Two regimes for effects of surface disorder on the zero-bias conductance peak of tunnel junctions involving d-wave superconductors

TL;DR

This paper develops a theory describing how surface disorder affects the zero-bias conductance peak in tunnel junctions with d-wave superconductors, revealing two regimes separated by a critical impurity concentration.

Contribution

It introduces a threshold impurity concentration that distinguishes two regimes of surface disorder effects on the ZBCP, including impurity band formation and suppression mechanisms.

Findings

Below threshold, impurities reduce ZBCP weight without broadening.

Impurity bands form and can be resolved at low impurity concentrations.

Above threshold, ZBCP is destroyed or broadened depending on impurity strength.

Abstract

Impurity-induced quasiparticle bound states on a pair-breaking surface of a d-wave superconductor are theoretically described, taking into account hybridization of impurity- and surface-induced Andreev states. Further a theory for effects of surface disorder (of thin impurity surface layer) on the low-bias conductance of tunnel junctions is developed. We find a threshold $n_c$ for surface impurity concentration $n_S$, which separates the two regimes for surface impurity effects on the zero-bias conductance peak (ZBCP). Below the threshold, surface impurities do not broaden the ZBCP, but effectively reduce its weight and generate impurity bands. For low $n_S$ impurity bands can be, in principle, resolved experimentally, being centered at energies of bound states induced by an isolated impurity on the surface. For larger $n_S$ impurity bands are distorted, move to lower energies and, beginning with the threshold concentration $n_S=n_c$, become centered at zero energy. With increasing $n_S$ above the threshold, the ZBCP is quickly destroyed in the case of strong scatterers, while it is gradually suppressed and broaden in the presence of weak impurity potentials. More realistic cases, taking into account additional broadening, not related to the surface disorder, are also considered.