# Phase coherent electron transport in asymmetric cross-like Andreev interferometers

## TL;DR

This paper provides a theoretical analysis of quantum coherent electron transport in asymmetric cross-like Andreev interferometers, highlighting how geometric and electron-hole asymmetries influence phase-dependent currents and their controllability.

## Contribution

It reveals the crucial role of asymmetries in enabling Aharonov-Bohm-like effects and phase-coherent currents in these interferometers, advancing understanding of their transport properties.

## Key findings

- Asymmetries induce Aharonov-Bohm-like contributions to supercurrent.
- Phase-coherent currents depend on voltage, temperature, and topology.
- Electron-hole asymmetry causes odd-in-phase current components.

## Abstract

We present a detailed theoretical description of quantum coherent electron transport in voltage-biased cross-like Andreev interferometers. Making use of the charge conjugation symmetry encoded in the quasiclassical formalism, we elucidate a crucial role played by geometric and electron-hole asymmetries in these structures. We argue that a non-vanishing Aharonov-Bohm-like contribution to the current $I_S$ flowing in the superconducting contour may develop only in geometrically asymmetric interferometers making their behavior qualitatively different from that of symmetric devices. The current $I_N$ in the normal contour -- along with $I_S$ -- is found to be sensitive to phase-coherent effects thereby also acquiring a $2\pi$-periodic dependence on the Josephson phase. In asymmetric structures this current develops an odd-in-phase contribution originating from electron-hole asymmetry. We demonstrate that both phase dependent currents $I_S$ and $I_N$ can be controlled and manipulated by tuning the applied voltage, temperature and system topology, thus rendering Andreev interferometers particularly important for future applications in modern electronics.