Non equilibrium transport and dynamics in conventional and topological superconducting junctions

• Applicant: Gianluca Rastelli, Ph.D.
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2016 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 326061083

• Final Report Year: 2021

Final Report Abstract

Many physicists have started to apply concepts derived from topology, a branch of mathematics dealing with the global properties of objects and their arrangement in space, to the study of physical problems. Topology in low-dimensional systems nowadays plays a central role in many research areas ranging from quantum to classical physics. However, topology can play a fundamental role in higher-dimensional spaces defined by control parameters that play the role of synthetic dimensions. Higher dimensional topological systems have a more complex structure than in low dimensions and their fundamental nature has to be still understood. Quantum topological systems are promising for the realization of qubits which can be topologically protected against the detrimental interaction with the environment. Working in a higher-dimensional space can be an additional resource for novel and more robust protection from noise. Unfortunately, current proposals in the area of condensed matter rarely allow to engineer controlled and higher-dimensional topologies. For instance, topological superconductors often require hardly tunable exotic materials and are limited to three spatial dimensions. An experimental implementation has been realized in ultra-cold atoms but has never been achieved in solid-state devices which the majority of quantum hardware is made of. Hence, there is an urgent need to propose engineered and scalable realizations of higher-dimensional topological quantum systems. Therefore, the main part of the project focused on the topological MJJs. We showed that the nontrivial topology is accessible in the microwave response of the system. All ingredients of our proposals are within reach using current Josephson junctions and quantum microwave technologies. Moreover, similarly to Majorana particles, the non-Abelian quantum ground state of our proposal can in principle be utilized for holonomic quantum manipulations. At the same time, we investigated the charge transport in superconducting junctions hosting YSR states. Owing to recent scanning tunneling microscope (STM) experiments of magnetic impurities on superconducting substrates that host localized Yu-Shiba-Rusinov (YSR) states, we addressed the problem of charge transport mediated by the YSR states.

Publications

• Nonequilibrium Andreev bound states population in short superconducting junctions coupled to a resonator, Phys. Rev. B 96, 144510 (2017)
  Raffael L. Klees, Gianluca Rastelli, Wolfgang Belzig
  
• Decoherence in the quantum Ising model with transverse dissipative interaction in the strongcoupling regime, Phys. Rev. A 98, 052109 (2018)
  Hannes Weisbrich, Cyril Saussol, Wolfgang Belzig, Gianluca Rastelli
  
• Decoherence and relaxation of topological states in extended quantum Ising models, SciPost Phys. 6, 037 (2019)
  Hannes Weisbrich, Wolfgang Belzig, Gianluca Rastelli
  
• Interplay between Yu-Shiba-Rusinov states and multiple Andreev reflections, Phys. Rev. B 101, 235445 (2020)
  Alberto Villas, Raffael L. Klees, Haonan Huang, Christian R. Ast, Gianluca Rastelli, Wolfgang Belzig, Juan Carlos Cuevas
  
• Microwave spectroscopy reveals the quantum geometric tensor of topological Josephson matter, Phys. Rev. Lett. 124, 197002 (2020)
  Raffael L. Klees, Gianluca Rastelli, Juan Carlos Cuevas, Wolfgang Belzig
  
• Geometric Rabi Oscillations and Landau-Zener transitions in non-Abelian system
  Hannes Weisbrich Gianluca Rastelli, Wolfgang Belzig
  
• Ground-state quantum geometry in superconductor–quantum dot chains, Phys. Rev. B 103, 014516 (2021)
  Raffael L. Klees, Juan Carlos Cuevas, Wolfgang Belzig, Gianluca Rastelli
  
• Second Chern number and non-Abelian Berry phase in topological superconducting systems, PRX Quantum 2, 010310 (2021)
  Hannes Weisbrich, Raffael L. Klees, Gianluca Rastelli, Wolfgang Belzig
  
• Spin-dependent tunneling between individual superconducting bound states
  H. Huang, J. Senkpiel, C. Padurariu, R. Drost, A. Villas, R. L. Klees, A. Levy Yeyati, J. C. Cuevas, B. Kubala, J. Ankerhold, K. Kern, C. R. Ast
  
• Tunneling processes between Yu-Shiba-Rusinov bound states, Phys. Rev. B 103, 155407 (2021)
  Alberto Villas, Raffael L. Klees, G. Morrás, Haonan Huang, Christian R. Ast, Gianluca Rastelli, Wolfgang Belzig, Juan Carlos Cuevas