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Register a new userEffects of Disorder on the Transport of Collective Modes in an Excitonic Condensate
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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 signatures of the EI that distinguish it from a normal insulator. To address this, we focus on a clear qualitative difference between the two phases: the existence of Goldstone modes born by the spontaneous breaking of a $U(1)$ symmetry in the EI. Even if this mode is gapped, as occurs in the case of an approximate symmetry, this branch of collective modes remains a fundamental feature of the low-energy dynamics of the EI provided the symmetry-breaking is small. We study a simple model that realizes an excitonic condensate, and use mean field theory within the random-phase approximation to determine its collective modes. We subsequently develop a diagrammatic method to incorporate the effects of disorder perturbatively, and use it to determine the scattering rate of the collective modes. We interpret our results within an an effective field theory. The collective modes are found to be robust against symmetry-preserving disorder, implying an experimental fingerprint unique to the EI: the ballistic propagation of low-lying modes over mesoscopic distances, at electronic-scale velocities. We suggest this could affect thermal transport at low temperatures, and could be observed via spatially-resolved pump-probe spectroscopy through the coherent response of phonons that hybridize with the collective modes.
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We consider a two-band spinless model describing an excitonic insulator (EI) on the two-dimensional square lattice with anisotropic hopping parameters and electron-phonon (el-ph) coupling, inspired by the EI candidate Ta$_2$NiSe$_5$. We systematically study the nature of the collective excitations in the ordered phase which originates from the interband Coulomb interaction and the el-ph coupling. When the ordered phase is stabilized only by the Coulomb interaction (pure EI phase), its collective response exhibits a massless phase mode in addition to the amplitude mode. We show that in the BEC regime, the signal of the amplitude mode becomes less prominent and that the anisotropy in the phase mode velocities is relaxed compared to the model bandstructure. Through coupling to the lattice, the phase mode acquires a mass and the signal of the amplitude mode becomes less prominent. Importantly, character of the softening mode at the boundary between the normal semiconductor phase and the ordered phase depends on the parameter condition. In particular, we point out that even for el-ph coupling smaller than the Coulomb interaction the mode that softens to zero at the boundary can have a phonon character. We also discuss how the collective modes can be observed in the optical conductivity. Furthermore, we study the effects of nonlocal interactions on the collective modes and show the possibility of realizing a coexistence of an in-gap mode and an above-gap mode split off from the single amplitude mode in the system with the local interaction only.
We report single layer resistivities of 2-dimensional electron and hole gases in an electron-hole bilayer with a 10nm barrier. In a regime where the interlayer interaction is stronger than the intralayer interaction, we find that an insulating state ($drho/dT < 0$) emerges at $Tsim1.5{rm K}$ or lower, when both the layers are simultaneously present. This happens deep in the $$metallic regime, even in layers with $k_{F}l>500$, thus making conventional mechanisms of localisation due to disorder improbable. We suggest that this insulating state may be due to a charge density wave phase, as has been expected in electron-hole bilayers from the Singwi-Tosi-Land-Sjolander approximation based calculations of L. Liu {it et al} [{em Phys. Rev. B}, {bf 53}, 7923 (1996)]. Our results are also in qualitative agreement with recent Path-Integral-Monte-Carlo simulations of a two component plasma in the low temperature regime [ P. Ludwig {it et al}. {em Contrib. Plasma Physics} {bf 47}, No. 4-5, 335 (2007)]
The nonlinear optical response of an excitonic insulator coupled to lattice degrees of freedom is shown to depend in strong and characteristic ways on whether the insulating behavior originates primarily from electron-electron or electron-lattice interactions. Linear response optical signatures of the massive phase mode and the amplitude (Higgs) mode are identified. Upon nonlinear excitation resonant to the phase mode, a new in-gap mode at twice the phase mode frequency is induced, leading to a huge second harmonic response. Excitation of in-gap phonon modes leads to different and much smaller effects. A Landau-Ginzburg theory analysis explain these different behavior and reveals that a parametric resonance of the strongly excited phase mode is the origin of the photo-induced mode in the electron-dominant case. The difference in the nonlinear optical response serve as a measure of the dominant mechanism of the ordered phase.
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 between phonon modes and the phase mode of the condensate. We develop a theoretical framework to support this explanation and propose that electronic interactions provide a significant contribution to the ordered phase in Ta$_2$NiSe$_5$. These results allow us to understand how the condensates collective modes transport energy and interact with other degrees of freedom. Our study provides a unique paradigm for the investigation and manipulation of these properties in strongly correlated materials.
We study the time evolution of excitonic states after photo-excitation in the one-dimensional spin-less extended Falicov-Kimball model. Several numerical methods are employed and benchmarked against each other: time-dependent mean-field simulations, the second-Born approximation (2BA) within the Kadanoff-Baym formalism, the generalized Kadanoff-Baym Ansatz (GKBA) implemented with the 2BA and the infinite time-evolving block decimation (iTEBD) method. It is found that the GKBA gives the best agreement with iTEBD and captures the relevant physics. We find that excitations to the particle-hole continuum and resonant excitations of the equilibrium exciton result in a qualitatively different dynamics. In the former case, the exciton binding energy remains positive and the frequency of the corresponding coherent oscillations is smaller than the band gap. On the other hand, resonant excitations trigger a collective mode whose frequency is larger than the band gap. We discuss the origin of these different behaviors by evaluating the nonequilibrium susceptibility using the nonthermal distribution and a random phase approximation. The peculiar mode with frequency larger than the band gap is associated with a partial population inversion with a sharp energy cutoff. We also discuss the effects of the cooling by a phonon bath. We demonstrate the real-time development of coherence in the polarization, which indicates excitonic condensation out of equilibrium.
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