Low-energy transport theory of hybrid topologically superconducting devices

本提案的目的是推进包含拓扑超导体（TSs）的超导混合器件中输运的理论描述。我们采用同等对待马约拉纳准粒子态和连续准粒子态的哈密顿方法，并计划研究三个子项目：1)对于具有破时反转不变性的d类情况，哈密顿方法先前已成功应用于简单隧道结输运的研究。我们在这里进入下一个复杂的层次，研究对应于N- ts -N， TS-N-TS和TS-TS-TS器件的y结设置，其中N指的是正常引线。这些器件可以用t结纳米线在实验中实现。对于N-TS-N三结，我们将研究电导张量和电流噪声相互关系，这可能允许独特的马约拉纳特征。对于TS-N-TS情况，我们研究了连续准粒子的存在如何影响费米子宇称开关行为，以及它如何随着与N引线的隧道耦合的增加而演变。对于TS-TS-TS设置，我们将确定电流-电压特性和电流噪声相互关系。亚隙行为预计受安德烈夫反射的支配。我们还计划测试四方态的出现，即由非平衡共振条件稳定的四粒子束缚态。2)对于对称类DIII的时反转不变TS线，我们计划确定边界格林函数，以研究具有任意接触透明的基本隧道结中的输运。我们将从N-TS情况开始，在这种情况下，人们可以再次期望电导的分析结果。除了电导外，我们还将分析射击噪声。对于S-TS的情况，其中S指的是S波BCS超导体，因为TS导线不再是无自旋的，我们期望有限约瑟夫森电流。此外，Andreev反射应该是可能的，并且这种结的I-V曲线应该包含特征子隙特征。对于TS-TS结，我们将确定平衡约瑟夫森电流-相位关系，噪声特性和电压偏置触点的I-V曲线。最后，我们还将分析diii类和d类TS线之间的隧道结会发生什么。3)这里采用的形式主义的一个明显优点是，人们可以考虑多体相互作用的影响。在这个子项目中，我们研究了涉及d类TS导线的基本隧道结，其中相互作用通过接触中的相关量子点（QD）进入。因此，我们将研究N-QD-TS， TS-QD-TS和S-QD-TS结，其中量子点由单能级安德森杂质模型描述。我们将发展和应用图摄动理论以及量子蒙特卡罗模拟。

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.