Disorder Suppression of Charge Density Waves in the Honeycomb Holstein Model

TL;DR

This study uses quantum Monte Carlo simulations to explore how disorder affects charge-density-wave order in the honeycomb Holstein model, revealing that disorder suppresses the CDW phase and influences electronic transport.

Contribution

It provides the first detailed analysis of disorder effects on charge-density-wave transitions in the honeycomb Holstein model using determinant quantum Monte Carlo methods.

Findings

Disorder suppresses the charge-density-wave phase.

Disorder extends the phase boundary of CDW order.

Disorder reduces electron kinetic energy and conductivity.

Abstract

The formation of charge-density-wave order in Dirac fermion systems via electron-phonon coupling represents a significant topic in condensed matter physics. In this work, we investigate this phenomenon within the Holstein model on the honeycomb lattice, with a specific focus on the effect of disorder. While the interplay between electron-electron interactions and disorder has long been a central theme in the field, recent attention has increasingly turned to the combined influence of disorder and electron-phonon coupling. Using determinant quantum Monte Carlo simulations, we concentrate on the phase transitions of charge-density-wave order on the honeycomb lattice. Disorder is introduced through the random hopping of electrons in the system, which can localize electrons via the Anderson effect. Our primary result is that disorder suppresses the charge-density-wave phase, and the interplay between disorder and electron-phonon interactions extends the phase area. We also determine the transition temperature \(\beta_c\) to the ordered phase as a function of the electron-phonon coupling. Additionally, we observed a suppression of electron kinetic energy and dc conductivity under disorder, highlighting the role of Anderson localization in the degradation of electronic transport. These findings offer significant theoretical insight into the stability and critical phenomena of correlated phases in disordered two-dimensional systems.