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. The possibility that the properties of fermion-exciton condensates could be a hybrid of the properties of fermion pair condensates and exciton condensates is discussed, and future experimental and computational exploration of this new class of condensate, which may potentially be realizable in a bilayer of superconductors, is anticipated.
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…
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.
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…
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.
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 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…
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 …
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.
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…
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 present an algebraic framework for identifying the order parameter and the possible phases of quantum systems that is based on identifying the local dimension $N$ of the quantum operators and using the SU(N) group representing the generators of generalized spin-particle mappings. We illustrate this for $N$=3 by presenting for any spatial dimension the exact solution of the bilinear-biquadratic $S$=1 quantum Heisenberg model at a high symmetry point. Through this solution we rigorously show that itinerant ferromagnetism and Bose-Einstein condensation may coexist.
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…
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.
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 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 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…
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 …
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.…
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…
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…
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…
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…
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.
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 …
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 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 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 …
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 …
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…
The formation and condensation of excitonic bound states of conduction-band electrons and valence-band holes surely belongs to one of the most exciting ideas of contemporary solid state physics. In this short review we present the latest progress in this field reached by the density-matrix-renormalization-group (DMRG) calculations within various extensions of the Falicov-Kimball model. Particular attention is paid to a description of crucial mechanisms (interactions) that affect the stability of the excitonic phase, and namely: (i) the interband $d$-$f$ Coulomb interaction, (ii) the $f$-electr…
Using the band structure calculation and mean-field analysis of the derived three-chain Hubbard model with phonon degrees of freedom, we discuss the origin of the orthorhombic-to-monoclinic phase transition of the layered chalcogenide Ta$_2$NiSe$_5$. We show that the Bose-Einstein condensation of excitonic electron-hole pairs cooperatively induces the instability of the phonon mode at momentum $q\rightarrow 0$ in the quasi-one-dimensional Ta-NiSe-Ta chain, resulting in the structural phase transition of the system. The calculated single-particle spectra reproduce the deformation of the band st…
We study the metal-insulator transition in individual self-assembled quantum wires and report optical evidences of metallic liquid condensation at low temperatures. Firstly, we observe that the temperature and power dependence of the single nanowire photoluminescence follow the evolution expected for an electron-hole liquid in one dimension. Secondly, we find novel spectral features that suggest that in this situation the expanding liquid condensate compresses the exciton gas in real space. Finally, we estimate the critical density and critical temperature of the phase transition diagram at $n…
The unusual two-photon emission by Bose-condensed excitons caused by simultaneous recombination of two excitons with opposite momenta leaving the occupation numbers of excitonic states with momenta $p nonequal to 0$ unchanged (below coherent two-exciton recombination) is investigated. Raman scattering accompanied by the analogous two-exciton recombination (or creation) is also analyzed. The excess momentum equal to the change of the electromagnetic field momentum in these processes can be transferred to phonons or impurities. The processes under consideration take place if there is Bose conden…
We investigate the quasiparticle excitation of the bilayer quantum Hall (QH) system at total filling factor $ν_{\mathrm{T}} = 1$ in the limit of negligible interlayer tunneling under tilted magnetic field. We show that the intrinsic quasiparticle excitation is of purely pseudospin origin and solely governed by the inter- and intra-layer electron interactions. A model based on exciton formation successfully explains the quantitative behavior of the quasiparticle excitation gap, demonstrating the existence of a link between the excitonic QH state and the composite fermion liquid. Our results pro…
An odd number of gapless Dirac fermions is guaranteed to exist at a surface of a strong topological insulator. We show that in a thin-film geometry and under external bias, electron-hole pairs that reside in these surface states can condense to form a coherent exciton condensate, similar in general terms to the exciton condensate recently argued to exist in a biased graphene bilayer, but with different topological properties. Such a `topological' exciton condensate (TEC) exhibits a host of unusual properties; the most interesting among them is the fractional charge +-e/2 carried by a singly qu…
We study the combined effects of local and nonlocal hybridization on the formation and condensation of the excitonic bound states in the extended Falicov-Kimball model by the density-matrix-renormalization-group (DMRG) method. Analysing the resultant behaviours of the excitonic momentum distribution $N(q)$ we found, that unlike the local hybridization $V$, which supports the formation of the $q=0$ momentum condensate, the nonlocal hybridization $V_n$ supports the formation of the $q=π$ momentum condensate. The combined effect of local and nonlocal hybridization further enhances the excitonic c…
Using Diffusion Monte Carlo simulations we have investigated the ground state of a symmetric electron-hole bilayer and determined its phase diagram at T=0. We find clear evidence of an excitonic condensate, whose stability however is affected by in-layer electronic correlation. This stabilizes the electron-hole plasma at large values of the density or inter-layer distance, and the Wigner crystal at low density and large distance. We have also estimated pair correlation functions and low order density matrices, to give a microscopic characterization of correlations, as well as to try and estima…
