Tunable exciton condensates in two dimensional electron gas systems under strong magnetic field exhibits anomalous Hall transport owing to mutual Coulomb coupling, and have attracted a lot of research activity. Here, we explore another framework using topological flat band models in the absence of Landau levels, for realizing the many-body exciton phases of two-component fermions under strong intercomponent interactions. By developing new diagnosis based on the state-of-the-art density-matrix renormalization group and exact diagonalization, we show the theoretical discovery of the emergence of Halperin (111) quantum Hall effect at a total filling factor $ν=1$ in the lowest Chern band under strong Hubbard repulsion, which is classified by the unique ground state with bulk charge insulation and spin superfluidity, The topological nature is further characterized by one edge branch of chiral propagating Luttinger modes with level counting $1,1,2,3,5,7$ in consistent with the conformal field theory description. Moreover, with nearest-neighbor repulsions, we propose the Halperin (333) fractional quantum Hall effect at a total filling factor $ν=1/3$ in the lowest Chern band.
It is shown that exciton condensates exhibit an incredible richness in the role that fundamental symmetries play whether manifest or broken. We investigate the appearance of the singlet and the triplet excitonic condensates under spin-orbit coupling (SOC) and consider realistic couplings to the radiation field as manipulated by the fundamental symmetries related to spin, time, orbital and particle degrees of freedom. The role of the strong SOC in inducing a ground state with coexisting singlet and triplet components is shown. It is also shown that the ground state of an excitonic condensate, i…
New free energy related signatures of the condensed excitons in Double Quantum Wells (DQW) are predicted and experiments are proposed to measure the effects. These signatures are related to the measurement of a conceptually new kind of force ($\approx 10^{-9} N$) due to the condensate. This force, which may be coined as the Exciton Condensate (EC)-force is attractive and reminiscent of the Casimir force between two perfect metallic plates, but also distinctively different from it by its driving mechanism and dependence on the parameters of the condensate. The proposed experiments here are base…
We show that the "dark condensates" that arise when excitons form a Bose-Einstein condensate in a material with an indirect bandgap are not completely dark to optical emission. Rather, such states are "leaky condensates" in which optical emission is facilitated by many-body interactions. We analyze the properties of these leaky condensates in the context of twisted bilayers of transition metal dichalcogenides, which host strongly interacting excitons and an indirect bandgap. We show that this interaction-driven "leaky" emission dominates photoluminescence at low temperatures, with distinctive …
We predict that the collision of two fully dark exciton condensates produces interference fringes which are not only dark but also bright. So, quite surprisingly, the collision of coherent states made of dark excitons produces light. This remarkable effect, which is many-body in essence, comes from the composite boson nature of excitons, through the fermion exchanges they can have which transform dark states into bright states. The possibility of optically detecting quantum coherence in a regime where the system is hidden by its total darkness, was up to now considered as hopeless.
Double-layer electron systems in the quantum Hall regime have excitonic condensate ground states when the layers are close together and the total Landau level filling factor is close to an odd integer. In this paper we discuss the microscopic physics of these states and recent progress toward building a theory of the anomalous collective transport effects that occur in separately contacted bilayers when the condensate is present.
We study the bilayer quantum Hall system at total filling factor ν_T = 1 within a bosonization formalism which allows us to approximately treat the magnetic exciton as a boson. We show that in the region where the distance between the two layers is comparable to the magnetic length, the ground state of the system can be seen as a finite-momentum condensate of magnetic excitons provided that the excitation spectrum is gapped. We analyze the stability of such a phase within the Bogoliubov approximation firstly assuming that only one momentum Q0 is macroscopically occupied and later we consider t…
Magneto-transport and drag measurements on a quasi-Corbino 2D electron bilayer at the systems total filling factor 1 (v_tot=1) reveal a drag voltage that is equal in magnitude to the drive voltage as soon as the two layers begin to form the expected v_tot=1 exciton condensate. The identity of both voltages remains present even at elevated temperatures of 0.25 K. The conductance in the current carrying layer vanishes only in the limit of strong coupling between the two layers and at T->0 K which suggests the presence of an excitonic circular current.
