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.

Topological isoconductance signatures in Majorana nanowires

We consider transport properties of a hybrid device composed by a quantum dot placed between normal and superconducting reservoirs, and coupled to a Majorana nanowire: a topological superconducting segment hosting Majorana bound states (MBSs) at the opposite ends. It is demonstrated that if highly nonlocal and nonoverlapping MBSs are formed in the system, the zero-bias Andreev conductance through the dot exhibits characteristic isoconductance profiles with the shape depending on the spin asymmetry of the coupling between the dot and the topological superconductor. Otherwise, for overlapping MBSs with less degree of nonlocality, the conductance is insensitive to the spin polarization and the isoconductance signatures disappear. This allows to propose an alternative experimental protocol for probing the nonlocality of the MBSs in Majorana nanowires.

Dual Negative Differential of Heat Generation in a Strongly Correlated Quantum Dot Side-Coupled to Majorana Bound States

We study theoretically the properties of local heat originated from energy exchange between electrons passing through a quantum dot (QD) coupled to a phonon bath. The dot is sandwiched between two normal metal leads and also side-coupled to Majorana bound states (MBSs) formed at opposite ends of a topological superconductor nanowire. We find that in addition to the negative differential of heat generation (NDHG) in the Coulomb blockade regime, another NDHG emerges near the leads’ Fermi level due to the dot-MBS coupling. This dual NDHG effect is robust against the variation of intradot Coulomb interaction strength, and disappears if the QD is coupled to regular Fermions. Direct hybridization between the MBSs reduces their impacts on the electronic transport processes, and eliminates the dual NDHG effect. Our results show that the dual NDHG effect is quite efficient for inferring the existence of MBSs, and may remedy some limitations of the detection schemes relying on tunneling spectroscopy technique.