Topological transconductance quantization in a four-terminal Josephson junction

Abstract

Recently we predicted that the Andreev bound state spectrum of 4-terminal Josephson junctions may possess topologically protected zero-energy Weyl singularities, which manifest themselves in a quantized transconductance in units of $4e^2/h$ when two of the terminals are voltage biased [R.-P. Riwar et al., Nature Commun. 7, 11167 (2016)]. Here, using the Landauer-Büttiker scattering theory, we compute numerically the currents flowing through such a structure in order to assess the conditions for observing this effect. We show that the voltage below which the transconductance becomes quantized is determined by the interplay of non-adiabatic transitions between Andreev bound states and inelastic relaxation processes. We demonstrate that the topological quantization of the transconductance can be observed at voltages of the order of $10^{-2}\Delta /e$, $\Delta$ being the superconducting gap in the leads.

11 pages, 12 figures; the inset in the top of Fig. 3 is corrected compared with the published version

References in corpus (23)

• Topological Insulators
• Topological insulators and superconductors
• Unpaired Majorana fermions in quantum wires
• Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs
• Experimental discovery of Weyl semimetal TaAs
• Observation of the fractional ac Josephson effect: the signature of Majorana particles
• Experimental observation of Weyl points
• Josephson Current and Noise at a Superconductor-Quantum Spin Hall Insulator-Superconductor Junction
• Hamiltonian approach to the transport properties of superconducting quantum point contacts
• AC JOSEPHSON EFFECT IN A SINGLE QUANTUM CHANNEL
• 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
• Singularities of Andreev spectrum in multi-terminal Josephson junction
• Sub-Gap Structure in the Conductance of a Three-Terminal Josephson Junction
• Ac Josephson Effect in Topological Josephson Junctions
• Anomalous Topological Pumps and Fractional Josephson Effects
• Multipair DC-Josephson Resonances in a biased all-superconducting Bijunction
• Voltage-induced Shapiro steps in a superconducting multi-terminal structure
• Closing the proximity gap in a metallic Josephson junction between three superconductors
• Multiple Andreev reflections in hybrid multiterminal junctions
• Order, disorder and tunable gaps in the spectrum of Andreev bound states in a multi-terminal superconducting device
• Cross-correlations of coherent multiple Andreev reflections

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