Quantization of Conductance Minimum and Index Theorem

TL;DR

This paper demonstrates that the minimum zero-bias conductance in a normal metal-nodal superconductor junction is quantized, linked to the Atiyah-Singer index, and depends on the number of perfect transmission channels, especially under strong impurity scattering.

Contribution

It establishes a connection between the quantized conductance minimum and the Atiyah-Singer index, providing a novel topological interpretation of conductance in such junctions.

Findings

$G_{min}$ is quantized at $(4e^2/h) N_{ZES}$ under strong impurity scattering.

$N_{ZES}$ equals the number of perfect transmission channels.

The index $N_{ZES}$ corresponds to the Atiyah-Singer index from mathematics.

Abstract

We discuss the minimum value of the zero-bias differential conductance $G_{\textrm{min}}$ in a junction consisting of a normal metal and a nodal superconductor preserving time-reversal symmetry. Using the quasiclassical Green function method, we show that $G_{\textrm{min}}$ is quantized at $ (4e^2/h) N_{\mathrm{ZES}}$ in the limit of strong impurity scatterings in the normal metal. The integer $N_{\mathrm{ZES}}$ represents the number of perfect transmission channels through the junction. An analysis of the chiral symmetry of the Hamiltonian indicates that $N_{\mathrm{ZES}}$ corresponds to the Atiyah-Singer index in mathematics.