Subgap spectrum of normal-superconductor nanowire junctions: helical regime and Majorana bound states from exceptional points

Oral presentation given at the SpinTech VIII and the 8th International School & Conference on Spintronics and Quantum Information Technology, held on August 10-13th, 2015, in Basel, Switzerland.The linear conductance through a helical region, such as a depleted semiconducting nanowire with strong Rashba spin-orbit coupling and in the presence of a Zeeman field, is expected to exhibit a reentrant behavior with a helical gap of half-quantum conductance [1]. If one takes into account the finite length of the depleted section, this ideal scenario changes and the conductance acquires superimposed Fabry-Perot oscillations [2,3]. These normal transport features translate into distinct subgap states when the leads become superconducting (i.e. in a SNS junction geometry). In particular, Fabry-Perot resonances within the helical gap become zero-energy crossings, well below the critical field Bc at which the superconducting leads become topological. As a function of Zeeman field or Fermi energy, these crossings form characteristic loops and evolve continuously into Majorana bound states as the Zeeman field exceeds Bc. As I will argue, this characteristic loop pattern could be used to unambiguously identify the helical regime in nanowires [3]. Interestingly, when a helical normal region becomes a long contact in a NS geometry, the junction may host Majorana states well below Bc (namely with S in the trivial regime) after crossing an `exceptional point' in parameter space, defined as a degeneracy in the complex eigenvalues of the effective non-Hermitian Hamiltonian of the NS junction. The Majorana character of these states, derived from the eigenvalue bifurcation at the exceptional point, is protected by particle-hole symmetry and is not a result of fine tuning while their finite lifetime can be tuned to arbitrarily large values as the junction approaches perfect Andreev reflection. I will show how exceptional-point Majoranas exhibit the full range of properties associated to conventional closed-system Majorana bound states, while not requiring topological superconductivity [4]