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Register a new userCollective Modes in Excitonic Insulators: Effects of Electron-Phonon Coupling and Signatures in Optical Response
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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.
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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.
Bardasis-Schrieffer modes in superconductors are fluctuations in subdominant pairing channels, e.g., d-wave fluctuations in an s-wave superconductor. This Rapid Communication shows that these modes also generically occur in excitonic insulators. In s-wave excitonic insulators, a p-wave Bardasis-Schrieffer mode exists below the gap energy, is optically active and hybridizes strongly with photons to form Bardasis-Schrieffer polaritons, which are observable in both far-field and near-field optical experiments.
We show that in excitonic insulators with $s$-wave electron-hole pairing, an applied electric field (either pulsed or static) can induce a $p$-wave component to the order parameter, and further drive it to rotate in the $s+ip$ plane, realizing a Thouless charge pump. In one dimension, each cycle of rotation pumps exactly two electrons across the sample. Higher dimensional systems can be viewed as a stack of one dimensional chains in momentum space in which each chain crossing the fermi surface contributes a channel of charge pumping. Physics beyond the adiabatic limit, including in particular dissipative effects is discussed.
We show that in electron-hole bilayers with excitonic order arising from conduction and valence bands formed by atomic orbitals that transform differently under inversion, nonzero interlayer tunneling leads to a second order Josephson effect. This means the interlayer electrical current is related to the phase of the excitonic order parameter as $J = J_c sin2theta$ instead of $J = J_c sin theta$, and that the system has two degenerate ground states that can be switched by an interlayer voltage. In a three dimensional stack of alternating electron-hole planes or a two dimensional stack of chains, the second order Josephson coupling can lead to a Weyl semimetal or a quantum anomalous hall insulator, respectively. A generic order parameter steering effect is demonstrated, whereby electric field pulses perpendicular to the layers and chains can steer the order parameter phase between the two degenerate ground states. The steering is also applicable to the excitonic insulator candidate Ta$_2$NiSe$_5$.
Vacancy centers in diamond have proven to be a viable solid-state platform for quantum coherent opto-electronic applications. Among the variety of vacancy centers, silicon-vacancy (SiV) centers have recently attracted much attention as an inversion-symmetric system that is less susceptible to electron-phonon interactions. Nevertheless, phonon-mediated processes still degrade the coherent properties of SiV centers, however characterizing their electron-phonon coupling is extremely challenging due to their weak spectroscopic signatures and remains an open experimental problem. In this paper we theoretically investigate signatures of electron-phonon coupling in simulated linear and nonlinear spectra of SiV centers. We demonstrate how even extremely weak electron-phonon interactions, such as in SiV centers, may be completely characterized via nonlinear spectroscopic techniques and even resolved between different fine-structure transitions.
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