Electronic structure of d-wave superconducting quantum wires

TL;DR

This paper investigates the electronic spectra of d-wave superconducting quantum wires, revealing how surface interference effects influence quasiparticle states, with implications for observable surface phenomena and potential exotic pairing states.

Contribution

It provides analytical and numerical analysis of surface and interference effects on quasiparticle spectra in d-wave superconducting wires, highlighting differences based on wire width and orientation.

Findings

Spectra depend on wire width and surface orientation.

Odd N wires have doubly degenerate spectra; even N wires show split levels.

Surface-induced Friedel oscillations are observable via STM.

Abstract

We present analytical and numerical results for the electronic spectra of wires of a d-wave superconductor on a square lattice. The spectra of Andreev and other quasiparticle states, as well as the spatial and particle-hole structures of their wave functions, depend on interference effects caused by the presence of the surfaces and are qualitatively different for half-filled wires with even or odd number of chains. For half-filled wires with an odd number of chains N at (110) orientation, spectra consist of N doubly degenerate branches. By contrast, for even N wires, these levels are split, and all quasiparticle states, even the ones lying above the maximal gap, have the characteristic properties of Andreev bound states. These Andreev states above the gap can be interpreted as a consequence of an infinite sequence of Andreev reflections experienced by quasiparticles along their trajectories bounded by the surfaces of the wire. Our microscopic results for the local density of states display atomic-scale Friedel oscillations due to the presence of the surfaces, which should be observable by scanning tunneling microscopy. For narrow wires the self-consistent treatment of the order parameter is found to play a crucial role. In particular, we find that for small wire widths the finite geometry may drive strong fluctuations or even stablilize exotic quasi-1D pair states with spin triplet character.