Atomic scale elastic textures coupled to electrons in superconductors

TL;DR

This paper develops an atomic scale theory linking lattice distortions to electronic structure in superconductors, revealing how elastic textures influence local electronic properties and quasiparticle states.

Contribution

It introduces a unified approach connecting atomic scale elastic textures with continuum elasticity and their impact on electronic states in superconductors.

Findings

Elastic textures around defects modulate local electronic structure.

Lattice deformations depress the superconducting order parameter.

Elasticity propagates electronic responses over long distances.

Abstract

We present an atomic scale theory of lattice distortions using strain related variables and their constraint equations. Our approach connects constrained atomic length scale variations to continuum elasticity and describes elasticity at all length scales. We apply the general approach to a two-dimensional square lattice with a monatomic basis, and find the atomic scale elastic textures around a structural domain wall and a single defect, as exemplary textures. We clarify the microscopic origin of gradient terms, some of which are included phenomenologically in Landau-Ginzburg theory. The obtained elastic textures are used to investigate the effects of elasticity-driven lattice deformation on the nanoscale electronic structure in superconductor by solving the Bogliubov-de Gennes equations with the electronic degrees of freedom coupled to the lattice ones. It is shown that the order parameter is depressed in the regions where the lattice deformation takes place. The calculated local density of states suggests the electronic structure is strongly modulated as a response to the lattice deformation-- the elasticity propagates the electronic response over long distances. In particular, it is possible for the trapping of low-lying quasiparticle states around the defects. These predictions could be directly tested by STM experiments in superconducting materials.