U(1) $\times$ U(1) / Z$_2$ Kosterlitz-Thouless transition of the Larkin-Ovchinnikov phase in an anisotropic two-dimensional system

TL;DR

This paper investigates the Kosterlitz-Thouless transition of the stripe-ordered Larkin-Ovchinnikov phase in a 2D system of coupled fermionic tubes, deriving transition temperatures and phase behavior from a microscopic model.

Contribution

It introduces an effective anisotropic XY model to describe KT transitions in a stripe-ordered LO phase and calculates transition temperatures based on microscopic parameters.

Findings

KT transition temperature scales with intertube tunneling for small t_perp

System undergoes a first-order transition to normal phase at high t_perp

Method applicable to Goldstone excitations of stripe orders involving charge or spin

Abstract

We study Kosterlitz-Thouless (KT) transitions of the Larkin-Ovchinnikov (LO) phase for a two-dimensional system composed of coupled one-dimensional tubes of fermions. The LO phase here is characterized by a stripe structure (periodic in only one direction) in the order parameter. The low energy excitations involve the oscillation of the stripe and the fluctuation of the phase, which can be described by an effective theory composed of two anisotropic XY models. We compute from a microscopic model the coefficients of the XY models from which the KT transition temperatures are determined. We found the $T^{KT} \propto t_{\perp}$ for small intertube tunneling $t_{\perp}$. As $t_{\perp}$ increases the system undergoes a first-order transition to the normal phase at zero temperature. Our method can be used to determine the Goldstone excitations of any stripe order involving charge or spin degrees of freedom.