Superconductivity and charge order of confined Fermi systems

TL;DR

This study uses quantum Monte Carlo simulations to explore how confinement and inhomogeneous density affect superconductivity and charge order in the attractive Hubbard model, revealing complex local behaviors and critical temperature estimates.

Contribution

It introduces a detailed analysis of confined Fermi systems with inhomogeneous density, comparing local-density approximation with ab initio methods, and estimates critical temperatures.

Findings

Pair correlations are strong in incommensurate regions at low temperatures.

Charge order is enhanced at sites with one fermion per site.

Certain LDA features at integer filling are suppressed in the full treatment.

Abstract

The low-temperature properties of the two-dimensional attractive Hubbard model are strongly influenced by the fermion density. Away from half-filling, there is a finite-temperature transition to a phase with s-wave pairing order. However, the critical temperature is suppressed to zero at half-filling, where long-range charge-density-wave order also appears, degenerate with superconductivity. This paper presents Determinant Quantum Monte Carlo simulations of the attractive Hubbard model in the presence of a confining potential V which makes the fermion density \rho{} inhomogeneous across the lattice. Pair correlations are shown to be large at low temperatures in regions of the trapped system with incommensurate filling, and to exhibit a minimum as the local density \rho(i) passes through one fermion per site. In this ring of \rho=1, charge order is enhanced. A comparison is made between treating V within the local-density approximation (LDA) and in an ab initio manner. It is argued that certain sharp features of the LDA result at integer filling do not survive the proximity of doped sites. The critical temperature of confined systems of fixed characteristic density is estimated.