A minimal model of an artificial topological material realized in a two-terminal Josephson junction threaded by Aharonov-Casher fluxes

TL;DR

This paper models a two-terminal Josephson junction with quantum dots and Aharonov-Casher fluxes, revealing Weyl nodes in the Andreev bound state spectrum and proposing a method to detect their topological charge through Berry curvature measurements.

Contribution

It introduces a minimal theoretical framework for topological features in Josephson junctions with AC fluxes and demonstrates how to identify Weyl nodes via adiabatic current measurements.

Findings

Weyl nodes are present in the Andreev bound state spectrum.

Topological charge of nodes can be measured through Berry curvature.

The model provides a way to probe topological properties in superconducting devices.

Abstract

We investigate a minimal model of a two-terminal Josephson junction with conventional superconducting (SC) leads and a pair of interconnected quantum dots in the presence of two Aharonov-Casher (AC) fluxes. The Andreev bound state spectrum features Weyl nodes within a three-dimensional synthetic Brillouin zone defined in the space of these AC fluxes and the SC phase difference. The aim is to determine the location and topological charge of these nodes by probing the Berry curvature on closed surfaces that may enclose them. This is achieved by adiabatically varying the superconducting phase difference and AC fluxes along a path on these surfaces and measuring the associated currents. We define the kinematic curvature as the cross product of a tangent vector along the path and the vector of these currents. In the adiabatic regime, the path-averaged kinematic curvature provides a quantized response equal to the topological charge enclosed by the surface, provided the path uniformly and densely covers it.