Discrete-Lattice Model for Surface Bound States and Tunneling in d-Wave Superconductors

TL;DR

This paper presents a discrete-lattice model for surface bound states in d-wave superconductors, revealing their superposition nature and introducing a graphical method to analyze them, along with a momentum-dependent lifetime effect.

Contribution

It introduces a novel discrete-lattice approach and graphical construction to analyze surface bound states and their lifetimes in d-wave superconductors.

Findings

Surface bound states are superpositions of multiple excitations.

A graphical method describes the bound states in the surface Brillouin zone.

A momentum-dependent lifetime broadening is derived and explained.

Abstract

Surface bound states in a discrete-lattice model of a $d_{x^2 - y^2}$ cuprate superconductor are shown to be, in general, coherent superpositions of an incoming excitation and more than one outgoing excitation, and a simple graphical construction based on a surface Brillouin zone is developed to describe their nature. In addition, a momentum-dependent lifetime contribution to the width of these bound states as observed in tunneling experiments is derived and elucidated in physical terms.