The Two-Dimensional Rashba-Holstein Model: A Quantum Monte Carlo Approach

TL;DR

This study uses Quantum Monte Carlo simulations to explore how Rashba spin-orbit coupling influences charge-density wave and superconducting phases in the Holstein model, revealing phase transitions and the impact of spin-orbit effects.

Contribution

It provides the first unbiased finite-temperature Quantum Monte Carlo analysis of the Rashba-Holstein model, uncovering phase stability, quantum phase transitions, and symmetry enhancements.

Findings

Rashba metal is unstable, favoring CDW formation at all RSOC values.

Quantum phase transition between semi-metal and CDW occurs at strong interactions.

Enhanced symmetry in the antiadiabatic limit unifies SC and CDW orders.

Abstract

In this work, we investigate the impact of Rashba spin-orbit coupling (RSOC) on the formation of charge-density wave (CDW) and superconducting (SC) phases in the Holstein model on a half-filled square lattice. Using unbiased finite-temperature Quantum Monte Carlo simulations, we go beyond mean-field approaches to determine the ground state order parameter as a function of RSOC and phonon frequency. Our results reveal that the Rashba metal is unstable due to particle-hole instabilities, favoring the emergence of a CDW phase for any RSOC value. In the limit of a pure Rashba hopping, the model exhibits a distinct behavior with the appearance of four Weyl cones at half-filling, where quantum phase transitions are expected to occur at strong interactions. Indeed, a quantum phase transition, belonging to the Gross-Neveu Ising universality class between a semi-metal and CDW emerges at finite phonon frequency dependent coupling $\lambda_c$. In the antiadiabatic limit we observe an enhanced symmetry in the infrared that unifies SC and CDW orders. These results advance our understanding of competing CDW and SC phases in systems with spin-orbit coupling, providing insights that may help clarify the behavior of related materials.