Abstract
Majorana fermions act as their own antiparticle, and they have long been thought to be confined to the realm of pure theory. However, interest in them has recently resurfaced, as it was realized through the work of Kitaev that some experimentally accessible condensed matter systems can host these exotic excitations as bound states on the boundaries of 1D chains, and that their topological and non-abelian nature holds promise for quantum computation. Unambiguously detecting the experimental signatures of Majorana bound states has turned out to be challenging, as many other phenomena lead to similar experimental behaviour. Here, we computationally study a ring comprised of two Kitaev model chains with tunnel coupling between them, where an applied magnetic field allows for Aharonov-Bohm interference in transport through the resulting ring structure. We use a non-equilibrium Green's function technique to analyse the transport properties of the ring in both the presence and absence of Majorana zero modes. Further, we show that these results are robust against weak disorder in the presence of an applied magnetic field. This computational model suggests another signature for the presence of these topologically protected bound states can be found in the magnetic field dependence of devices with loop geometries.
Highlights
Majorana fermions were postulated in 1937 as fermionic excitations that act as their own antiparticle [1], but so far they have not been experimentally shown to exist in nature
In this paper we study the interplay between the AB effect and Majorana zero modes (MZMs), and expand on these previous works by analyzing the transport characteristics of an AB ring formed by two coupled Kitaev nanowires
In general if a voltage bias is applied to the device the onsite potential becomes spatially dependent and the integral in Eq (6) must be taken over a range of energies. These complications are important in discussing real devices, they do not change the underlying physics and so we focus on the zero-bias limit
Summary
Majorana fermions were postulated in 1937 as fermionic excitations that act as their own antiparticle [1], but so far they have not been experimentally shown to exist in nature. Previous studies have investigated the case of MZMs in a finite nanowire [47,48] Such models are useful as all experimentally realizable devices are finite, which limits what can be understood from the bulk properties of the materials hosting MZMs. The relation between AB interference and Majorana bound states in such a loop geometry has previously been studied using a scattering matrix approach with the wide-band approximation [49]. We show that mapping the energy resolved transmission through an AB ring comprising two MZMs displays the expected resonance at zero energy Mapping this resonance as a function of magnetic field, on-site potential, or superconducting order parameter results in characteristic responses, suggesting the possibility of unambiguously distinguishing MZMs from trivial bound states.
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