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

Abstract

We propose a protocol to locally detect the Berry curvature of the ground state of a three-terminal Josephson junction with a quantum dot based on a synchronic detection of the currents flowing into the reservoir leads when an ac modulation is applied in the device. This local gauge invariant quantity is expressed in terms of the instantaneous Green’s function of the Bogoliubov–de Gennes Hamiltonian, and thus correctly accounts for the topological contribution from both the quasiparticle continuum and the Andreev bound states of the junction. We analyze the contribution to the Berry curvature from the latter by introducing an effective low-energy model. In addition, we propose to induce topological properties in the system by breaking time-reversal symmetry with a microwave field in the large frequency nonresonant 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 two-dimensional honeycomb Haldane lattice and provides a realization of this celebrated model in a solid state device. A relation between the Floquet Berry curvature and the transconductance of the driven system is derived.