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In this minireview, we outline the recent experimental and theoretical progress in the creation, characterization and manipulation of Majorana bound states (MBSs) in semiconductor-superconductor (SC) hybrid structures. After an introductory overview of the broader field we specifically focus on four of our recent projects in this direction. We show that the emergence of Fano resonances in the differential conductance in a normal lead-Majorana nanowire-quantum dot setup can be exploited to determine if a single MBS is contacted by the normal lead and the quantum dot providing an experimental test of the non-locality of MBSs. In the second project, the tunnel-coupling to two MBSs in an $s$-wave SC-Majorana nanowire Josephson junction (JJ) leads to a finite contribution of the MBSs to the equilibrium Josephson current probing directly the local spin-singlet contribution of the Majorana pair. We then shift our focus from MBSs forming in nanowire systems to MBSs forming in topological JJs. In a single sheet of buckled silicene with proximity induced superconductivity two local electric fields can be used to tune the junction between a topologically trivial and topologically non-trivial regime. In a Corbino geometry topological Josephson junction two MBSs harbored in Josephson vortices can rotate along the JJ and, in the course of this, will be exchanged periodically in the phase difference of the JJ. The tunneling current in a metal tip coupled to the JJ is shown to exhibit signs of the anyonic braiding phase of two MBSs.
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We present measurements of the transport properties of hybrid structures consisting of a Kondo AuFe film and a superconducting Al film. The temperature dependence of the resistance indicates the existence of the superconducting proximity effect in the Kondo AuFe wires over the range of $sim0.5$ $mu$m. Electronic phase coherence in the Kondo AuFe wires has been confirmed by observing the Aharanov-Bohm effect in the magnetoresistance of the loop structure. The amplitude of the magnetoresistance oscillations shows a reentrant behavior with a maximum at $sim$ 870 mK, which results from an interplay between the Kondo effect and the superconducting proximity effect.
We analyse the full counting statistics of charge transfer through a Majorana bound state coupled to an STM tip and show how they can be used for an unambiguous identification of the bound state at the end of the wire. Additionally, we show how to generate Majorana bound states in a simple setup involving a ferromagnetic wire on a superconducting substrate.
We study how the shape of a periodic magnetic field affects the presence of Majorana bound states (MBS) in a nanowire-superconductor system. Motivated by the field configurations that can be produced by an array of nanomagnets, we consider spiral fields with an elliptic cross-section and fields with two sinusoidal components. We show that MBS are robust to imperfect helical magnetic fields. In particular, if the amplitude of one component is tuned to the value determined by the superconducting order parameter in the wire, the MBS can exist even if the second component has a much smaller amplitude. We also explore the effect of the chemical potential on the phase diagram. Our analysis is both numerical and analytical, with good agreement between the two methods.
We investigate the subgap bulk transport through short and wide superconducting hybrid structures based on HgTe quantum wells (QWs). We show that the differential conductance of a normal metal-insulator-superconductor (NIS) proximity structure behaves in a qualitatively different way with respect to the topological phase of the HgTe QW. We compare the differential conductance for the NIS structure within the wave-matching method based on the Bogoliubov-de Gennes equation and the matrix method based on the normal-state scattering matrix and find that the two models agree for highly-doped N and S contacts. We also show that the effect of a possible Rashba spin-orbit interaction on the differential conductance can be significant for weakly doped N and S contacts. Our findings should be important in samples with a large aspect ratio where bulk contributions in transport are dominant.
The most promising mechanisms for the formation of Majorana bound states (MBSs) in condensed matter systems involve one-dimensional systems (such as semiconductor nanowires, magnetic chains, and quantum spin Hall insulator (QSHI) edges) proximitized to superconducting materials. The choice between each of these options involves trade-offs between several factors such as reproducibility of results, system tunability, and robustness of the resulting MBS. In this article, we propose that a combination of two of these systems, namely a magnetic chain deposited on a QSHI edge in contact with a superconducting surface, offers a better choice of tunability and MBS robustness compared to magnetic chain deposited on bulk. We study how the QSHI edge interacts with the magnetic chain, and see how the topological phase is affected by edge proximity. We show that MBSs near the edge can be realized with lower chemical potential and Zeeman field than the ones inside the bulk, independently of the chains magnetic order (ferromagnetic or spiral order). Different magnetic orderings in the chain modify the overall phase diagram, even suppressing the boundless topological phase found in the bulk for chains located at the QSHI edge. Moreover, we quantify the quality of MBSs by calculating the Majorana Polarization (MP) for different configurations. For chains located at the edge, the MP is close to its maximum value already for short chains. For chains located away from the edge, longer chains are needed to attain the same quality as chains located at the edge. The MP also oscillates in phase with the in-gap states, which is relatively unexpected as peaks in the energy spectrum corresponds to stronger overlap of MBSs.
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