Solid-state calculation of crystalline color superconductivity

TL;DR

This paper performs a detailed solid-state-like calculation of the crystalline structure of the LOFF phase in color superconductors, revealing the BCC structure's energetic favorability near the phase transition.

Contribution

It introduces a computational method to analyze 3D crystal structures of the LOFF phase without small amplitude assumptions, advancing understanding of its ground state.

Findings

BCC structure is more energetically favorable than 1D modulation near the phase transition

Higher-order terms are significant in the Ginzburg-Landau approach

Develops a scheme to diagonalize large Hamiltonian matrices efficiently

Abstract

It is generally believed that the inhomogeneous Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase appears in a color superconductor when the pairing between different quark flavors is under the circumstances of mismatched Fermi surfaces. However, the real crystal structure of the LOFF phase is still unclear because an exact treatment of 3D crystal structures is rather difficult. In this work we present a solid-state-like calculation of the ground-state energy of the body-centered cubic (BCC) structure for two-flavor pairing by diagonalizing the Hamiltonian matrix in the Bloch space without assuming a small amplitude of the order parameter. We develop a computational scheme to overcome the difficulties in diagonalizing huge matrices. Our results show that the BCC structure is energetically more favorable than the 1D modulation in a narrow window around the conventional LOFF-normal phase transition point, which indicates the significance of the higher-order terms in the Ginzburg-Landau approach.