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Register a new userGap oscillations and Majorana bound states in magnetic chains on superconducting honeycomb lattices
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Added by
Luis Gregorio Dias da Silva
Publication date
2018
fields
Physics
and research's language is
English
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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.
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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.
We theoretically obtain the phase diagram of localized magnetic impurity spins arranged in a one-dimensional chain on top of a one- or two-dimensional electron gas with Rashba spin-orbit coupling. The interactions between the spins are mediated by the Ruderman-Kittel-Kasuya-Yosida (RKKY) mechanism through the electron gas. Recent work predicts that such a system may intrinsically support topological superconductivity when a helical spin-density wave is formed in the spins, and superconductivity is induced in the electron gas. We analyze, using both analytical and numerical techniques, the conditions under which such a helical spin state is stable in a realistic situation in the presence of disorder. We show that it becomes unstable towards the formation of (anti) ferromagnetic domains if the disorder in the impurity spin positions $delta R$ becomes comparable with the Fermi wave length. We also examine the stability of the helical state against Gaussian potential disorder in the electronic system using a diagrammatic approach. Our results suggest that in order to stabilize the helical spin state, and thus the emergent topological superconductivity, a sufficiently strong Rashba spin-orbit coupling, giving rise to Dzyaloshinskii-Moriya interactions, is required.
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.
The experimental study of edge states in atomically-thin layered materials remains a challenge due to the difficult control of the geometry of the sample terminations, the stability of dangling bonds and the need to measure local properties. In the case of graphene, localised edge modes have been predicted in zig-zag and bearded edges, characterised by flat dispersions connecting the Dirac points. Polaritons in semiconductor microcavities have recently emerged as an extraordinary photonic platform to emulate 1D and 2D Hamiltonians, allowing the direct visualization of the wavefunctions in both real- and momentum-space as well as of the energy dispersion of eigenstates via photoluminescence experiments. Here we report on the observation of edge states in a honeycomb lattice of coupled micropillars. The lowest two bands of this structure arise from the coupling of the lowest energy modes of the micropillars, and emulate the {pi} and {pi}* bands of graphene. We show the momentum space dispersion of the edge states associated to the zig-zag and bearded edges, holding unidimensional quasi-flat bands. Additionally, we evaluate polarisation effects characteristic of polaritons on the properties of these states.
Majorana quasi-particles may arise as zero-energy bound states in vortices on the surface of a topological insulator that is proximitized by a conventional superconductor. Such a system finds its natural realization in the iron-based superconductor FeTe$_{0.55}$Se$_{0.45}$ that combines bulk $s$-wave pairing with spin helical Dirac surface states, and which thus comprises the ingredients for Majorana modes in absence of an additional proximitizing superconductor. In this work, we investigate the emergence of Majorana vortex modes and lattices in such materials depending on parameters like the magnetic field strength and vortex lattice disorder. A simple 2D square lattice model here allows us to capture the basic physics of the underlying materials system. To address the problem of disordered vortex lattice, which occurs in real systems, we adopt the technique of the singular gauge transformation which we modify such that it can be used in a system with periodic boundary conditions. This approach allows us to go to larger vortex lattices than otherwise accessible, and is successful in replicating several experimental observations of Majorana vortex bound states in the FeTe$_{0.55}$Se$_{0.45}$ platform. Finally it can be related to a simple disordered Majorana lattice model that should be useful for further investigations on the role of interactions, and towards topological quantum computation.
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