broken but the system remains magnetic…
Persistence of charge ordering instability to Coulomb engineering in the excitonic insulator candidate TiSe$_2$
University of St Andrews（圣安德鲁斯大学）；Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）；Universität Hamburg（汉堡大学）；STFC Central Laser Facility, Research Complex at Harwell（STFC 哈韦尔研究综合体中央激光设施）；Bremen Center for Computational Materials Science（不来梅计算材料科学中心）
The density-matrix-renormalization-group (DMRG) method and the Hartree-Fock (HF) approximation with the charge-density-wave (CDW) instability are used to study a formation and condensation of excitonic bound states in the generalized Falicov-Kimball model. In particular, we examine effects of various factors, like the $f$-electron hopping, the local and nonlocal hybridization, as well as the increasing dimension of the system on the excitonic momentum distribution $N(q)$ and especially on the number of zero momentum excitons $N_0=N(q=0)$ in the condensate. It is found that the negative values …
Fingerprints of Excitonic Collective Modes in the Two-Dimensional Electron Gas
Friedrich-Schiller-Universät Jena（耶拿弗里德里希·席勒大学）；Ruhr University Bochum（波鸿鲁尔大学）；École Polytechnique, Institut Polytechnique de Paris（巴黎综合理工学院，巴黎理工学院）；Synchrotron SOLEIL（SOLEIL同步辐射中心）
The BCS to Bose-Einstein condensation (BEC) crossover of electron-hole (e-h) pairs in optically excited semiconductors is studied using the two-band Hubbard model with both repulsive and attractive interactions. Applying the self-consistent t-matrix approximation combined with a local approximation, we examine the properties of a normal phase and an excitonic instability. The transition temperature from the normal phase to an e-h pair condensed one is studied to clarify the crossover from an e-h BCS-like state to an excitonic Bose-Einstein condensation, which takes place on increasing the e-h …
The excitonic insulator Ta$_2$NiSe$_5$ experiences a first-order structural transition under pressure from rippled to flat layer-structure at Ps = 3 GPa, which drives the system from an almost zero-gap semiconductor to a semimetal. The pressure-induced semimetal, with lowering temperature, experiences a transition to another semimetal with a partial-gap of 0.1-0.2 eV, accompanied with a monoclinic distortion analogous to that occurs at the excitonic transition below Ps. We argue that the partial-gap originates primarily from a symmetry-allowed hybridization of Ta-conduction and Ni-valence band…
An excitonic magnet hosts a condensate of spin-triplet excitons composed of conduction-band electrons and valence-band holes, and may be described by the two-orbital Hubbard model. When the Hamiltonian has the nearest-neighbor interorbital hopping integrals with $d$-wave symmetry and the number of electrons is slightly away from half filling, the $\boldsymbol{k}$-space spin texture appears in the excitonic phase with a broken time-reversal symmetry. We then show that, applying electric field to this doped excitonic magnet along a particular direction, a pure spin current emerges along its orth…
The theory of doped excitonic insulators is reinvestigated in light of recent experiments on hexaborides. For the appropriate valley-degenerate X_3,X_3' band structure, ``intra-valley'' condensation is energetically favored. Ferromagnetism occurs upon doping due to the quenching of kinetic energy at the otherwise direct first-order excitonic insulator-metal transition. The phase diagram includes states of spatially inhomogeneous density and magnetization at low temperatures.
We present a comprehensive study of a one-dimensional two-orbital model at and below quarter-filling that realizes a number of unconventional phases. In particular, we find an excitonic density wave in which excitons quasi-condense with finite center of mass momentum and an order parameter that changes phase with wave-vector $Q$. In this phase, excitons behave as hard-core bosons without charge order. In addition, excitons can pair to form bi-excitons in a state that is close to a charge density-wave instability. When pairing dominates over the inter-orbital repulsion, we encounter a regime in…
We consider a spinless extended Falicov--Kimball model at half-filling, for the case of opposite-parity bands. Within the Hartree--Fock approach, we calculate the excitation energies in the chiral phase, which is a possible mean-field solution in the presence of a hybridisation. It is shown that the chiral phase is unstable. We then briefly review the accumulated results on stability and degeneracies of the excitonic insulator phase. Based on these, we conclude that the presence of both hybridisation and narrow-band hopping is required for electronic ferroelectricity.
