Pseudodiffusive transmission of nodal Dirac fermions through a clean d-wave superconductor

TL;DR

This paper demonstrates that in a clean d-wave superconductor, electron and hole transmission exhibit pseudodiffusive 1/L scaling at zero energy, akin to massless Dirac fermions, unaffected by tunnel barriers.

Contribution

It reveals the pseudodiffusive transmission behavior of nodal Dirac fermions in d-wave superconductors, including effects of tunnel barriers on electrical and thermal currents.

Findings

Electrical and thermal currents scale as 1/L at zero energy.

Tunnel barriers reduce the slope of electrical current scaling.

Thermal current scaling remains unaffected by tunnel barriers.

Abstract

We calculate the transmission of electrons and holes between two normal-metal electrodes (N), separated over a distance L by an impurity-free superconductor (S) with d-wave symmetry of the order parameter. Nodal lines of vanishing excitation gap form ballistic conduction channels for coupled electron-hole excitations, described by an anisotropic two-dimensional Dirac equation. We find that the transmitted electrical and thermal currents, at zero energy, both have the pseudodiffusive 1/L scaling characteristic of massless Dirac fermions - regardless of the presence of tunnel barriers at the NS interfaces. Tunnel barriers reduce the slope of the 1/L scaling in the case of the electrical current, while leaving the thermal current unaffected.