Berry curvature tomography and realization of topological Haldane model in driven three-terminal Josephson junctions

TL;DR

This paper introduces a method to measure Berry curvature in three-terminal Josephson junctions using AC modulation and Green functions, and demonstrates how to induce and analyze topological phases akin to the Haldane model via microwave driving.

Contribution

It presents a novel protocol for local Berry curvature detection and shows how to realize topological properties in Josephson junctions through microwave-induced symmetry breaking.

Findings

Berry curvature can be detected via Green functions in Josephson junctions.

Topological phases similar to the Haldane model can be engineered with microwave fields.

Floquet-Berry curvature relates to measurable transconductance in driven systems.

Abstract

We propose a protocol to locally detect the Berry curvature of a three terminal Josephson junction with a quantum dot based on a synchronic detection when an AC modulation is applied in the device. This local gauge invariant quantity is expressed in terms of the instantaneous Green function of the Bogoliubov-de Gennes Hamiltonian. We analyze the contribution to the Berry curvature from both the quasi-particle excitations and the Andreev bound state levels by introducing an effective low-energy model. In addition, we propose to induce topological properties in the junction by breaking time-reversal symmetry with a microwave field in the non-resonant regime. In the last case, the Floquet-Andreev levels are the ones that determine the topological structure of the junction, which is formally equivalent to a 2D-honeycomb Haldane lattice. A relation between the Floquet Berry curvature and the transconductance of the driven system is derived.