FFLO- and N\'eel States in finite-size Systems

TL;DR

This paper explores how boundary conditions in finite-size systems affect the pairing order parameter in fermionic superfluids, revealing that fixed boundaries enforce real pairing functions and impact FFLO and Ne9el states.

Contribution

It demonstrates that fixed boundary conditions lead to real pairing amplitudes in finite systems, influencing the existence and nature of FFLO and Ne9el states.

Findings

Pairing amplitude can be chosen as real in finite systems with fixed boundaries.

Boundary conditions drastically affect FFLO state properties.

Results extend to antiferromagnetic states in the Hubbard model.

Abstract

The general structure of the $s$-wave fermionic superfluid pairing order parameter is discussed for systems in thermal equilibrium. We demonstrate that for finite-size systems with fixed boundary conditions the pairing-amplitude may always be chosen as a {\it real} function in space, in contrast to systems underlying periodic boundary conditions, with drastical consequences for several postulated Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states. Using a simple mapping, we also investigate the consequences of our results for antiferromagnetic equilibrium states in a repulsive Hubbard model.