Berry phase in superconducting multiterminal quantum dots

Abstract

We report on the study of the non-trivial Berry phase in superconducting multiterminal quantum dots biased at commensurate voltages. Starting with the time-periodic Bogoliubov-de Gennes equations, we obtain a tight binding model in the Floquet space, and we solve these equations in the semiclassical limit. We observe that the parameter space defined by the contact transparencies and quartet phase splits into two components with a non-trivial Berry phase. We use the Bohr-Sommerfeld quantization to calculate the Berry phase. We find that if the quantum dot level sits at zero energy, then the Berry phase takes the values ${\phi }_B=0$ or ${\phi }_B=\pi$. We demonstrate that this non-trivial Berry phase can be observed by tunneling spectroscopy in the Floquet spectra. Consequently, the Floquet-Wannier-Stark ladder spectra of superconducting multiterminal quantum dots are shifted by half-a-period if ${\phi }_B=\pi$. Our numerical calculations based on Keldysh Green's functions show that this Berry phase spectral shift can be observed from the quantum dot tunneling density of states.

arXiv comment15 pages, 7 figures. Supplemental Material as ancillary file (3 pages, 5 figures), manuscript in final form

References in corpus (29)

• Topological Insulators
• Berry Phase Effects on Electronic Properties
• Quantum state engineering with Josephson-junction devices
• Advances in the Physics of Magnetic Skyrmions and Perspective for Technology
• Quantum interference and Klein tunneling in graphene heterojunctions
• Geometric quantum computation with NMR
• Landau-Zener-Stuckelberg interferometry
• Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard
• Observation of Berry's Phase in a Solid State Qubit
• Detection of Geometric Phases in Superconducting Nanocircuits
• Klein Backscattering and Fabry-Perot Interference in Graphene Heterojunctions
• Multi-terminal Josephson junctions as topological materials
• Non-equilibrium Josephson effect through helical edge states
• Single fermion manipulation via superconducting phase differences in multiterminal Josephson junctions
• Dynamics of Majorana States in a Topological Josephson Junction
• Fabry-Pérot interference in gapped bilayer graphene with broken anti-Klein tunneling
• The $\omega$-SQUIPT: phase-engineering of Josephson topological materials
• Topological transconductance quantization in a four-terminal Josephson junction
• Production of non-local quartets and phase-sensitive entanglement in a superconducting beam splitter
• Berry Phase Effect on Exciton Transport and Bose Einstein Condensate
• Non-local Supercurrent of Quartets in a Three-Terminal Josephson Junction
• Sub-Gap Structure in the Conductance of a Three-Terminal Josephson Junction
• Tuning anti-Klein to Klein tunneling in bilayer graphene
• Ac Josephson Effect in Topological Josephson Junctions
• Multipair DC-Josephson Resonances in a biased all-superconducting Bijunction
• Closing the proximity gap in a metallic Josephson junction between three superconductors
• Simple Floquet-Wannier-Stark-Andreev viewpoint and emergence of low-energy scales in a voltage-biased three-terminal Josephson junction
• Engineering the Floquet spectrum of superconducting multiterminal quantum dots
• Partially resummed perturbation theory for multiple Andreev reflections in a short three-terminal Josephson junction

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• A quantum interferometer for quartets in superconducting three-terminal Josephson junctions
• Ultralong-distance quantum correlations in three-terminal Josephson junctions
• Driven Andreev molecule
• Proposal for detecting the $\pi -$shifted Cooper quartet supercurrent
• Quartet Tomography in Multiterminal Josephson Junctions
• Energy distribution controlled ballistic Josephson junction
• Long-range coupling between superconducting dots induced by periodic driving
• Multiplet Supercurrents in a Josephson Circuit
• Magnetointerferometry of multiterminal Josephson junctions
• Self-heating effects and switching dynamics in graphene multiterminal Josephson junctions
• Ballistic Andreev interferometers
• Phase dynamics in an AC driven multiterminal Josephson junction analogue
• Revisiting the adiabatic limit in ballistic multiterminal Josephson junctions
• Dynamical Stabilization of Multiplet Supercurrents in Multi-terminal Josephson Junctions
• Multiterminal ballistic Josephson junctions coupled to normal leads