The excitonic insulator (EI) state is a strongly correlated many-body ground state, arising from an instability in the band structure towards exciton formation. We show that the flat valence and conduction bands of a semiconducting diatomic Kagome lattice, as exemplified in a superatomic graphene lattice, can possibly conspire to enable an interesting triplet EI state, based on density functional theory (DFT) calculations combined with many-body GW and Bethe-Salpeter Equation(BSE). Our results indicate that massive carriers in flat bands with highly localized electron and hole wavefunctions si…
We consider a dynamical phase transition induced by a short optical pulse in a system prone to thermodynamical instability. We address the case of pumping to excitons whose density contributes directly to the order parameter. To describe both thermodynamic and dynamic effects on equal footing, we adopt a view of the excitonic insulator for the phase transition and suggest a formation of the Bose condensate for the pumped excitons. The work is motivated by experiments in donor-acceptor organic compounds with a neutral-ionic phase transition coupled to the spontaneous lattice dimerization and to…
We explore the spontaneous formation of an excitonic insulator state at the semimetal-semiconductor transition of mixed-valence materials in the framework of the spinless Falicov-Kimball model with direct $f$-$f$ electron hopping. Adapting the projector-based renormalization method, we obtain a set of renormalization differential equations for the extended Falicov-Kimball model parameters and finally derive analytical expressions for the order parameter, as well as for the renormalized $c$- and $f$-electron dispersions, momentum distributions, and wave-vector resolved single-particle spectral …
Using quantum Monte Carlo simulations we have mapped out the zero temperature phase diagram of a symmetric electron-hole bilayer with twofold valley degeneracy, as function of the interlayer distance $d$ and in-layer density $n$. We find that the effect of the valley degeneracy is to shrink the region of stability of the excitonic condensate, in favor of quadriexcitons at small $d$ and of the four-component plasma at large $d$, with minor effects on the value of the excitonic condensate fraction. The enclosure of the condensate in a density window possibly explains why anomalous tunnelling con…
The excitonic insulator is an intriguing electronic phase of quasi-condensed excitons. A prominent candidate is the small bandgap semiconductor Ta2NiSe5, in which excitons are believed to undergo a BEC-like transition. But experimental evidence for the existence of a coherent condensate in this material is still missing. A direct fingerprint of such a state would be the observation of its collective modes, which are equivalent to the Higgs- and Goldstone-modes in superconductors. Here we report evidence for the existence of a coherent amplitude response in the excitonic insulator phase of Ta2N…
While various excitonic insulators have been studied in the literature, due to the perceived too-small spin splitting, spin-triplet excitonic insulator is rare. In two-dimensional systems such as a graphone, however, it is possible, as revealed by first-principles calculations coupled with Bethe-Salpeter equation. The critical temperature, given by an effective Hamiltonian, is 11.5 K. While detecting excitonic insulators is still a daunting challenge, the condensation of triplet excitons will result in spin superfluidity, which can be directly measured by a transport experiment. Nonlocal diele…
Excitons, quasiparticles of electrons and holes bound by Coulombic attraction, are created transiently by light and play an important role in optoelectronics, photovoltaics and photosynthesis. While they are also predicted to form spontaneously in a small gap semiconductor or a semimetal, leading to a Bose-Einstein condensate at low temperature, their material realization has been elusive without any direct evidence. Here we detect the direct photoemission signal from spontaneously formed excitons in a debated excitonic insulator candidate Ta2NiSe5. Our symmetry-selective angle-resolved photoe…
Transition metal dichalcogenides (TMDs), whether in bulk or in monolayer form, exhibit a rich variety of charge-density-wave (CDW) phases and stronger periodic lattice distortions. While the actual role of nesting has been under debate, it is well understood that the microscopic interaction responsible for the CDWs is the electron-phonon coupling. The case of TiSe$_2$ is however unique in this family in that the normal state above the critical temperature $T_\mathrm{CDW}$ is characterized by a small quasiparticle bandgap as measured by ARPES, so that no nesting-derived enhancement of the susce…
In Mott insulators with the t^4_{2g} electronic configuration such as of Re^{3+}, Ru^{4+}, Os^{4+}, and Ir^{5+} ions, spin-orbit coupling dictates a Van Vleck-type nonmagnetic ground state with angular momentum J=0, and the magnetic response is governed by gapped singlet-triplet excitations. We derive the exchange interactions between these excitons and study their collective behavior on different lattices. In perovskites, a conventional Bose condensation of excitons into a magnetic state is found, while an unexpected one-dimensional behavior supporting spin-liquid states emerges in honeycomb …
