Quantization of Conductance Minimum and Index Theorem

Abstract

We discuss the minimum value of the zero-bias differential conductance $G_{\text{min}}$ 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 $G_{\text{min}}$ 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.

5 pages, 1 figure

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