Abstract
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.
Highlights
Majorana bound states (MBS) can emerge as topologically protected and spatially-separated zero-energy excitations localized at the opposite ends of a one-dimensional (1D) topological superconductor [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]
Their nonabelian exchange statistics [1, 18, 19] may lead to the realization of fault-tolerant quantum computation [20,21,22,23,24,25,26,27]. 1D topological superconductivity can be realized in Majorana nanowires, i.e., proximitized semiconducting nanowires with strong spinorbit coupling and broken time-reversal symmetry [4,5,6,7,8,9,10,11,12,13,14,15,16,17], in epitaxial 1D semiconductor-superconductor heterostructures [28,29,30], arrays of magnetic atoms deposited on a conventional superconductor [31,32,33,34,35,36,37,38,39,40,41], or optically-trapped ultracold fermionic atoms coupled to a molecular BEC cloud [42,43,44,45]
We find that the Majorana/Andreev crossover from impurity-induced Andreev bound states (ABS) to quasi-MBS [86] and from inhomogeneities-induced ABS to MBS [95, 96, 98] can be described as a transition between the two limiting cases of fully-separated Majorana modes (fs-MM) and fully-overlapping Majorana modes (fo-MM), which can be alternatively viewed as a fusion of two MM into a single Dirac-fermion mode
Summary
Majorana bound states (MBS) can emerge as topologically protected and spatially-separated zero-energy excitations localized at the opposite ends of a one-dimensional (1D) topological superconductor [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] Their nonabelian exchange statistics [1, 18, 19] may lead to the realization of fault-tolerant quantum computation [20,21,22,23,24,25,26,27]. Whereas MBS are exponentially localized at the edges of the nanowire or, equivalently, at a topological domain wall, ABS are localized anywhere inside the wire, typically near inhomogeneities or impurities, and do not necessarily exhibit exponential localization [88, 94,95,96, 98]
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