Probing Fermi sea topology by Andreev state transport

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.

Main: 4 pages, 3 figures. Supplemental: 3 sections, 2 figures. Published version

References in corpus (6)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Josephson effect in ballistic graphene
• Andreev rectifier: a nonlocal conductance signature of topological phase transitions
• Topological Multipartite Entanglement in a Fermi Liquid
• Quantized Nonlinear Transport with Ultracold Atoms

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• Euler--Chern Correspondence via Topological Superconductivity
• Symmetry-Enforced Fermi Surfaces
• Generic reduction theory for Fermi sea topology in metallic systems
• Quantum oscillation in Hopf-link semimetals
• Quantized nonlinear transport and its breakdown in Fermi gases with Berry curvature
• Chiral adiabatic transmission protected by Fermi surface topology
• Anomalous quasiparticle lifetime in geometric quantum critical metals