Abstract
We calculate the conductance of a ballistic point contact to a superconducting wire, produced by the s-wave proximity effect in a semiconductor with spin–orbit coupling in a parallel magnetic field. The conductance G as a function of contact width or Fermi energy shows plateaux at half-integer multiples of 4e2/h if the superconductor is in a topologically nontrivial phase. In contrast, the plateaux are at the usual integer multiples in the topologically trivial phase. Disorder destroys all plateaux except the first, which remains precisely quantized, consistent with previous results for a tunnel contact. The advantage of a ballistic contact over a tunnel contact as a probe of the topological phase is the strongly reduced sensitivity to finite voltage or temperature.
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GENERAL SCIENTIFIC SUMMARY Introduction and background. Majorana fermions are particles that are their own antiparticle, and are predicted to appear as midgap excitations in so-called topological superconductors. The discovery of Majorana fermions as emergent particles in condensed matter would be very remarkable, since they have never been observed as elementary particles in nature. They would be an ideal building block for a quantum computer, because of their reduced sensitivity to decoherence. The central problem that we have addressed is this: how do we distinguish a Majorana fermion from conventional subgap excitations in a topological superconductor?
Main results. We show (see figure) that the signature of a Majorana fermion in a topological superconductor is the half-integer quantization of the conductance of a ballistic point contact (in units of the fundamental superconducting conductance quantum 4e2/h). In contrast, a conventional superconductor without Majorana fermions shows the usual integer quantization. The lowest conductance plateau is robust against disorder and perturbations, and can thus be used as a robust probe of Majorana fermions. Furthermore, the possibility of working in a regime where the point contact is transparent relaxes the requirements on voltage and temperature. Finally, the half-integer quantization is 'smoking gun' evidence for Majorana fermions—it cannot be faked by other subgap excitations.
Wider implications. The half-integer quantization is reminiscent of the celebrated half-integer quantum Hall effect in graphene, and indeed in both cases the origin is a topologically protected zero-mode, which contributes only half the usual amount to the conductance.
Figure. Conductance of a ballistic point contact connected to a superconductor, as a function of Fermi energy (in units of the spin-orbit coupling energy). The blue and red traces are in the topologically trivial and nontrivial phases, respectively. The half-integer plateaux are a signature of the appearance of Majorana fermions in the nontrivial phase.