Solitonic ground states in (color-) superconductivity

TL;DR

This paper develops a framework to analyze inhomogeneous superconducting phases, finding solitonic structures that are energetically favored over homogeneous phases in a 3+1D model, with implications for phase transitions and excitation spectra.

Contribution

It introduces a general mean-field approach for inhomogeneous (color-) superconductivity beyond Ginzburg-Landau theory, revealing solitonic ground states in a 3+1D toy model.

Findings

Solitonic gap functions are energetically favored over homogeneous phases.

A wider window for the inhomogeneous phase exists compared to simple plane-wave ansatz.

Continuous and first-order phase transitions are observed at different boundaries.

Abstract

We present a general framework for analyzing inhomogeneous (color-) superconducting phases in mean-field approximation without restriction to the Ginzburg-Landau approach. As a first application, we calculate real gap functions with general one-dimensional periodic structures for a 3+1-dimensional toy model having two fermion species. The resulting solutions are energetically favored against homogeneous superconducting (BCS) and normal conducting phases in a window for the chemical potential difference which is about twice as wide as for the most simple plane-wave ansatz ("Fulde-Ferrell phase"). At the lower end of this window, we observe the formation of a soliton lattice and a continuous phase transition to the BCS phase. At the higher end of the window the gap functions are sinusoidal, and the transition to the normal conducting phase is of first order. We also discuss the quasiparticle excitation spectrum in the inhomogeneous phase. Finally, we compare the gap functions with the known analytical solutions of the 1+1-dimensional theory.