Charge-Density-Wave Transitions of Dirac Fermions Coupled to Phonons

TL;DR

This study investigates how electron-phonon interactions induce charge-density-wave order in Dirac fermions on a honeycomb lattice, revealing a phase diagram with quantum and thermal critical points and universality classes.

Contribution

It provides the first unbiased quantum Monte Carlo analysis of charge-density-wave transitions in Dirac fermion systems coupled to phonons, identifying critical points and universality classes.

Findings

Phase diagram with quantum and thermal critical points

Quantum transition consistent with Gross-Neveu-Ising universality

Thermal transition consistent with bosonic Ising universality

Abstract

The spontaneous generation of charge-density-wave order in a Dirac fermion system via the natural mechanism of electron-phonon coupling is studied in the framework of the Holstein model on the honeycomb lattice. Using two independent and unbiased quantum Monte Carlo methods, the phase diagram as a function of temperature and coupling strength is determined. It features a quantum critical point as well as a line of thermal critical points. Finite-size scaling appears consistent with fermionic Gross-Neveu-Ising universality for the quantum phase transition, and bosonic Ising universality for the thermal phase transition. The critical temperature has a maximum at intermediate couplings. Our findings motivate experimental efforts to identify or engineer Dirac systems with sufficiently strong and tunable electron-phonon coupling.