Interacting spinless fermions on the square lattice: Charge order, phase separation, and superconductivity

TL;DR

This paper explores the phase diagram of spinless fermions on a square lattice, revealing superconducting, charge-ordered, and phase-separated states influenced by interaction strength, temperature, and electron density.

Contribution

It applies a novel projective truncation approximation to analyze phase transitions and inhomogeneous states in a model of spinless fermions.

Findings

Homogeneous p+ip superconducting phase at high/low densities for attractive interaction

Phase separation occurs near half filling between superconducting phases

Charge-ordered and disordered phases depend on doping and interaction strength

Abstract

We investigate the phase diagram of spinless fermions on a square lattice with nearest-neighbor interaction, using the recently developed projective truncation approximation in Green's function equation of motion. For attractive interaction, the ground state is in an homogeneous p + ip superconducting (SC) phase at high or low electron densities. Near half filling is a phase separation (PS) between the SC phases. Allowing inhomogeneous solution, we obtain p-wave SC domains with positive interface energy. As temperature increases, the SC phases transit into normal phases above Tsc, generating an homogeneous normal phase (far away from n = 1/2), or a PS between normal phases with different densities (close to n = 1/2). Further increasing temperature to Tps, the PS disappears and the particle-hole symmetry of the Hamiltonian is recovered. For repulsive interaction, depending on electron filling, the ground state is in charge-ordered phase (half filling), charge-disordered phase (large hole/electron doping), or PS between them (weak doping). At finite temperature, the regime of charge order phase moves to finite V and extends to finite doping regime.