We theoretically examine a scheme for projectively reading out the parity state of a pair of Majorana bound states (MBS) using a tunnel coupled quantum dot. The dot is coupled to one end of the topological wire but isolated from any reservoir, and is capacitively coupled to a charge sensor for measurement. The combined parity of the MBS-dot system is conserved and charge transfer between the MBS and dot only occurs through resonant tunnelling. Resonance is controlled by the dot potential through a local gate and by the MBS energy splitting due to the overlap of the MBS pair wavefunctions. The latter splitting can be tuned from zero (topologically protected regime) to a finite value by gate-driven shortening of the topological wire. Simulations show that the oscillatory nature of the MBS splitting is not a fundamental obstacle to readout, but requires precise gate control of the MBS spatial position and dot potential. With experimentally realistic parameters, we find that high-fidelity parity readout is achievable given nanometer-scale spatial control of the MBS, and that there is a tradeoff between required precisions of temporal and spatial control. Use of the scheme to measure the MBS splitting versus separation would present a clear signature of topological order, and could be used to test the robustness of this order to spatial motion, a key requirement in certain schemes for scalable topological qubits. We show how the scheme can be extended to distinguish valid parity measurements from invalid ones due to gate calibration errors.Comment: 3 figures; added two tables in updated versio

Semiconductor-superconductor hybrid systems provide a promising platform for hosting unpaired Majorana fermions towards the realisation of fault-tolerant topological quantum computing. In this study, we employ the Keldysh Non-Equilibrium Green's function formalism to model quantum transport in normal-superconductor junctions. We analyze III-V semiconductor nanowire Josephson junctions (InAs/Nb) using a three-dimensional discrete lattice model described by the Bogoliubovde Gennes Hamiltonian in the tight-binding approximation, and compute the Andreev bound state spectrum and current-phase relations. Recent experiments [Zuo et al., Phys. Rev. Lett. 119,187704 (2017)] and [Gharavi et al., arXiv:1405.7455v2 (2014] reveal critical current oscillations in these devices, and our simulations confirm these to be an interference effect of the transverse sub-bands in the nanowire. We add disorder to model coherent scattering and study its effect on the critical current oscillations, with an aim to gain a thorough understanding of the experiments. The oscillations in the disordered junction are highly sensitive to the particular realisation of the random disorder potential, and to the gate voltage. A macroscopic current measurement thus gives us information about the microscopic profile of the junction. Finally, we study dephasing in the channel by including elastic phase-breaking interactions. The oscillations thus obtained are in good qualitative agreement with the experimental data, and this signifies the essential role of phase-breaking processes in III-V semiconductor nanowire Josephson junctions. arXiv:1902.10947v3 [cond-mat.mes-hall]

Conductance signatures that signal the presence of Majorana zero modes in a three terminal nanowire-topological superconductor hybrid system are analyzed in detail, in both the clean nanowire limit and in the presence of non-coherent dephasing interactions. In the coherent transport regime for a clean wire, we point out contributions of the local Andreev reflection and the non-local transmissions toward the total conductance lineshapes while clarifying the role of contact broadening on the Majorana conductance lineshapes at the magnetic field parity crossings. Interestingly, at larger B-field parity crossings, the contribution of the Andreev reflection process decreases which is compensated by the non-local processes in order to maintain the conductance quantum regardless of contact coupling strength. In the non-coherent transport regime, we include dephasing that is introduced by momentum randomization processes, that allows one to smoothly transition to the diffusive limit. Here, as expected, we note that while the Majorana character of the zero modes is unchanged, there is a reduction in the conductance peak magnitude that scales with the strength of the impurity scattering potentials. Dephasing due to fluctuating impurities is shown to affect the conductance lineshapes in ways that are distinguishable from the effects of contact-induced tunnel broadening. Most importantly our results reveal that the addition of dephasing in the set up does not lead to any notable length dependence to the conductance of the zero modes, contrary to what one would expect in a gradual transition to the diffusive limit. We believe this work paves a way for a systematic introduction of scattering processes into the realistic modeling of Majorana nanowire hybrid devices and assessing topological signatures in such systems in the presence of non-coherent scattering processes.

The superconducting proximity effect is probed experimentally in Josephson junctions fabricated with InAs nanowires contacted by Nb leads. Contact transparencies [Formula: see text] are observed. The electronic phase coherence length at low temperatures exceeds the channel length. However, the elastic scattering length is a few times shorter than the channel length. Electrical measurements reveal two regimes of quantum transport: (i) the Josephson regime, characterised by a dissipationless current up to ∼100 nA, and (ii) the quantum dot (QD) regime, characterised by the formation of Andreev bound states (ABS) associated with spontaneous QDs inside the nanowire channel. In regime (i), the behaviour of the critical current I versus an axial magnetic field [Formula: see text] shows an unexpected modulation and persistence to fields [Formula: see text] T. In the QD regime, the ABS are modelled as the current-biased solutions of an Anderson-type model. The applicability of devices in both transport regimes to Majorana fermion experiments is discussed.

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