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Low-energy transport theory of hybrid topologically superconducting devices

混合拓扑超导器件的低能输运理论

基本信息

批准号：
322948903
负责人：
Professor Dr. Reinhold Egger
金额：
--
依托单位：
Lehrstuhl IV: Theoretische Festkörperphysik
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2016
资助国家：
德国
起止时间：
2015-12-31 至 2020-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/322948903?language=en
关键词：
Low energy transport theory hybrid

项目摘要

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.

该提案的目标是推进包含拓扑超导体（TS）的超导混合器件中的输运的理论描述。我们采用的哈密顿方法，它对待马约拉纳和连续准粒子状态在平等的基础上，并计划研究三个子项目：1）对于D类的情况下，时间反演不变性破坏，哈密顿方法已成功地应用于研究通过简单的隧道结的输运。在此，我们将进入下一个复杂级别，并研究对应于N-TS-N、TS-N-TS和TS-TS-TS器件的Y结设置，其中N指的是正常导线。这些器件可以通过采用T结纳米线来实验实现。对于N-TS-N三结，我们将研究电导张量和电流噪声互相关，这可能允许独特的马约拉纳签名。对于TS-N-TS的情况下，我们研究了如何建议的费米子奇偶开关行为将受到连续准粒子的存在，以及它如何随着隧道耦合到N引线的增加而演变。对于TS-TS-TS设置，我们将确定电流-电压特性和电流噪声互相关。子间隙的行为预计将占主导地位的Andreev反射。我们还计划测试四重态的出现，即，非平衡共振条件下稳定的四粒子束缚态。2)对于对称类DIII的时间反演不变TS线，我们计划确定边界绿色的功能，以研究在任意接触透明的基本隧道结中的传输。我们将从N-TS情况开始，在那里我们可以再次期待电导的分析结果。除了电导，我们还将分析散粒噪声。对于S-TS的情况，其中S指的是s波BCS超导体，因为TS线不再是无自旋的，所以我们期望有限的约瑟夫森电流。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带隙特征。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，和电压偏置接触的I-V曲线。最后，我们还将分析DIII类和D类TS导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的优点是，人们可以考虑多体相互作用的影响。在这个子项目中，我们研究涉及D类TS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QD由单能级安德森杂质模型描述。我们将开发和应用图形微扰理论以及量子蒙特卡罗模拟。