We theoretically predict that a true bilayer exciton condensate,characterised by off-diagonal long range order and global phase coherence, can be created in one-dimensional solid state electron systems. The mechanism by which this happens is to introduce a single particle hybridization of electron and hole populations, which locks the phase of the relevant mode and hence invalidates the Mermin--Wagner theorem. Electron--hole interactions then amplify this tendency towards off-diagonal long range order, enhancing the condensate properties by more than an order of magnitude over the noninteracti…
Nesting in a semimetal can lead to an excitonic insulator state with spontaneous coherence between conduction and valence bands and a gap for charged excitations. In this paper we present a theory of the ferromagnetic state that occurs when the density of electrons in the conduction band and holes in the valence band differ. We find an unexpectedly rich doping-field phase diagram and an unusual collective excitation spectrum that includes two gapless collective modes. We predict regions of doping and external field in which phase-separated condensates of electrons and holes with parallel spins…
Charged excitons of composite fermions (CFs) are considered in the fractional quantum Hall effect. Energies of the charged CF excitons are computed at $ν=1/3$ as a function of the size of exciton. We show that the charged CF exciton with size of roton is lower in energy than the unbound state of a neutral roton and a lone charge. Therefore we propose that the lowest-energy excitation of the fractional quantum Hall effect is in fact due to the charged excitons of composite fermions composed of two CF-particles and one CF-hole. We believe that charged excitons of composite fermions shed new ligh…
Higgs modes in condensed matter physics have drawn attention because of analogies to the Higgs bosons of particle physics. Here we use a microscopic time-dependent mean-field theory to study the collective mode spectra of two-dimensional spatially indirect exciton (electron-hole pair) condensates, focusing on the Higgs modes, i.e., those that have a large weight in electron-hole pair amplitude response functions. We find that in the low exciton density (BEC) limit, the dominant Higgs modes of spatially indirect exciton condensates correspond to adding electron-hole pairs that are orthogonal to…
Using Monte Carlo simulation, we studied fractionalized phases in a model of exciton bose condensate and found evidence for an emergent photon in a finite size system. The fractionalized phase is a meta-stable Coulomb phase where an emergent photon arises as a gapless collective excitation of the excitons. We also studied a possibility of spiral* phase where fractionalization and long range spiral order of the exciton condensate coexist.
We explore a simple theoretical model to describe the properties of Bose condensed para-excitons in Cu2O. Taking into account the exciton-phonon interaction and introducing a coherent phonon part of the moving condensate, we derive the dynamic equations for the exciton-phonon condensate. Within the Bose approximation for excitons, we discuss the conditions for the moving inhomogeneous condensate to appear in the crystal. We calculate the condensate wave function and energy and a collective excitation spectrum in the semiclassical approximation. The stability conditions of the moving condensate…
We study the texture of the exciton condensate at low temperatures in an independently gated electron-hole bilayer system. A model Hamiltonian is solved in real space within a mean-field approximation. It is found that, with increased electron-hole density polarization, the system experiences phase transformations from the zero center-of-mass momentum superfluid state, through one- and two-dimensional exciton pair modulated states, into the normal state. At weak density polarization, the modulating state resembles the Larkin-Ovchinikov state in superconductors in the presence of an exchange fi…
We will discuss the relevant conditions to observe a critical tunneling current [New J. Phys. 10, 045018 (2008)] in electron double-layer systems at a total filling factor of 1 and find they are related to the effective layer separation and the temperature. Our studies suggest that the intensity of the critical tunneling behavior is also directly linked to the area of the sample.
