Drastic effect of weak interaction near special points in semiclassical multiterminal superconducting nanostructures

Abstract

A generic semiclassical superconducting nanostructure connected to multiple superconducting terminals hosts a quasi-continuous spectrum of Andreev states. The spectrum is sensitive to the superconducting phases of the terminals. It can be either gapped or gapless depending on the point in the multi-dimensional parametric space of these phases. Special points in this space correspond to setting some terminals to the phase 0 and the rest to the phase of $\pi$. For a generic nanostructure, three distinct spectra come together in the vicinity of a special point: two gapped phases of different topology and a gapless phase separating the two by virtue of topological protection. In this paper, we show that a weak interaction manifesting as quantum fluctuations of superconducting phases drastically changes the spectrum in a narrow vicinity of a special point. We develop an interaction model and derive a universal generic quantum action that describes this situation. The action is complicated by incorporating a non-local in time matrix order parameter, and its full analysis is beyond the scope of the present paper. Here, we identify and address two limits: the semiclassical one and the quantum one, concentrating on the first-order interaction correction in the last case. In both cases, we find that the interaction squeezes the domain of the gapless phase in the narrow vicinity of the point so the gapped phases tend to contact each other immediately, defying the topological protection. We identify the domains of strong coupling where the perturbation theory does not work. In the gapless phase, we find the logarithmic divergence of the first-order corrections. This leads us to an interesting hypothesis: weak interaction might induce an exponentially small gap in the formerly gapless phase.

References in corpus (32)

• Fault-tolerant quantum computation by anyons
• Random-Matrix Theory of Quantum Transport
• Circuit Quantum Electrodynamics
• Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems
• Superconducting Qubits: Current State of Play
• Realizing Majorana zero modes in superconductor-semiconductor heterostructures
• From Andreev to Majorana bound states in hybrid superconductor-semiconductor nanowires
• Multi-terminal Josephson junctions as topological materials
• Single fermion manipulation via superconducting phase differences in multiterminal Josephson junctions
• The $\omega$-SQUIPT: phase-engineering of Josephson topological materials
• Topological transconductance quantization in a four-terminal Josephson junction
• The multi-terminal Josephson effect
• Supercurrent Flow in Multi-Terminal Graphene Josephson Junctions
• Topological Andreev bands in three-terminal Josephson junctions
• Microwave Spectroscopy Reveals the Quantum Geometric Tensor of Topological Josephson Matter
• Non-trivial Chern numbers in three-terminal Josephson junctions
• Singularities of Andreev spectrum in multi-terminal Josephson junction
• Sub-Gap Structure in the Conductance of a Three-Terminal Josephson Junction
• Transport Studies in a Gate-Tunable Three-Terminal Josephson Junction
• Weyl Josephson Circuits
• Observation of Conductance Quantization in InSb Nanowire Networks
• Coherent transport properties of a three-terminal hybrid superconducting interferometer
• Topological supercurrents interaction and fluctuations in the multiterminal Josephson effect
• Topological properties of multi-terminal superconducting nanostructures: effect of a continuous spectrum
• Closing the proximity gap in a metallic Josephson junction between three superconductors
• Non-Abelian monopoles in the multiterminal Josephson effect
• Order, disorder and tunable gaps in the spectrum of Andreev bound states in a multi-terminal superconducting device
• Spin-Weyl quantum unit: theoretical proposal
• Weyl discs: theoretical prediction
• Spintronics with a Weyl point in superconducting nanostructures
• Topology protection-unprotection transition: an example from multi-terminal superconducting nanostructures
• Single charge transport in a fully superconducting SQUISET locally tuned by self-inductance effects