Zero-energy Andreev surface bound states in the lattice model

TL;DR

This paper investigates the conditions under which zero-energy Andreev surface bound states occur in lattice models of d-wave superconductors, emphasizing the influence of surface orientation and lattice parameters.

Contribution

It provides a detailed analysis of zero-energy Andreev surface states in lattice models, considering both nearest and next-nearest neighbor interactions and various surface orientations.

Findings

Zero-energy Andreev states depend strongly on surface orientation.

States appear only when certain lattice parameters are odd.

Results highlight the sensitivity of surface states to lattice and surface conditions.

Abstract

The conditions for zero-energy Andreev surface bound states to exist are found for the lattice model of d-wave superconductor with arbitrary surface orientation. Both nearest neighbors and next nearest neighbors models are considered. It is shown that the results are very sensitive to the surface orientation. In particular, for half-filled $(hl0)$-surface zero-energy Andreev surface states only appear under the condition that $h$ and $l$ are odd simultaneously