On Local Symmetric Order Parameters of Vortex Lattice States

TL;DR

This paper introduces a refined definition of local symmetric order parameters for vortex lattice states in singlet superconductors, clarifying their phase relations and winding numbers.

Contribution

It provides a new formalism for defining local s-wave, d-wave, and p-wave order parameters with well-defined symmetry and phase properties in vortex lattice states.

Findings

Defined local OPs as representations of C_4 symmetry

Established phase relations under lattice translations

Calculated winding numbers for s-wave and d-wave OPs

Abstract

This paper gives a new refined definition of local symmetric order parameters (OPs)(s-wave, d-wave and p-wave order parameters) of vortex lattice states for singlet superconductivity. s-wave, d-wave and p-wave OPs at a site (m,n) are defined as A, B and E representations of the four fold rotation C_4 at the site (m,n) of nearest neighbor OPs <a_{(m,n)\downarrow}a_{(m+1,n)\uparrow}> etc. The new OPs have a well defined nature such that an OP(e.g. d-wave) at the site obtained under translation by a lattice vector (of the vortex lattice) from a site (m,n) is expressed by the corresponding OP (e.g. d-wave) at the site (m,n) times a phase factor. The winding numbers of s-wave and d-wave OPs are given.