Generalization of Blonder-Tinkham-Klapwijk theory to particle-hole mixing boundary conditions: \pi-shift and conductance dips

TL;DR

This paper extends the Blonder-Tinkham-Klapwijk theory to include non-diagonal boundary conditions, explaining anomalous conductance dips via phase c-shift, influenced by magnetic moments, and provides a quantitative model for interface properties.

Contribution

It introduces a generalized boundary condition framework in BTK theory to account for phase c-shift effects in conductance spectra, addressing previously unexplained experimental features.

Findings

Conductance dips are explained by phase c-shift between bulk and interface.

Quantitative conditions for polarization and transparency are identified.

The model reproduces anomalous conductance features observed experimentally.

Abstract

We generalize the Blonder-Tinkham-Klapwijk theory considering non-diagonal boundary conditions in the Bogoliubov-de Gennes scattering problem, to describe anomalous conductance features often reported for normal-metal/superconductor contacts. We calculate the differential conductance spectra showing that conductance dips, not expected in the standard formulation, are explained in terms of phase \pi-shift, between the bulk and the interface order parameter, possibly induced by a localized magnetic moment. A discretized model is used to give quantitative evaluation of the physical conditions, namely the polarization and transparency of the interface, needed to realize the phase gradient.