Peierls/Su-Schrieffer-Heeger polarons in two dimensions

TL;DR

This paper investigates two-dimensional Peierls/Su-Schrieffer-Heeger polarons using Diagrammatic Monte Carlo, revealing how different electron-phonon couplings affect ground-state momentum and effective mass, with implications for high-temperature superconductivity.

Contribution

It demonstrates how the properties of PSSH polarons depend on the type of displacement-modulated hopping in two dimensions, showing a continuous transition in ground-state momentum for one model and constant zero momentum for another.

Findings

Model A shows a transition from zero to finite ground-state momentum with increasing coupling.

Model B maintains zero ground-state momentum and exhibits a leveling-off of effective mass at strong coupling.

Light polarons at strong coupling could be relevant for high-temperature superconductivity.

Abstract

Polarons with different types of electron-phonon coupling have fundamentally different properties. When the dominant interaction is between the electron density and lattice displacement, the momentum of the ground state does not change and the polaron gets exponentially heavy at strong coupling. In contrast, one-dimensional Peierls/Su-Schrieffer-Heeger (PSSH) polarons with interaction originating from displacement-modulated hopping feature a shift of the ground-state momentum to finite values and moderate values of effective mass as coupling is increased REF[Phys. Rev. Lett. 105, 266605 (2010)]. Based on Diagrammatic Monte Carlo method, we investigate whether unusual properties of PSSH polarons depend on the type of the displacement-modulated hopping and to what degree they survive in higher dimension. We study two different PSSH models: with bosonic degrees of freedom residing on sites (model A) and bonds (model B) of the two-dimensional square lattice. For model A, we find that in both adiabatic and intermediate regimes, the momentum of the ground state experiences a continuous transition from zero to a finite value as a function of coupling strength. The transition is driven by quadratic instability of the dispersion function, implying that effective mass diverges at the critical point, and then decreases in an anisotropic fashion with increasing coupling. Unexpectedly, for model B, the momentum of the ground state always stays at zero and the effective mass increases monotonously with coupling. The increase is far from exponential and tends to level-off at strong interaction, resulting in relatively light polarons. Having light polarons in the strong coupling regime is crucial for the bi-polaron mechanism of high-temperature superconductivity REF[Phys. Rev. Lett. 121, 247001 (2018)].