# Topological Andreev Rectification

## TL;DR

This paper develops a theory for topological Andreev rectification in Josephson junctions with 2DEGs, showing that a robust, quantized conductance signal can reveal the Fermi sea's topology even in realistic device geometries.

## Contribution

It extends previous narrow junction models to realistic geometries, demonstrating the robustness of the topological conductance signal under certain scattering conditions.

## Key findings

- Rectified conductance remains quantized with suppressed large momentum scattering.
- Wider junctions and point contacts still exhibit robust conductance signals.
- Simulations suggest experimental observation is feasible in ballistic InAs and graphene devices.

## Abstract

We develop the theory of an Andreev junction, which provides a method to probe the intrinsic topology of the Fermi sea of a two-dimensional electron gas (2DEG). An Andreev junction is a Josephson $\pi$ junction proximitizing a ballistic 2DEG, and exhibits low-energy Andreev bound states that propagate $\textit{along}$ the junction. It has been shown that measuring the nonlocal Landauer conductance due to these Andreev modes in a narrow linear junction leads to a topological Andreev rectification (TAR) effect characterized by a quantized conductance that is sensitive to the Euler characteristic $\chi_F$ of the 2DEG Fermi sea. Here we expand on that analysis and consider more realistic device geometries that go beyond the narrow linear junction and fully adiabatic limits considered earlier. Wider junctions exhibit additional Andreev modes that contribute to the transport and degrade the quantization of the conductance. Nonetheless, we show that an appropriately defined $\textit{rectified conductance}$ remains robustly quantized provided large momentum scattering is suppressed. We verify and demonstrate these predictions by performing extensive numerical simulations of realistic device geometries. We introduce a simple model system that demonstrates the robustness of the rectified conductance for wide linear junctions as well as point contacts, even when the nonlocal conductance is not quantized. Motivated by recent experimental advances, we model devices in specific materials, including InAs quantum wells, as well as monolayer and bilayer graphene. These studies indicate that for sufficiently ballistic samples observation of the TAR effect should be within experimental reach.