An exciton is an electron-hole pair bound by attractive Coulomb interaction. Short-lived excitons have been detected by a variety of experimental probes in numerous contexts. An excitonic insulator, a collective state of such excitons, has been more elusive. Here, thanks to Nernst measurements in pulsed magnetic fields, we show that in graphite there is a critical temperature (T = 9.2 K) and a critical magnetic field (B = 47 T) for Bose-Einstein condensation of excitons. At this critical field, hole and electron Landau sub-bands simultaneously cross the Fermi level and allow exciton formation. By quantifying the effective mass and the spatial separation of the excitons in the basal plane, we show that the degeneracy temperature of the excitonic fluid corresponds to this critical temperature. This identification would explain why the field-induced transition observed in graphite is not a universal feature of three-dimensional electron systems pushed beyond the quantum limit.
The in-plane resistivity, Hall resistivity and magnetization of graphite were investigated in pulsed magnetic fields applied along the \textit{c}-axis. The Hall resistivity approaches zero at around 53 T where the in-plane and out-of-plane resistivities steeply decrease. The differential magnetization also shows an anomaly at around this field with a similar amplitude compared to that of de Haas-van Alphen oscillations at lower fields. This transition field appears insensitive to disorder, but reduces with doping holes. These results suggest the realization of the quantum limit states above 53…
Strong magnetic field induces at least two phase transitions in graphite beyond the quantum limit where many-body effects are expected. We report on a study using a state-of-the-art non-destructive magnet allowing to attain 90.5 T at 1.4 K, which reveals a new field-induced phase and evidence that the insulating state destroyed at 75 T is an excitonic condensate of electron-hole pairs. By monitoring the angle dependence of in-plane and out-of-plane magnetoresistance, we distinguish between the role of cyclotron and Zeeman energies in driving various phase transitions. We find that, with the no…
Exciton condensation in a two-band Hubbard model on a square lattice is studied with variational Monte Carlo method. We show that the phase transition from an excitonic insulator to a band insulator is induced by increasing the interband Coulomb interaction. To examine the character of the exciton condensation, the exciton pair amplitudes both in $\bm{k}$-space and in real space are calculated. Using these quantities, we discuss the BCS-BEC crossover within the excitonic insulator phase.
The Bose condensation of 2D dipolar excitons in quantum wells is numerically studied by the diffusion Monte Carlo simulation method. The correlation, microscopic, thermodynamic, and spectral characteristics are calculated. It is shown that, in structures of coupled quantum wells, in which low-temperature features of exciton luminescence have presently been observed, dipolar excitons form a strongly correlated system. Their Bose condensation can experimentally be achieved much easily than for ideal or weakly correlated excitons.
The exciton-phonon coupling in highly oriented pyrolytic graphite is studied using resonant inelastic X-ray scattering (RIXS) spectroscopy. With ~ 70 meV energy resolution, multiple low energy excitations associated with coupling to phonons can be clearly resolved in RIXS spectra. Using resonance dependence and the closed form for RIXS cross-section without considering the intermediate state mixing of phonon modes, the dimensionless coupling constant g is determined to be 5 and 0.4, corresponding to the coupling strength of 0.42 eV +/- 40 meV and 0.21 eV +/- 30 meV, for zone center and boundar…
We study the orbital diamagnetic susceptibility in excitonic condensation phase using the meanfield approximation for a two-band model defined on a square lattice. We find that, in semiconductors, the excitonic condensation acquires a finite diamagnetic susceptibility due to spontaneous hybridization between the valence and the conduction bands, whereas in semimetals, the diamagnetic susceptibility in the normal phase is suppressed by the excitonic condensation. We also study the orbital diamagnetic and Pauli paramagnetic susceptibilities of Ta2NiSe5 using a two-dimensional three-band model an…
We study the many-body physics in thin film topological band insulator, where the inter-edge Coulomb interaction can lead to an exciton condensation transition. We investigate the universality class of the exciton condensation quantum critical point. With different chemical potentials and interactions, the exciton condensation can belong to z = 2 mean field, or 3d XY, or Yukawa-Higgs universality classes. The interplay between exciton condensate and the time-reversal symmetry breaking is also discussed. Predictions of our work can be tested experimentally by tuning the chemical potentials on b…
We report on small-cluster exact-diagonalization calculations which prove the formation of electron-hole pairs (excitons) as prerequisite for spontaneous interlayer phase coherence in bilayer systems described by the extended Falicov-Kimball model. Evaluating the anomalous Green's function and momentum distribution function of the pairs, and thereby analyzing the dependence of the exciton binding energy, condensation amplitude, and coherence length on the Coulomb interaction strength, we demonstrate a crossover between a BCS-like electron-hole pairing transition and a Bose-Einstein condensatio…
The extended version of our reply to Comment on ``Critical Velocities in Exciton Superfluidity'' by S. G. Tikhodeev (Phys. Rev. Lett., 84 (2000), 3502 or from http://prl.aps.org/) is presented here. The principal question is discussed: does the moving exciton-phonon packet contain the coherent `nucleus', or the exciton-phonon condensate?
