Low-energy transport theory of hybrid topologically superconducting devices

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The goal of this proposal is to advance the theoretical description of transport in superconducting hybrid devices containing topological superconductors (TSs). We employ the Hamiltonian approach, which treats Majorana and continuum quasiparticle states on equal footing, and plan to study three subprojects: 1) For the class-D case with broken time reversal invariance, the Hamiltonian approach has previously been successfully applied to studies of transport through simple tunnel junctions. We here move to the next level of complexity and study Y-junction setups corresponding to N-TS-N, TS-N-TS, and TS-TS-TS devices, where N refers to a normal lead. These devices can be realized experimentally by employing T-junction nanowires. For the N-TS-N tri-junction, we will study the conductance tensor and current noise cross-correlations, which may allow for unique Majorana signatures. For the TS-N-TS case, we study how the proposed fermion parity switch behavior will be affected by the presence of continuum quasiparticles, and how it evolves with increasing tunnel coupling to the N lead. For the TS-TS-TS setup, we will determine the current-voltage characteristics and the current noise cross-correlations. The sub-gap behavior is expected to be dominated by Andreev reflections. We also plan to test for the occurrence of quartet states, i.e., four-particle bound states stabilized by nonequilibrium resonance conditions. 2) For time-reversal invariant TS wires of symmetry class DIII, we plan to determine the boundary Green's function in order to study transport in basic tunnel junctions with arbitrary contact transparency. We will start with the N-TS case, where one can again expect analytical results for the conductance. Besides the conductance, we will also analyze shot noise. For the S-TS case, where S refers to an s-wave BCS superconductor, since the TS wire is not spinless anymore, we expect a finite Josephson current. In addition, Andreev reflections should be possible, and the I-V curve of such a junction should contain characteristic sub-gap features. For TS-TS junctions, we will determine the equilibrium Josephson current-phase relation, noise properties, and the I-V curve of a voltage-biased contact. Finally, we will also analyze what happens for a tunnel junction between a class-DIII and a class-D TS wire. 3) A distinct advantage of the formalism employed here is that one can take into account many-body interaction effects. In this subproject, we study elementary tunnel junctions involving class-D TS wires, where interactions enter through a correlated quantum dot (QD) in the contact. We shall thus investigate N-QD-TS, TS-QD-TS and S-QD-TS junctions, where the QD is described by a single-level Anderson impurity model. We will develop and apply diagrammatic perturbation theory as well as quantum Monte Carlo simulations.