We investigate the equilibrium state and the collective modes of an excitonic insulator (EI) in a Fabry-Pérot cavity. In an EI, two bands of a semiconductor or semimetal spontaneously hybridize due to the Coulomb interaction between electrons and holes, leading to the opening of a gap. The coupling to the electromagnetic field reduces the symmetry of the system with respect to phase rotations of the excitonic order parameter from $U(1)$ to $Z_2$. While the reduction to a discrete symmetry would in general lead to a gapped phase mode and enhance the stability of the ordered phase, the coupling to the cavity leaves the mean-field ground state unaffected. Its energy remains invariant under $U(1)$ phase rotations, in spite of the lower $Z_2$ symmetry imposed by the cavity. In dipolar gauge, this can be traced back to the balancing of the linear light-matter coupling and the dipolar self-interaction at zero frequency. At nonzero frequency, however, the collective excitations do reflect the lower $Z_2$ symmetry, which shows that fluctuations beyond mean-field could play a crucial role in finding the true phase at finite temperature.
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 consider a generalization of the Dicke model. It describes localized, physically separated, saturable excitations, such as excitons bound on impurities, coupled to a single long-lived mode of an optical cavity. We consider the thermal equilibrium of the model at a fixed total number of excitons and photons. We find a phase in which both the cavity field and the excitonic polarization are coherent. This phase corresponds to a Bose condensate of cavity polaritons, generalized to allow for the fermionic internal structure of the excitons. It is separated from the normal state by an unusual ree…
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…
Excitonic insulating system is studied from the viewpoints of the orbital physics in strongly correlated electron systems. An effective model Hamiltonian for low-energy electronic states is derived from the two-orbital Hubbard model with a finite energy difference corresponding to the crystalline field splitting. The effective model is represented by the spin operators and the pseudo-spin operators for the spin-state degrees of freedom. The ground state phase diagram is analyzed by the mean-field approximation. In addition to the low-spin state and high-spin state phases, two kinds of the exci…
Weyl semi-metals are three dimensional generalizations of graphene with point-like Fermi surfaces. Their linear electronic dispersion leads to a window in the particle-hole excitation spectrum which allows for undamped propagation of collective excitations. We argue that interactions in Weyl semi-metals generically lead to well-defined exciton modes. However, using a minimal model for interactions, we show that the exciton binding energy is exponentially small for weak interactions. This is due to effective two-dimensional character in the space of particle-hole pairs that are available for bo…
We predict the formation and superfluidity of polaritons in an optical microcavity formed by excitons in gapped graphene embedded there and microcavity photons. The Rabi splitting related to the creation of an exciton in a graphene layer in the presence of the band gap is obtained. The analysis of collective excitations as well as the sound velocity is presented. We show that the superfluid density and temperature of the Kosterlitz-Thouless phase transition are decreasing functions of the energy gap.
We have studied the collective properties of two-dimensional (2D) excitons immersed within a quantum well which contains 2D excitons and a two-dimensional electron gas (2DEG). We have also analyzed the excitations for a system of 2D dipole excitons with spatially separated electrons and holes in a pair of quantum wells (CQWs) when one of the wells contains a 2DEG. Calculations of the superfluid density and the Kosterlitz-Thouless (K-T) phase transition temperature for the 2DEG-exciton system in a quantum well have shown that the K-T transition temperature increases with increasing exciton dens…
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.
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）
Excitonic insulators host a condensate of electron-hole pairs at equilibrium, giving rise to collective many-body effects. Although several materials have emerged as excitonic insulator candidates, evidence of long-range coherence is lacking and the origin of the ordered phase in these systems remains controversial. Here, using ultrafast pump-probe microscopy, we investigate the possible excitonic insulator Ta$_2$NiSe$_5$. Below 328 K, we observe the anomalous micrometer-scale propagation of coherent modes at velocities of the order of $\sim10^5$ m/s, which we attribute to the hybridization be…
We present a dynamical mean-field study of dynamical susceptibilities in two-band Hubbard model. Varying the model parameters we analyze the two-particle excitations in the normal as well as in the ordered phase, an excitonic condensate. The two-particle DMFT spectra in the ordered phase reveal the gapless Goldstone modes arising from spontaneous breaking of continuous symmetries. We also observe gapped Higgs mode, characterized by vanishing of the gap at the phase boundary. Qualitative changes observed in the spin susceptibility can be used as an experimental probe to identify the excitonic c…
An excitonic insulator (EI) is an unconventional quantum phase of matter in which excitons, bound pairs of electrons and holes, undergo Bose--Einstein condensation, forming a macroscopic coherent state. While its existence was first hypothesized half a century ago, the EI has eluded experimental observation in bulk materials for decades. In the last few years, a resurgence of interest in the subject has been driven by the identification of several candidate materials suspected to support an excitonic condensate. However, one obstacle in verifying the nature of these systems has been to find si…
The layered chalcogenide Ta$_{2}$NiSe$_{5}$ has been proposed to host an excitonic condensate in its ground state, a phase that could offer a unique platform to study and manipulate many-body states at room temperature. However, identifying the dominant microscopic contribution to the observed spontaneous symmetry breaking remains challenging, perpetuating the debate over the ground state properties. Here, using broadband ultrafast spectroscopy we investigate the out-of-equilibrium dynamics of Ta$_{2}$NiSe$_{5}$ and demonstrate that the transient reflectivity in the near-infrared range is conn…
According to the mean-field theory of Zittartz, when subject to a symmetry-breaking disorder, the order parameter and the energy gap of an excitonic insulator are gradually suppressed up to a critical disorder strength. Recently, Marchetti, Simons, and Littlewood have used a replica trick to investigate the effects of disorder on the condensation of cavity polaritons. Within their nonlinear sigma model, it was found that the saddle-point equations assume the form reported previously by Zittartz in the contest of the symmetry broken excitonic insulator, but with an order parameter, to which bot…
An emergent quantized field enriches quantum many-body systems. We propose an antiparticle analog of the exciton in semimetals as an emergent collective mode in interacting electron systems. We show that inter-band excitations in semimetals are generally comprised of both excitons and antiparticles of excitons. These two stand for two distinct inter-band collective modes in semimetals, having different energies and opposite conserved charges. The conserved charge here is a quantity conjugate to a joint U(1) symmetry of two electron's bands associated with the inter-band excitations. The opposi…