The idea of exciton condensation in solids was introduced in 1960's with the analogy to superconductivity in mind. While exciton supercurrents have been realized only in artificial quantum-well structures so far, the application of the concept of excitonic condensation to bulk solids leads to a rich spectrum of thermodynamic phases with diverse physical properties. In this review we discuss recent developments in the theory of exciton condensation in systems described by Hubbard-type models. In particular, we focus on the connections to their various strong-coupling limits that have been studi…
We studied the possibility of exciton condensation in a strongly correlated bilayer extended Hubbard model using Determinant Quantum Monte Carlo. To model both the onsite repulsion U and the interlayer interaction V we introduced a novel update scheme extending the standard Sherman-Morrison update. We observe that the sign problem increases dramatically with the inclusion of the interlayer interaction V, which prohibits at this stage a unequivocal conclusion regarding the presence of exciton condensation. However, enhancement of the interlayer tunneling results suggest that the strongest excit…
The stability of the excitonic condensation at low temperature driven by a coupling of electrons to vibrational degrees of freedom in semimetal two-dimensional electronic system is discussed. In the framework of the unrestricted Hartree-Fock approximation, we derive a set of equations to determine both the excitonic condensate order parameter and lattice displacement self-consistently. By lowering temperature we find out a semimetal-insulator transition in the system if the coupling is large enough. The insulating state typifies an excitonic condensation accompanied by a finite lattice distort…
The microscopic quantum interference associated with excitonic condensation in Ta$_2$NiSe$_5$ is studied in the BCS-type mean-field approximation. We show that in ultrasonic attenuation the coherence peak appears just below the transition temperature $T_{\rm c}$ whereas in NMR spin-lattice relaxation the rate rapidly decreases below $T_{\rm c}$; these observations can offer a crucial experimental test for the validity of the excitonic condensation scenario in Ta$_2$NiSe$_5$. We also show that the excitonic condensation manifests itself in a jump of the heat capacity at $T_{\rm c}$ as well as i…
We consider a two-orbital Hubbard model with Hund coupling and crystal-field splitting and show that in the vicinity of the high-spin/low-spin transition, crystal-field quenches can induce an excitonic condensation at initial temperatures above the highest ordering temperature in equilibrium. This condensation is the effect of an increase in the spin entropy and an associated cooling of the effective electronic temperature. We identify a dynamical phase transition and show that such quenches can result in long-lived nonthermal excitonic condensates which have no analogue in the equilibrium pha…
Motivated by recent observation of magnetic field induced transition in LaCoO3 we study the effect of external field in systems close to instabilities towards spin-state ordering and exciton condensation. We show that, while in both cases the transition can be induced by an external field, temperature dependencies of the critical field have opposite slopes. Based on this result we argue that the experimental observations select the exciton condensation scenario. We show that such condensation is possible due to high mobility of the intermediate spin excitations. The estimated width of the corr…
We have succeeded in trapping indirect excitons in coupled quantum wells in a harmonic potential minimum via inhomogeneous applied stress and electric field. These excitons exhibit a strong Stark shift (over 60 meV), long lifetime (100 ns), and high diffusivity (1000 cm$^2$/s). This approach is very promising for obtaining the high exciton density needed for Bose condensation of excitons in two dimensions.
