Phases of the two-band model of spinless fermions in one dimension

TL;DR

This paper analyzes the phase diagram of a two-band model of spinless fermions in one dimension, revealing how interchain hopping influences superconductivity and phase transitions in the system.

Contribution

It provides analytic expressions for correlation functions and characterizes the phase transition from superconductivity to a Luttinger liquid in this model.

Findings

Finite interchain hopping promotes superconductivity under repulsive interactions.

Superconducting pairs form only in the bonding band during the transition.

The phase diagram includes a mixed phase with unique pairing characteristics.

Abstract

We study the two-band model of spinless fermions in one dimension for weak repulsive interactions. In this case, the model is equivalent to the weakly interacting spinless two-leg ladder. We obtain analytic expressions for the superconducting pairing correlation function and the charge density correlation function, which show, that a finite interchain hopping t_p results in dominant superconductivity for repulsive interactions (for vanishing t_p, we recover previous results). We furthermore find that the transition from the superconducting phase to the usual one-dimensional (Luttinger) metal at large doping occurs via a mixed phase, where superconducting pairs are formed in the bonding band only. We give the phase diagram as a function of temperature and doping.