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

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.

Manifestation of Majorana modes overlap in the Aharonov–Bohm effect

“…It led to the hard SC gap induced by the proximity effect [7,8] and allowed to approach the theory predicted 2G 0 -height (G 0 = e 2 /h-the conductance quantum) of the zero-bias peak [9][10][11]. In spite of these advantages the nearly quantized peaks measured in the experiments are not sufficiently stable upon the variation of gate voltage and magnetic field [10,12] and can be related to the presence of trivial Andreev bound states which are rather ubiquitous in the inhomogeneous wires [13,14]. Moreover, other transport peculiarities related to the Majorana excitation have not been observed in practice yet.…”

“…In order to treat the transport problem analytically we first address to the Kitaev model at the symmetric point, t = Δ and μ = 0. Employing the Majorana-operator representation, a j = 1 2 γ jA + iγ jB , where γ jA,B = γ + jA,B , one can rewrite the device Hamiltonian (14) in the form…”

Prevalence of trivial zero-energy subgap states in nonuniform helical spin chains on the surface of superconductors

“…Therefore, when the rotation rate of the one-dimensional helical chain is nonuniform, the above mapping is to an effective Hamiltonian that is reminiscent of a one-dimensional semiconductor nanowire with spatially varying parameters. Such nanowires have been considered extensively and it has been shown that trivial zero-energy Andreev bound states (ABSs) are abundant in these systems [51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67].…”

“…In fact, it was shown that trivial Andreev bound states (ABSs) [49,50] are expected to be abundant in nanowires [38]. These trivial states can also result in zero-bias peaks which mimic MBSs and they occur, for instance, due nonuniformities in the nanowire parameters [51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67]. Despite several further signatures of MBSs being proposed, due to the high prevalence of possible zero-energy modes, it remains unclear if a conclusive measurement of MBSs can be performed in nanowire systems.…”

Manifestation of Majorana modes overlap in the Aharonov-Bohm effect

“…It led to the hard SC gap induced by the proximity effect [7,8] and allowed to approach the theory predicted 2G 0 -height (G 0 = e 2 /h -the conductance quantum) of the zero-bias peak [9,10,11]. In spite of these advantages the nearly quantized peaks measured in the experiments are not sufficiently stable upon the variation of gate voltage and magnetic field [10,12] and can be related to the presence of trivial Andreev bound states which are rather ubiquitous in the inhomogeneous wires [13,14]. Moreover, other transport peculiarities related to the Majorana excitation have not been observed in practice yet.…”