Extensive theoretical and experimental investigation has been conducted on fermion pair condensation and exciton condensation as distinct classes of Bose-Einstein-like condensation. In this work, the existence of a fermion-exciton condensate---a single quantum state in which character of both fermion pair and exciton condensates coexist---is established computationally in the low-particle-number ($N$) limit and theoretically in the large-$N$ thermodynamic limit. The trade-off between the fermion pair and excitonic character of the fermion-exciton condensate is shown to be elliptic in nature. T…
We address the lattice instability of 1T-TiSe2 in the framework of the exciton condensate phase. We show that, at low temperature, condensed excitons influence the lattice through electron-phonon interaction. It is found that at zero temperature, in the exciton condensate phase of 1T-TiSe2, this exciton condensate exerts a force on the lattice generating ionic displacements comparable in amplitude to what is measured in experiment. This is thus the first quantitative estimation of the amplitude of the periodic lattice distortion observed in 1T-TiSe2 as a consequence of the exciton condensate p…
The Bose-Einstein condensation of excitons into a single quantum state is known as exciton condensation. Exciton condensation, which potentially supports the frictionless flow of energy, has recently been realized in graphene bilayers and van der Waals heterostructures. Here we show that exciton condensates can be predicted from a combination of reduced density matrix theory and cumulant theory. We show that exciton condensation occurs if and only if there exists a large eigenvalue in the cumulant part of the particle-hole reduced density matrix. In the thermodynamic limit we show that the lar…
We estimate the condensation temperature for microcavity polaritons, allowing for their internal structure. We consider polaritons formed from localised excitons in a planar microcavity, using a generalised Dicke model. At low densities, we find a condensation temperature T_c \propto ρ, as expected for a gas of structureless polaritons. However, as T_c becomes of the order of the Rabi splitting, the structure of the polaritons becomes relevant, and the condensation temperature is that of a B.C.S.-like mean field theory. We also calculate the excitation spectrum, which is related to observable …
An extended, spinless Falicov-Kimball model in the presence of perpendicular magnetic field is investigated employing Hartree-Fock self-consistent mean-field theory in two dimensions. In the presence of an orbital field the hybridization-dependence of the excitonic average ${ Δ=<{{d_i}^\dagger} {f_i}>}$ is modified. The exciton responses in subtle different ways for different chosen values of the magnetic flux consistent with Hofstadter's well-known spectrum. The excitonic average is suppressed by the application of magnetic field. We further examine the effect of Coulomb interaction and $f$-e…
It is shown that the interconversion mechanism for the triplet excitons in Cu_2O suggested recently by G.M. Kavoulakis and A. Mysyrowicz in cond-mat/0001438 can be tested by the two-photon direct creation of the triplet excitons.
