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Register a new userEnhanced Majorana bound states in magnetic chains on superconducting topological insulator edges
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Added by
Luis Gregorio Dias da Silva
Publication date
2020
fields
Physics
and research's language is
English
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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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Magnetic chains on superconducting systems have emerged as a platform for realization of Majorana bound states (MBSs) in condensed matter systems with possible applications to topological quantum computation. In this work we study the MBSs formed in magnetic chains on two-dimensional honeycomb materials with induced superconductivity. We establish phase diagrams showing the topological regions (where MBSs appear), which are strongly dependent on the spiral angle along the chain of the magnetic moments. In particular, find large regions where the topological phase is robust even at large values of the local Zeeman field, thus producing topological regions without an upper bound. Moreover, we show that the energy oscillations of the MBSs can show very different behavior with magnetic field strength. In some parameter regimes we find increasing oscillations amplitudes and decreasing periods, while in the other regimes the complete opposite behavior is found with increasing magnetic field strength. We also find that the topological phase can become dependent on the chain length, particularly in topological regions with a very high or no upper bound. In these systems we see a very smooth evolution from MBSs localized at chain end points to in-gap Andreev bound states spread over the full chain.
The bulk-boundary correspondence establishes a connection between the bulk topological index of an insulator or superconductor, and the number of topologically protected edge bands or states. For topological superconductors in two dimensions the first Chern number is related to the number of protected bands within the bulk energy gap, and is therefore assumed to give the number of Majorana band states in the system. Here we show that this is not necessarily the case. As an example we consider a hexagonal-lattice topological superconductor based on a model of graphene with Rashba spin orbit coupling, proximity induced s-wave superconductivity, and a Zeeman magnetic field. We explore the full Chern number phase diagram of this model, extending what is already known about its parity. We then demonstrate that despite the high Chern numbers that can be seen in some phases these do not strictly always contain Majorana bound states.
Conventional $n$-dimensional topological superconductors (TSCs) have protected gapless $(n - 1)$-dimensional boundary states. In contrast to this, second-order TSCs are characterized by topologically protected gapless $(n - 2)$-dimensional states with usual gapped $(n - 1)$-boundaries. Here, we study a second-order TSC with a two-dimensional (2D) magnetic topological insulator (TI) proximity-coupled to a high-temperature superconductor, where Majorana bound states (MBSs) are localized at the corners of a square sample with gapped edge modes. Due to the mirror symmetry of the hybrid system considered here, there are two MBSs at each corner for both cases: d-wave and $s_{pm}$-wave superconducting pairing. We present the corresponding topological phase diagrams related to the role of the magnetic exchange interaction and the pairing amplitude. A detailed analysis, based on edge theory, reveals the origin of the existence of MBSs at the corners of the 2D sample, which results from the sign change of the Dirac mass emerging at the intersection of any two adjacent edges due to pairing symmetry. Possible experimental realizations are discussed. Our proposal offers a promising platform for realizing MBSs and performing possible non-Abelian braiding in 2D systems.
We study the proximity effect in a topological nanowire tunnel coupled to an s-wave superconducting substrate. We use a general Greens function approach that allows us to study the evolution of the Andreev bound states in the wire into Majorana fermions. We show that the strength of the tunnel coupling induces a topological transition in which the Majorana fermionic states can be destroyed when the coupling is very strong. Moreover, we provide a phenomenologial study of the effects of disorder in the superconductor on the formation of Majorana fermions. We note a non-trivial effect of a quasiparticle broadening term which can take the wire from a topological into a non-topological phase in certain ranges of parameters. Our results have also direct consequences for a nanowire coupled to an inhomogenous superconductor.
We consider a three-dimensional topological insulator (TI) wire with a non-uniform chemical potential induced by gating across the cross-section. This inhomogeneity in chemical potential lifts the degeneracy between two one-dimensional surface state subbands. A magnetic field applied along the wire, due to orbital effects, breaks time-reversal symmetry and lifts the Kramers degeneracy at zero-momentum. If placed in proximity to an $s$-wave superconductor, the system can be brought into a topological phase at relatively weak magnetic fields. Majorana bound states (MBSs), localized at the ends of the TI wire, emerge and are present for an exceptionally large region of parameter space in realistic systems. Unlike in previous proposals, these MBSs occur without the requirement of a vortex in the superconducting pairing potential, which represents a significant simplification for experiments. Our results open a pathway to the realisation of MBSs in present day TI wire devices.
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