Spectral properties of orbital polarons in Mott insulators

TL;DR

This paper investigates the spectral properties of orbital polarons in Mott insulators with orbital degrees of freedom, revealing different behaviors depending on orbital mobility and providing analytical and numerical results relevant for interpreting photoemission spectra.

Contribution

It introduces a detailed analysis of orbital polaron spectral functions in Mott insulators, contrasting immobile and mobile orbital cases, using various approximation methods and connecting to experimental spectra.

Findings

Immobile orbital flavors lead to trapped polarons with analytical spectral functions.

Active orbitals produce propagating polarons with anisotropic spectral functions.

Comparisons with Hubbard models validate the spectral predictions.

Abstract

We address the spectral properties of Mott insulators with orbital degrees of freedom, and investigate cases where the orbital symmetry leads to Ising-like superexchange in the orbital sector. The paradigm of a hole propagating by its coupling to quantum fluctuations, known from the spin t-J model, then no longer applies. We find instead that when one of the two orbital flavors is immobile, as in the Falicov-Kimball model, trapped orbital polarons coexist with free hole propagation emerging from the effective three-site hopping in the regime of large on-site Coulomb interaction U. The spectral functions are found analytically in this case within the retraceable path approximation in one and two dimensions. On the contrary, when both of the orbitals are active, as in the model for $t_{2g}$ electrons in two dimensions, we find propagating polarons with incoherent scattering dressing the moving hole and renormalizing the quasiparticle dispersion. Here, the spectral functions, calculated using the self-consistent Born approximation, are anisotropic and depend on the orbital flavor. Unbiased conclusions concerning the spectral properties are established by comparing the above results for the orbital t-J models with those obtained using the variational cluster approximation or exact diagonalization for the corresponding Hubbard models. The present work makes predictions concerning the essential features of photoemission spectra of certain fluorides and vanadates.