Exciton condensation indicating the spontaneous formation of electron-hole pair can cause the phase transition from a semimetal to an excitonic insulator by gap opening at the Fermi surface. While the idea of this excitonic insulator has been proposed for decades, current theoretical approaches can only provide qualitative descriptions, and a quantitative predicting tool is still missing. To shed insight on this problem, we developed an $ab~initio$ method based on the finite-temperature density functional theory and many-body perturbation theory to compute the exciton condensation critical beh…
We show that finite temperature variational cluster approximation (VCA) calculations on an extended Falicov-Kimball model can reproduce angle-resolved photoemission spectroscopy (ARPES) results on Ta2NiSe5 across a semiconductor-to-semiconductor structural phase transition at 325 K. We demonstrate that the characteristic temperature dependence of the flat-top valence band observed by ARPES is reproduced by the VCA calculation on the realistic model for an excitonic insulator only when the strong excitonic fluctuation is taken into account. The present calculations indicate that Ta2NiSe5 falls …
Recently strong evidence has been found in favor of a BCS-like condensation of excitons in 1\textit{T}-TiSe$_2$. Theoretical photoemission intensity maps have been generated by the spectral function calculated within the excitonic condensate phase model and set against experimental angle-resolved photoemission spectroscopy data. Here, the calculations in the framework of this model are presented in detail. They represent an extension of the original excitonic insulator phase model of Jérome \textit{et al.} [Phys. Rev. {\bf 158}, 462 (1967)] to three dimensional and anisotropic band dispersions…
Bose condensation has shaped our understanding of macroscopic quantum phenomena, having been realized in superconductors, atomic gases, and liquid helium. Excitons are bosons that have been predicted to condense into either a superfluid or an insulating electronic crystal. Using the recently developed momentum-resolved electron energy-loss spectroscopy (M-EELS), we study electronic collective modes in the transition metal dichalcogenide semimetal, 1T-TiSe$_2$. Near the phase transition temperature, T$_c$ = 190 K, the energy of the electronic mode falls to zero at nonzero momentum, indicating d…
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 …
Angle-resolved photoemission spectroscopy (ARPES) is a powerful probe of electron correlations in two-dimensional layered materials. In this Letter we demonstrate that ARPES can be used to probe the onset of exciton condensation in spatially-separated systems of electrons and holes created by gating techniques in either double-layer graphene or topological-insulator thin films.
Tunneling spectroscopy reveals evidence for interlayer electron-hole correlations in quantum Hall bilayer two-dimensional electron systems at layer separations near, but above, the transition to the incompressible exciton condensate at total Landau level filling $ν_T=1$. These correlations are manifested by a non-linear suppression of the Coulomb pseudogap which inhibits low energy interlayer tunneling in weakly-coupled bilayers. The pseudogap suppression is strongest at $ν_T=1$ and grows rapidly as the critical layer separation for exciton condensation is approached from above.
We use a combination of dynamical mean-field model calculations and LDA+U material specific calculations to investigate the low temperature phase transition in the compounds from the (Pr$_{1-y}$R$_y$)$_x$Ca$_{1-x}$CoO$_3$ (R=Nd, Sm, Eu, Gd, Tb, Y) family (PCCO). The transition, marked by a sharp peak in the specific heat, leads to an exponential increase of dc resistivity and a drop of the magnetic susceptibility, but no order parameter has been identified yet. We show that condensation of spin-triplet, atomic-size excitons provides a consistent explanation of the observed physics. In particul…
Coupled states of semiconductor quantum well (QW) excitons and photons in a two dimensional (2D) periodic lattice of microcavities are analyzed theoretically, revealing allowed bands and forbidden gaps in the energy spectrum of exciton polaritons. Photonic crystal exciton polaritons have spatially uniform excitonic constituent set by flat QWs, but exhibit periodic Bloch oscillations in the plane of QWs due to their photonic component. The envelope functions of photonic crystal exciton polaritons can be tailored via effective potential of a photonic crystal heterostructure, by using quasi-perio…
We investigate the nature of the magnetic excitations of a bilayer single-orbital Hubbard model in the intermediate-coupling regime. This model exhibits a quantum phase transition (QPT) between a paramagnetic (PM) and an insulating antiferromagnetic (AFM) phase at a critical value of the coupling strength. By using the random phase approximation, we show that the QPT is continuous when the PM state is a band insulator and that the corresponding quantum critical point (QCP) arises from the condensation of preformed excitons. These low-energy excitons reemerge on the other side of the QCP as the…
We use fermionic path integral quantum Monte Carlo to study the effects of fermion flavor on the physical properties of dipolar exciton condensates in double layer systems. We find that by including spin in the system weakens the effective interlayer interaction strength, yet this has very little effect on the Kosterlitz-Thouless transition temperature. We further find that, to obtain the correct description of screening, it is necessary to account for correlation in both the interlayer and intralayer interactions. We show that while the excitonic binding cannot completely surpress screening b…
We show that an interlayer exciton condensate doped into a strongly correlated Mott insulator exhibits a remarkable enhancement of the bandwidth of the magnetic excitations (triplons). This triplon is visible in the dynamical magnetic susceptibility and can be measured using resonant inelastic X-ray scattering. The bandwidth of the triplon scales with the exciton superfluid density, but only in the limit of strong correlations. As such the triplon bandwidth acts as a probe of exciton-spin interactions in the condensate.
