Charge order in an interacting monolayer under transverse bias

TL;DR

This paper investigates charge ordering and current flow in a driven monolayer system under bias, revealing a novel conducting charge-density-wave phase and analyzing phase transition universality classes.

Contribution

It introduces a comprehensive study of charge order and phase transitions in a biased monolayer using master equations, mean-field, and Monte Carlo methods, highlighting a new conducting charge-density-wave phase.

Findings

Discovery of a finite-bias conducting charge-density-wave phase

Identification of phase transition universality classes including Ising and DP2

Analysis of zero and finite temperature phase behaviors

Abstract

A monolayer of molecules or quantum dots sandwiched between electrodes can be driven out of equilibrium by the application of a bias voltage between the electrodes. We study charge ordering, i.e., the spontaneous formation of a charge density wave, and the perpendicular current in such a system within a master-equation approach augmented by mean-field and classical Monte Carlo methods. Our approach is suitable for weak tunneling between the monolayer and the electrodes. For a square lattice with nearest-neighbor Coulomb repulsion, we present a comprehensive study of the zero-temperature phases controlled by the on-site energy, the bias voltage, and the degeneracy of the occupied single-site state. One of the most interesting results is the prediction of a conducting charge-density-wave phase that only occurs at a finite bias voltage. We also study the universality classes of the phase transitions towards charge-ordered states at zero and nonzero temperatures. While all transitions at $T>0$ and some at $T=0$ belong to the two-dimensional Ising universality class, we also find an absorbing-to-active phase transition in the $\mathbb{Z}_2$ symmetric directed percolation (DP2) class at $T=0$.