I study the effects of particle-hole imbalance on the exciton superfluid formed in a topological insulator thin-film and obtain the mean-field phase diagram. At finite imbalance a spatially modulated condensate is formed, akin to the Fulde-Ferrel-Larkin-Ovchinikov state in a superconductor, which preempts a first-order transition from the uniform condensate to the normal state at low temperatures. The imbalance can be tuned by changing the chemical potential at the two surfaces separately or, alternatively, by an asymmetric application of Zeeman fields at constant chemical potential. A vortex …
In this work, we study the exciton-polariton condensate phase transition in a microcavity matter-light system in which electron-hole Coulomb interaction and matter-light coupling effects are treated on an equal footing. In the framework of the unrestricted Hartree-Fock approximation applying the two-dimensional exciton-polariton model, we derive the self-consistent equations determining simultaneously the excitonic and the photonic condenstate order parameters. In the thermal equilibrium limit, we find a condensed state of the exciton-polariton systems and phase diagrams are then constructed. …
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 explore a nonlinear field model to describe the interplay between the ability of excitons to be Bose-condensed and their interaction with other modes of a crystal. We apply our consideration to the long-living para-excitons in Cu2O. Taking into account the exciton-phonon interaction and introducing a coherent phonon part of the moving condensate, we derive the dynamic equations for the exciton-phonon condensate. These equations can support localized solutions, and we discuss the conditions for the moving inhomogeneous condensate to appear in the crystal. We calculate the condensate wave fun…
We explore a nonlinear field model to describe the interplay between the ability of excitons to be Bose condensed and their interaction with other modes of a crystal. We apply our consideration to the long-living paraexcitons in Cu2O. Taking into account the exciton-phonon interaction and introducing a coherent phonon part of the moving condensate, we solve quasi-stationary equations for the exciton-phonon condensate. These equations support localized solutions, and we discuss the conditions for the inhomogeneous condensate to appear in the crystal. Allowable values of the characteristic width…
A real-space formulation is given for the recently discussed exciton condensate in a symmetrically biased graphene bilayer. We show that in the continuum limit an oddly-quantized vortex in this condensate binds exactly one zero mode per valley index of the bilayer. In the full lattice model the zero modes are split slightly due to intervalley mixing. We support these results by an exact numerical diagonalization of the lattice Hamiltonian. We also discuss the effect of the zero modes on the charge content of these vortices and deduce some of their interesting properties.
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…
As a sequel to the previous work [Phys. Rev. B 72, 235104 (2005)] we present a vortex description of the fractionalized phase in exciton bose condensate. Magnetic flux line and monopole of the 3+1D emergent U(1) gauge theory are identified in the exciton picture. A bundle of vortex/anti-vortex pairs of all flavors of excitons corresponds to the magnetic flux line and a point at which the vortices and anti-vortices recombine is identified as magnetic monopole. This completes the magnetic sector of the low energy excitation in the fractionalized phase.
The effect of impurities which induce local interlayer tunneling in bilayer exciton condensates is discussed. We show that a localized single fermion bound state emerges inside the gap for any strength of impurity scattering and calculate the dependence of the impurity state energy and wave function on the potential strength. We show that such an impurity induced single fermion state enhances the interlayer coherence around it, and is similar to the superconducting proximity effect. As a direct consequence of these single impurity states, we predict that a finite concentration of such impuriti…
Using the dynamical mean-field approximation we investigate formation of excitonic condensate in the two-band Hubbard model in the vicinity of the spin-state transition. With temperature and band filling as the control parameters we realize all symmetry allowed spin-triplet excitonic phases, some exhibiting a ferromagnetic polarization. While the transitions are first-order at low temperatures, at elevated temperatures continuous transitions are found that give rise to a multi-critical point. Rapid but continuous transition between ferromagnetic and non-magnetic excitonic phases allows switchi…
In the Anderson lattice model for a mixed-valent system, the $d-f$ hybridization can possess a $p$-wave symmetry. The strongly-correlated insulating phase in the mean-field approximation is shown to be a $p$-wave Bose condensate of excitons with a spontaneous lattice deformation. We study the equilibrium and linear response properties across the insulator-metal transition. Our theory supports the empirical correlation between the lattice deformation and the magnetic susceptibility and predicts measurable ultrasonic and high-frequency phonon behavior in mixed-valent semiconductors.