We study the excitonic insulating (EI) phase in the two-band Hubbard models on the Penrose tiling. Performing the real-space mean-field calculations systematically, we obtain the ground state phase diagrams for the vertex and center models. We find that, in some regimes, the stable EI phase is induced by small interband interactions. We argue that this originates from the electron-hole pairing for the completely or nearly degenerate states, which are characteristic of the Penrose tiling. We also study spatial distribution of the order parameter, mapping it to the perpendicular space.
That excitons in solids might condense into a phase-coherent ground state was proposed about 40 years ago, and has been attracting experimental and theoretical attention ever since. Although experimental confirmation has been hard to come by, the concepts released by this phenomenon have been widely influential. This tutorial review discusses general aspects of the theory of exciton and polariton condensates, focussing on the reasons for coherence in the ground state wavefunction, the BCS to Bose crossover(s) for excitons and for polaritons, and the relationship of the coherent condensates to …
Graphite under high magnetic field exhibits consecutive metal-insulator (MI) transitions as well as re-entrant insulator-metal (IM) transition in the quasi-quantum limit at low temperature. In this paper, we identify the low-$T$ insulating phases as excitonic insulators with spin nematic orderings. We first point out that graphite under the relevant field regime is in the charge neutrality region, where electron and hole densities compensate each other. Based on this observation, we introduce interacting electron models with electron pocket(s) and hole pocket(s) and enumerate possible umklapp …
We study the electron-hole pair (or excitonic) condensation in the extended Falicov-Kimball model at finite temperatures based on the cluster mean-field-theory approach, where we make the grand canonical exact-diagonalization analysis of small clusters using the sine-square deformation function. We thus calculate the ground-state and finite-temperature phase diagrams of the model, as well as its optical conductivity and single-particle spectra, thereby clarifying how the preformed pair states appear in the strong-coupling regime of excitonic insulators. We compare our results with experiment o…
We study by a consistent mean-field scheme the role on the single- and two-particle properties of a local electron-electron repulsion in the Bernevig, Hughes and Zhang model of a quantum spin Hall insulator. We find that the interaction fosters the intrusion between the topological and non-topological insulators of a new insulating and magnetoelectric phase that breaks spontaneously inversion and time reversal symmetries, but not their product. The approach to this phase from both topological and non-topological sides is signalled by the softening of two exciton branches, i.e., whose binding e…
At a large displacement field, in rhomboedral and Bernal-stacked graphene a normal paramagnetic state transitions to a correlated state. Recent experiments showed that such systems have several phase transitions as a function of the carrier density. The phase adjacent to a paramagnetic state has anomalously high resistance and reduced degeneracy of the Fermi sea. We show that both phenomena can be explained through a concept of partial intervalley exciton condensation: a fraction of particles condenses into excitons, and another forms an intervalley coherent Fermi liquid. The exciton part of t…
Fractionalized phases are studied in a low energy theory of exciton bose condensate in a multi-band insulator. It is shown that U(1) gauge theory with either fractionalized boson or fermion can emerge out of a single model depending on the coupling constants. Both the statistics and spin of the fractionalized particles are dynamically determined, satisfying the spin-statistics theorem in the continuum limit. We present two mutually consistent descriptions for the fractionalization. In the first approach, it is shown that fractionalized degree of freedom emerges from reduced phase space constra…
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 …
An experiment is proposed, on the coherent quantum dynamics of a semiconductor microcavity containing quantum dots. Modeling the experiment using a generalized Dicke model, we show that a tailored excitation pulse can create an energy-dependent population of excitons, which subsequently evolves to a quantum condensate of excitons and photons. The population is created by a generalization of adiabatic rapid passage, and then condenses due to a dynamical analog of the BCS instability.
