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Register a new userA proposal to probe quantum non-locality of Majorana fermions in tunneling experiments
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Topological Majorana fermion (MF) quasiparticles have been recently suggested to exist in semiconductor quantum wires with proximity induced superconductivity and a Zeeman field. Although the experimentally observed zero bias tunneling peak and a fractional ac-Josephson effect can be taken as necessary signatures of MFs, neither of them constitutes a sufficient smoking gun experiment. Since one pair of Majorana fermions share a single conventional fermionic degree of freedom, MFs are in a sense fractionalized excitations. Based on this fractionalization we propose a tunneling experiment that furnishes a nearly unique signature of end state MFs in semiconductor quantum wires. In particular, we show that a teleportation-like experiment is not enough to distinguish MFs from pairs of MFs, which are equivalent to conventional zero energy states, but our proposed tunneling experiment, in principle, can make this distinction.
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We show how a quantum dot with a ballistic single-channel point contact to a superconductor can be created by means of a gate electrode at the edge of a quantum spin Hall insulator (such as an InAs/GaSb quantum well). A weak perpendicular magnetic field traps a Majorana zero-mode, so that it can be observed in the gate-voltage-averaged differential conductance <dI/dV> as a 4e^2/h zero-bias peak above a (2/3{pi}^2 - 4)e^2/h background. The one-dimensional edge does not permit the braiding of pairs of Majorana fermions, but this obstacle can be overcome by coupling opposite edges at a constriction, allowing for a demonstration of non-Abelian statistics.
Each end of a Kitaev chain in topological phase hosts a Majorana fermion. Zero bias conductance peak is an evidence of Majorana fermion when the two Majorana fermions are decoupled. These two Majorana fermions are separated in space and this nonlocal aspect can be probed when the two are coupled. Crossed Andreev reflection is the evidence of the nonlocality of Majorana fermions. Nonlocality of Majorana fermions has been proposed to be probed by noise measurements since simple conductance measurements cannot probe it due to the almost cancellation of currents from electron tunneling and crossed Andreev reflection. Kitaev ladders on the other hand host subgap Andreev states which can be used to control the relative currents due to crossed Andreev reflection and electron tunneling. We propose to employ Kitaev ladder in series with Kitaev chain and show that the transconductance in this setup can be used as a probe of nonlocality of Majorana fermions by enhancing crossed Andreev reflection over electron tunneling.
Thermodynamic measurements of magnetic fluxes and I-V characteristics in SQUIDs offer promising paths to the characterization of topological superconducting phases. We consider the problem of macroscopic quantum tunneling in an rf-SQUID in a topological superconducting phase. We show that the topological order shifts the tunneling rates and quantum levels, both in the parity conserving and fluctuating cases. The latter case is argued to actually enhance the signatures in the slowly fluctuating limit, which is expected to take place in the quantum regime of the circuit. In view of recent advances, we also discuss how our results affect a $pi$-junction loop.
We report on the observation of excitation of Majorana fermions in a Nb-InSb nanowire quantum dot-Nb hybrid system. The InSb nanowire quantum dot is formed between the two Nb contacts by weak Schottky barriers and is thus in the regime of strong couplings to the contacts. Due to the proximity effect, the InSb nanowire segments covered by superconductor Nb contacts turn to superconductors with a superconducting energy gap $Delta^*$. Under an applied magnetic field larger than a critical value for which the Zeeman energy in the InSb nanowire is $E_zsim Delta^*$, the entire InSb nanowire is found to be in a nontrivial topological superconductor phase, supporting a pair of Majorana fermions, and Cooper pairs can transport between the superconductor Nb contacts via the Majorana fermion states. This transport process will be suppressed when the applied magnetic field becomes larger than a second critical value at which the transition to a trivial topological superconductor phase occurs in the system. This physical scenario has been observed in our experiment. We have found that the measured zero-bias conductance for our hybrid device shows a conductance plateau in a range of the applied magnetic field in quasi-particle Coulomb blockade regions.
Majorana bound states are interesting candidates for applications in topological quantum computation. Low energy models allowing to grasp their properties are hence conceptually important. The usual scenario in these models is that two relevant gapped phases, separated by a gapless point, exist. In one of the phases, topological boundary states are absent, while the other one supports Majorana bound states. We show that a customary model violates this paradigm. The phase that should not host Majorana fermions supports a fractional soliton exponentially localized at only one end. By varying the parameters of the model, we describe analytically the transition between the fractional soliton and two Majorana fermions. Moreover, we provide a possible physical implementation of the model. We further characterize the symmetry of the superconducting pairing, showing that the odd-frequency component is intimately related to the spatial profile of the Majorana wavefunctions.
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