Majorana/Andreev crossover and the fate of the topological phase transition in inhomogeneous nanowires

Majorana bound states (MBS) and Andreev bound states (ABS) in realistic Majorana nanowires setups have similar experimental signatures which make them hard to distinguishing one from the other. Here, we characterize the continuous Majorana/Andreev crossover interpolating between fully-separated, partially-separated, and fully-overlapping Majorana modes, in terms of global and local topological invariants, fermion parity, quasiparticle densities, Majorana pseudospin and spin polarizations, density overlaps and transition probabilities between opposite Majorana components. We found that in inhomogeneous wires, the transition between fully-overlapping trivial ABS and nontrivial MBS does not necessarily mandate the closing of the bulk gap of quasiparticle excitations, but a simple parity crossing of partially-separated Majorana modes (ps-MM) from trivial to nontrivial regimes. We demonstrate that fully-separated and fully-overlapping Majorana modes correspond to the two limiting cases at the opposite sides of a continuous crossover: the only distinction between the two can be obtained by estimating the degree of separations of the Majorana components. This result does not contradict the bulk-edge correspondence: Indeed, the field inhomogeneities driving the Majorana/Andreev crossover have a length scale comparable with the nanowire length, and therefore correspond to a nonlocal perturbation which breaks the topological protection of the MBS.

Conductance asymmetries in mesoscopic superconducting devices due to finite bias

Tunneling conductance spectroscopy in normal metal-superconductor junctions is an important tool for probing Andreev bound states in mesoscopic superconducting devices, such as Majorana nanowires. In an ideal superconducting device, the subgap conductance obeys specific symmetry relations, due to particle-hole symmetry and unitarity of the scattering matrix. However, experimental data often exhibits deviations from these symmetries or even their explicit breakdown. In this work, we identify a mechanism that leads to conductance asymmetries without quasiparticle poisoning. In particular, we investigate the effects of finite bias and include the voltage dependence in the tunnel barrier transparency, finding significant conductance asymmetries for realistic device parameters. It is important to identify the physical origin of conductance asymmetries: in contrast to other possible mechanisms such as quasiparticle poisoning, finite-bias effects are not detrimental to the performance of a topological qubit. To that end we identify features that can be used to experimentally determine whether finite-bias effects are the source of conductance asymmetries.

Fundamental dissipation due to bound fermions in the zero-temperature limit

The ground state of a fermionic condensate is well protected against perturbations in the presence of an isotropic gap. Regions of gap suppression, surfaces and vortex cores which host Andreev-bound states, seemingly lift that strict protection. Here we show that in superfluid 3He the role of bound states is more subtle: when a macroscopic object moves in the superfluid at velocities exceeding the Landau critical velocity, little to no bulk pair breaking takes place, while the damping observed originates from the bound states covering the moving object. We identify two separate timescales that govern the bound state dynamics, one of them much longer than theoretically anticipated, and show that the bound states do not interact with bulk excitations.