Femtosecond time-resolved mid-infrared reflectivity is used to investigate the electron and phonon dynamics occurring at the direct band gap of the excitonic insulator Ta$_2$NiSe$_5$ below the critical temperature of its structural phase transition. We find that the phonon dynamics show a strong coupling to the excitation of free carriers at the Γ point of the Brillouin zone. The optical response saturates at a critical excitation fluence $F_C = 0.30~\pm~0.08$~mJ/cm$^2$ due to optical absorption saturation. This limits the optical excitation density in Ta$_2$NiSe$_5$ so that the system cannot …
Direct-gap materials hold promises for excitonic insulator. In contrast to indirect-gap materials, here the difficulty to distinguish from a Peierls charge density wave is circumvented. However, direct-gap materials still suffer from the divergence of polarizability when the band gap approaches zero, leading to diminishing exciton binding energy. We propose that one can decouple the exciton binding energy from the band gap in materials where band-edge states have the same parity. First-principles calculations of two-dimensional GaAs and experimentally mechanically exfoliated single-layer TiS 3…
Using the mean-field approximation, we study the $k$-space spin textures and local spin currents emerged in the spin-triplet excitonic insulator states of the two-band Hubbard model defined on the square and triangular lattices. We assume a noninteracting band structure with a direct band gap and introduce $s$-, $p$-, $d$-, and $f$-type cross-hopping integrals, i.e., the hopping of electrons between different orbitals on adjacent sites with four different symmetries. First, we calculate the ground-state phase diagrams in the parameter space of the band filling and interaction strengths, whereb…
Using a combination of ultraviolet-vacuum ultraviolet reflectivity and spectroscopic ellipsometry, we observe a resonant exciton at an unusually high energy of 6.3eV in epitaxial graphene. Surprisingly, the resonant exciton occurs at room temperature and for a very large number of graphene layers $N$$\approx$75, thus suggesting a poor screening in graphene. The optical conductivity ($σ_1$) of resonant exciton scales linearly with number of graphene layer (up to \emph{at least} 8 layers) implying quantum character of electrons in graphene. Furthermore, a prominent excitation at 5.4eV, which is …
We consider the single-particle density of states (DOS) in the strongly correlated double layer (DL) system, without applied external fields. We demonstrate an unusual collapse effect in the spectrum of the normal single-particle spectral function at the particular high-symmetry point corresponding to the specific bunching-point solution of the chemical potential in the Frenkel channel. We show that at the low-temperature limit the anomalous spectral function obeys a concave like structure, which is directly related to the interlayer pair formation and condensation. We calculate the normal DOS…
Recently, we employed electronic polarization-resolved Raman spectroscopy to reveal the strongly correlated excitonic insulator (EI) nature of Ta2NiSe5, Volkov et al. [arXiv:2007.07344], and also showed that for Ta$_2$Ni(Se$_{1-x}$S$_x$)$_5$ alloys the critical excitonic fluctuations diminish with sulfur concentration x exposing a cooperating lattice instability that takes over for large x, Volkov et al. [arXiv:2104.07032]. Here we focus on the lattice dynamics of this EI family. We identify all Raman-active optical phonons of fully symmetric and ac-quadrupole-like symmetries and study their e…
Electron-hole mixing-induced fine structure in alkaline earth hexaborides leads to lower energy (temperature) scales, and thus stronger tendency toward an excitonic instability, than in their doped counterparts (viz. Ca(1-x)La(x)B(6), x=0.005), which are high Curie temperature, small moment ferromagnets. Comparison of Fermi surfaces and spectral distributions with de Haas - van Alphen (dHvA), optical, transport, and tunneling data indicates that SrB6 remains a fermionic semimetal down to (at least) 5 K, rather than forming an excitonic condensate. For the doped system the Curie temperature is …
The excitonic insulator is an electronically-driven phase of matter that emerges upon the spontaneous formation and Bose condensation of excitons. Detecting this exotic order in candidate materials is a subject of paramount importance, as the size of the excitonic gap in the band structure establishes the potential of this collective state for superfluid energy transport. However, the identification of this phase in real solids is hindered by the coexistence of a structural order parameter with the same symmetry as the excitonic order. Only a few materials are currently believed to host a domi…
We investigate the controversial case of charge-density-wave (CDW) order in single layer 1T-TiSe$_2$ by employing the density functional perturbation theory with on-site Hubbard interactions. The results emphasize the crucial role of electron correlations via Hubbard corrections in order to capture the accurate electronic structure, low- and high-temperature limits of the CDW phonon mode, and temperature-charge phase diagram. We show, in close agreement with the experiments, that total phase diagram consists of both commensurate and incommensurate CDW regions, where the latter coincide with th…
We propose a mechanism of the spin Seebeck effect attributed to excitonic condensation in a nonmagnetic insulator. We analyze a half-filled two-orbital Hubbard model with a crystalline field splitting in the strong coupling limit. In this model, the competition between the crystalline field and electron correlations brings about an excitonic insulating state, where the two orbitals are spontaneously hybridized. Using the generalized spin-wave theory and Boltzmann transport equation, we find that a spin current generated by a thermal gradient is observed in the excitonic insulating state withou…