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…
We propose a projector-based renormalization framework to study exciton-polariton Bose-Einstein condensation in a microcavity matter-light system. Treating Coulomb interaction and electron-hole/photon coupling effects on an equal footing we analyze the ground-state properties of the exciton polariton model according to the detuning and the excitation density. We demonstrate that the condensate by its nature shows a crossover from an excitonic insulator (of Bose-Einstein respectively BCS type) to a polariton and finally photonic condensed state as the excitation density increases at large detun…
We examine the competition between the charge-density wave (CDW) instability and the excitonic condensate (EC) in spatially separated layers of electrons and holes. The CDW and the EC order parameters (OPs), described by two different mechanisms and hence two different transition temperatures $T^{CDW}_c$ and $T^{EC}_c$, are self-consistently coupled by a microscopic mean field theory. We discuss the results in our model specifically focusing on the transition-metal dichalcogenides which are considered as the most typical examples of strongly coupled CDW/EC systems with atomic layer separations…
It is shown that the Rashba and Dresselhaus spin orbit couplings enhance the conclusive power in the experiments on the excitonic condensed state by at least three low temperature effects. First, spin orbit coupling facilitates the photoluminescense measurements via enhancing the bright contribution in the otherwise dominantly dark exciton condensed state. The second is the presence of a power law temperature dependence of the thermodynamic observables in low temperatures and the weakening of the second order transition at the critical temperature. The third is the appearance of the nondiagona…
We employ mean-field approximation to investigate the interplay between the nontrivial band topology and the formation of excitonic insulator (EI) in a one-dimensional chain of atomic $s-p$ orbitals in the presence of repulsive inter-orbital Coulomb interaction. We find that our model, in a non-interacting regime, admits topological and trivial insulator phases, whereas, in strong Coulomb interaction limit, the chiral symmetry is broken and the system undergoes a topological-excitonic insulator phase transition. The latter phase transition stems from an orbital pseudomagnetization and band inv…
We have studied theoretically the Bose-Einstein condensation (BEC) of two-dimensional excitons in a ring with small random width variation. We derive a nonlinear Gross-Pitaevkii equation (GPE) for such a condensate. Our numerical solution of the ground state of the GPE displays a necklace-like structure in the presence of small random variation of ring width. This is a consequence of the interplay between random potential and the nonlinear repulsive term of the GPE. Our result suggests that the formation of ring and necklace-like structures observed recently in the photoluminescence of quantum…
We discuss the possibility for a moving droplet of excitons and phonons to form a coherent state inside the packet. We describe such an inhomogeneous state in terms of Bose-Einstein condensation and prescribe it a macroscopic wave function. Existence and, thus, coherency of the Bose-core inside the droplet can be checked experimentally by letting two moving packets to interact.
We show that for the very same reason that excitons are bright, i.e. coupled to photons, they have a higher energy than dark excitons, even for electrons spatially separated from holes, such as in a double quantum well. Indeed, the same channel which produces the finite electron-hole effective overlap responsible for the absorption and emission of photon allows for Coulomb interband exchange processes, which are nothing but a sequence of virtual recombination and creation of one electron-hole pair. Consequently, this additional repulsive electron-hole Coulomb exchange interaction exists for br…
The charge density wave phase transition of 1T-TiSe2 is studied by angle-resolved photoemission over a wide temperature range. An important chemical potential shift which strongly evolves with temperature is evidenced. In the framework of the exciton condensate phase, the detailed temperature dependence of the associated order parameter is extracted. Having a mean-field-like behaviour at low temperature, it exhibits a non-zero value above the transition, interpreted as the signature of strong excitonic fluctuations, reminiscent of the pseudo-gap phase of high temperature superconductors. Integ…
