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 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.

arXiv comment5 pages, 4 figures, supplementary material

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• The Multi-terminal Inverse AC Josephson Effect
• Topological phase diagram of a three-terminal Josephson junction: From the conventional to the Majorana regime
• Ground-state quantum geometry in superconductor-quantum dot chains
• Multi-terminal Josephson junctions: a road to topological flux networks
• Zero-bias crossings and peculiar Shapiro maps in graphene Josephson junctions
• Quantum circuits with multiterminal Josephson-Andreev junctions
• A quantum interferometer for quartets in superconducting three-terminal Josephson junctions
• Ultralong-distance quantum correlations in three-terminal Josephson junctions
• Floquet Spectrum and Two-Terminal Conductance of a Transition Metal Dichalcogenide Ribbon under a Circularly Polarized Laser Field
• Proposal for detecting the $\pi -$shifted Cooper quartet supercurrent
• Magnetointerferometry of multiterminal Josephson junctions
• Multiplet Supercurrents in a Josephson Circuit
• Full tomography of topological Andreev bands in graphene Josephson junctions
• Self-heating effects and switching dynamics in graphene multiterminal Josephson junctions
• Quantum transport phenomena induced by time-dependent fields
• Josephson tunnel junction arrays and Andreev weak links: linked by a single energy-phase relation
• Theory of Berry Singularity Markers: Diagnosing Topological Phase Transitions via Lock-In Tomography
• Multiterminal ballistic Josephson junctions coupled to normal leads
• Dynamical Stabilization of Multiplet Supercurrents in Multi-terminal Josephson Junctions