We investigate magnetic excitations in iridium insulators with pentavalent Ir$^{5+}$ ($5d^4$) ions with strong spin-orbit coupling. We obtain a microscopic model based on the local Ir$^{5+}$ multiplets involving $J=0$ (singlet), $J=1$ (triplet), and $J=2$ (quintet) spin-orbital states. We get effective interactions between these multiplets on square and face-centered-cubic (fcc) structures of magnetic ions in the layered-perovskites and the double-perovkites, in particular Ba$_2$YIrO$_6$. Further, we derive an effective spin-orbital Hamiltonian in terms of bond bosons and explore possible inst…
We show that the coupling to vibrational degrees of freedom can drive a semimetal excitonic-insulator quantum phase transition in an one-dimensional two-band f-c electron system at zero temperature. The insulating state typifies an excitonic condensate accompanied by a finite lattice distortion. Using the projector-based renormalization method we analyze the ground-state and spectral properties of the interacting electron-phonon model at half-filling. In particular we calculate the momentum dependence of the excitonic order parameter function and determine the finite critical interaction stren…
The formation of intra-layer and inter-layer exciton condensates in a model of a double monolayer Weyl semi-metal is studied in the strong coupling limit using AdS/CFT duality. We find a rich phase diagram which includes phase transitions between inter-layer and intra-layer condensates as the charge densities and the separation of the layers are varied. The tendency to inter-layer condensation is strongest when the charge densities are balanced so that the weak coupling electron and hole Fermi surfaces would be nested. For systems with multiple species of massless Fermions, we find a novel pha…
The condensation of electron-hole (e-h) pairs is studied at zero temperature and in the presence of a weak spin-orbit coupling (SOC) in the inversion-layer quantum wells. Under realistic conditions, a perturbative SOC can have observable effects in the order parameter of the experimentally long-searched-for excitonic condensate. Firstly, the fermion exchange symmetry is absent for the e-h pairs indicating a counterexample to the known classification schemes of fermion pairing. With the lack of fermion exchange, the condensate spin has no definite parity. Additionally, the excitonic SOC breaks …
The Bose-Einstein condensation of excitons continues to garner immense attention as a prototypical example for observing emergent properties from many-body quantum effects. In particular, Titanium Diselenide (TiSe$_2$) is a promising candidate for realizing exciton condensation and was experimentally observed only very recently. Surprisingly, the condensate was experimentally characterized by a soft plasmon mode that only exists near the transition temperature, $T_c$, of the charge density wave (CDW). Here, we characterize and analyze the experimental spectra using linear-response time-depende…
The competition of interactions implies the compensation of standard mechanisms which leads to the emergence of exotic phases between conventional phases. The extended Hubbard model (EHM) is a fundamental example for the competition of the local Hubbard interaction and the nearest-neighbor density-density interaction, which at half-filling and in one dimension leads to a bond order wave (BOW) between a charge density wave (CDW) and a quasi-long-range order Mott insulator (MI). We study the full momentum-resolved excitation spectrum of the one dimensional EHM in the CDW phase and clarify the re…
Slave rotor mean field (SRMF) theory is employed to study exciton formation in the extended Falicov-Kimball Model (EFKM). In this theory, charge and spin (or orbital) degrees are treated as independent degrees of freedom, coupled by a constraint. Using this formalism in single as well as cluster extension, we capture the effective many body scales beyond conventional mean-field theory. While the formation of exciton is favored by the interband hybridization $V$, it is strongly influenced by the on-site Coulomb interaction $U$. Beyond a critical hybridization, there is a condensation of exciton…
We studied the possibility of exciton condensation in Mott insulating bilayers. In these strongly correlated systems an exciton is the bound state of a double occupied and empty site. In the strong coupling limit the exciton acts as a hard-core boson. Its physics are captured by the exciton t-J model, containing an effective XXZ model describing the exciton dynamics only. Using numerical simulations and analytical mean field theory we constructed the ground state phase diagram. Three homogeneous phases can be distinguished: the antiferromagnet, the exciton checkerboard crystal and the exciton …
