Collective modes in excitonic insulators: Effects of electron-phonon coupling and signatures in the optical response

Abstract

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 reduced. Through coupling to the lattice, the phase mode acquires a mass and the signal of the amplitude mode becomes less prominent. Importantly, the character of the softening mode at the boundary between the normal semiconductor phase and the ordered phase depends on the parameters. 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 local interactions only.

Ultrafast melting and recovery of collective order in the excitonic insulator Ta2NiSe5

“…1b ), with alternating chains of tantalum and nickel atoms in each of the stacked atomic planes 20 . A number of studies that support the hypothesis of an EI phase in Ta 2 NiSe 5 have emerged in the past few years 21 – 26 , and very recently the first detection of collective excitations in this system was reported 27 and explained theoretically 28 , 29 . However, the existence of a simultaneous structural phase transition at T c 20 still calls into question the effective contribution of electronic correlations to the low-temperature behaviour of this material, and further efforts are required to directly study the properties of the EI order parameter and to develop a complete microscopic description of the interactions that govern this phase.…”

Finite-temperature photoemission in the extended Falicov-Kimball model: a case study for Ta$_2$NiSe$_5$

“…Finally we wish to stress that the investigated EFKM has to be considered as a generic but very simplistic model for the excitonic transition in solids. For example, the interplay between the electronic and lattice instability [49], which is intensively discussed for Ta 2 NiSe 5 too [55][56][57][58], cannot be addressed. Moreover, recent and perhaps more realistic models of Ta 2 NiSe 5 [59] include also an off-site hybridization: In such a system the excitonic insulator transition arises from the spontaneous breaking of a residual discrete symmetry, rather than by that of a continuous symmetry related to the conservation of the relative charge between valence and conduction electrons [26].…”

Graphene as a source of entangled plasmons

“…For example, monolayer hexagonal boron nitride [97,98] should exhibit strong second order optical nonlinearity due to broken inversion symmetry of the crystal lattice, and would be a natural platform for generating entanglement between the long lived hyperbolic phonon polaritons [99][100][101][102][103][104][105][106][107][108]. Similar nonlinear processes exist for optical phonons in SiC [109], Josephson plasmons in layered superconductors [110][111][112][113] and the collective modes in excitonic insulators [114][115][116][117][118].…”