Motivated by recent experiments searching for Majorana fermions (MFs) in hybrid semiconducting-superconducting nanostructures, we consider a realistic tight-binding model and analyze its transport behavior numerically. In particular, we take into account the presence of a superconducting contact, used in real experiments to extract the current, which is usually not included in theoretical calculations. We show that important features emerge that are absent in simpler models, such as the shift in energy of the proximity gap signal, and the enhanced visibility of the topological gap for increased spin-orbit interaction. We find oscillations of the zero bias peak as a function of the magnetic field and study them analytically. We argue that many of the experimentally observed features hint at an actual spin-orbit interaction larger than the one typically assumed. However, even taking into account all the known ingredients of the experiments and exploring many parameter regimes for MFs, we are not able to reach full agreement with the reported data. Thus, a different physical origin for the observed zero-bias peak cannot be excluded.

We consider the problem of quasiparticle poisoning in a nanowire-based realization of a Majorana qubit, where a spin-orbit-coupled semiconducting wire is placed on top of a (bulk) superconductor. By making use of recent experimental data exhibiting evidence of a low-temperature residual non-equilibrium quasiparticle population in superconductors, we show by means of analytical and numerical calculations that the dephasing time due to the tunneling of quasiparticles into the nanowire may be problematically short to allow for qubit manipulation.Comment: 10 pages, 7 figure

We propose and study a realistic model for the decoherence of topological qubits, based on Majorana fermions in one-dimensional topological superconductors. The source of decoherence is the fluctuating charge on a capacitively coupled gate, modeled by non-interacting electrons. In this context, we clarify the role of quantum fluctuations and thermal fluctuations and find that quantum fluctuations do not lead to decoherence, while thermal fluctuations do. We explicitly calculate decay times due to thermal noise and give conditions for the gap size in the topological superconductor and the gate temperature. Based on this result, we provide simple rules for gate geometries and materials optimized for reducing the negative effect of thermal charge fluctuations on the gate

We consider a model of ballistic quasi-one dimensional semiconducting wire with intrinsic spinorbit interaction placed on the surface of a bulk s-wave superconductor (SC), in the presence of an external magnetic field. This setup has been shown to give rise to a topological superconducting state in the wire, characterized by a pair of Majorana-fermion (MF) bound states formed at the two ends of the wire. Here we demonstrate that, besides the well-known direct overlap-induced energy splitting, the two MF bound states may hybridize via elastic tunneling processes through virtual quasiparticles states in the SC, giving rise to an additional energy splitting between MF states from the same as well as from different wires. Here we consider a model of a wire with Rashba SOI brought into contact with a bulk s-wave SC. Due to the interplay of proximity-induced superconductivity, SOI, and magnetic field, the wire is expected to enter a topological superconducting (TSC) phase for strong enough magnetic fields, and to host MF bound states localized at its two ends 21-23 . The energy of an isolated MF is pinned to the Fermi level inside the mini gap, due to its topological nature. In realistic finite-size wires the two end MF wave functions overlap, and such coupling leads to the splitting in energy of the otherwise doubly degenerate level. In most theoretical approaches, after one has calculated the proximity-induced gap in the wire, one usually forgets about the bulk SC and works with an effective model for the wire. The smallness of the energy splitting of the MF state, relevant for quantum computing purposes, is then determined by the relation between the wire length L and the MF localization length ξ w . Namely, in order to have an exponentially small splitting, it is necessary to require L ξ w . However, we show here that coupling between MFs can be established also through the SC, on a relevant length scale dictated by the coherence length ξ s in the SC (modified by inverse power-law corrections in L). In such cases, the energy splitting is exponentially suppressed in the regime L ξ s . This SC-mediated effect becomes significant if ξ s > ξ w , and, together with other decoherence mechanisms 27-30 , it could become an important issue. On the other hand, this effect also provides useful signatures that can help to identify MFs experimentally.Generally speaking, tunneling between normal leads via an s-wave SC can occur via elastic single-electron cotunneling processes or via local or crossed Andreev reflection 31-33 , which is a two-particle tunneling process. Tunneling in systems with MFs are different in that sense. Two MF states form a single complex fermionic state and coupling via the anomalous propagator of the SC is thus not possible. Still, we show here that hybridization between two MFs can be induced by coherent tunneling of electrons via virtual quasiparticle states of the SC.Model.-The setups considered here are schematically arXiv:1305.4187v2 [cond-mat.mes-hall]

We consider electronic transport through semiconducting nanowires (W) with spin-orbit interaction (SOI), in a hybrid N-W-N setup where the wire is contacted by normal-metal leads (N). We investigate the conductance behavior of the system as a function of gate and bias voltage, magnetic field, wire length, temperature, and disorder. The transport calculations are performed numerically and are based on standard recursive Green's function techniques. In particular, we are interested in understanding if and how it is possible to deduce the strength of the SOI from the transport behavior. This is a very relevant question since so far no clear experimental observation in that direction has been produced. We find that the smoothness of the electrostatic potential profile between the contacts and the wire plays a crucial role, and we show that in realistic regimes the N-W-N setup may mask the effects of SOI, and a trivial behavior with apparent vanishing SOI is observed. We identify an optimal parameter regime, with neither too smooth nor too abrupt potentials, where the signature of SOI is best visible, with and without Fabry-Pérot oscillations, and is most resilient to disorder and temperature effects.