Probing Fermi sea topology by Andreev state transport

TL;DR

This paper proposes a method to determine the topology of the Fermi sea in 2D electron gases by analyzing Andreev state transport in Josephson junctions, revealing a quantized conductance linked to the Fermi sea's Euler characteristic.

Contribution

It introduces a novel approach to probe Fermi sea topology through Andreev state transport in Josephson junctions, connecting topological features to measurable conductance quantization.

Findings

Andreev states' dispersion reflects Fermi sea topology.

Quantized conductance probes the Euler characteristic of the Fermi sea.

Feasibility of measurement in various 2DEG materials is analyzed.

Abstract

We show that the topology of the Fermi sea of a two-dimensional electron gas (2DEG) is reflected in the ballistic Landauer transport along a long and narrow Josephson $\pi$-junction that proximitizes the 2DEG. The low-energy Andreev states bound to the junction are shown to exhibit a dispersion that is sensitive to the Euler characteristic of the Fermi sea ($\chi_F$). We highlight two important relations: one connects the electron/hole nature of Andreev states to the convex/concave nature of Fermi surface critical points, and one relates these critical points to $\chi_F$. We then argue that the transport of Andreev states leads to a quantized conductance that probes $\chi_F$. An experiment is proposed to measure this effect, from which we predict an $I$-$V$ characteristic that not only captures the topology of Fermi sea in metals, but also resembles the rectification effect in diodes. Finally, we evaluate the feasibility of measuring this quantized response in graphene, InAs and HgTe 2DEGs.