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Register a new userMajorana fermion chain at the Quantum Spin Hall edge
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We study a realization of a 1d chain of Majorana bound states at the interfaces between alternating ferromagnetic and superconducting regions at a quantum spin Hall insulator edge. In the limit of well separated Majoranas, the system can be mapped to the transverse field Ising model. The disordered critical point can be reached by tuning the relative magnitude or phases of the ferromagnetic and superconducting order parameters. We compute the voltage dependence of the tunneling current from a metallic tip into the Majorana chain as a direct probe of the random critical state.
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Superconductivity and the quantum Hall effect are considered to be two cornerstones of condensed matter physics. The realization of hybrid structures where these two effects coexist has recently become an active field of research. In this work, we study a Josephson junction where a central region in the quantum Hall regime is proximitized with superconductors that can be driven to a topological phase with an external Zeeman field. In this regime, the Majorana modes that emerge at the ends of each superconducting lead couple to the chiral quantum Hall edge states. This produces distinguishable features in the Andreev levels and Fraunhofer patterns that could help in detecting not only the topological phase transition but also the spin degree of freedom of these exotic quasiparticles. The current phase relation and the spectral properties of the junction throughout the topological transition are fully described by a numerical tight-binding calculation. In pursuance of the understanding of these results, we develop a low-energy spinful model that captures the main features of the numerical transport simulations in the topological phase.
A hybrid setup consisting of a superconductivity-proximitized quantum spin Hall (QSH) insulator and a quantum anomalous Hall (QAH) insulator is proposed for chiral injection of electrons into the Majorana bound state (MBS). An unexplored region of the phase space involving the exchange field induced boost of the helical edge state is then proposed for the detection of the MBS. 2-D transport simulations of our proposed setup is compared with the corresponding setup in the absence of the QAH region, when moderate disorder and a small but finite bulk out-of-plane magnetic field and a Rashba field are included. The remarkable contrast between the two results demonstrates the possibility for an unprecedented immunity from disorder-induced masking of the MBS detection in our proposed setup.
Topological insulators are a newly discovered phase of matter characterized by a gapped bulk surrounded by novel conducting boundary states. Since their theoretical discovery, these materials have encouraged intense efforts to study their properties and capabilities. Among the most striking results of this activity are proposals to engineer a new variety of superconductor at the surfaces of topological insulators. These topological superconductors would be capable of supporting localized Majorana fermions, particles whose braiding properties have been proposed as the basis of a fault-tolerant quantum computer. Despite the clear theoretical motivation, a conclusive realization of topological superconductivity remains an outstanding experimental goal. Here we present measurements of superconductivity induced in two-dimensional HgTe/HgCdTe quantum wells, a material which becomes a quantum spin Hall insulator when the well width exceeds d_{C}=6.3 nm. In wells that are 7.5 nm wide, we find that supercurrents are confined to the one-dimensional sample edges as the bulk density is depleted. However, when the well width is decreased to 4.5 nm the edge supercurrents cannot be distinguished from those in the bulk. These results provide evidence for superconductivity induced in the helical edges of the quantum spin Hall effect, a promising step toward the demonstration of one-dimensional topological superconductivity. Our results also provide a direct measurement of the widths of these edge channels, which range from 180 nm to 408 nm.
We show that quasi-one-dimensional (1D) quantum wires can be written onto the surface of magnetic topological insulator (MTI) thin films by gate arrays. When the MTI is in a quantum anomalous Hall (QAH) state, MTI$/$superconductor quantum wires have especially broad stability regions for both topological and non-topological states, facilitating creation and manipulation of Majorana particles on the MTI surface.
We use the SU(2) slave fermion approach to study a tetrahedral spin 1/2 chain, which is a one-dimensional generalization of the two dimensional Kitaev honeycomb model. Using the mean field theory, coupled with a gauge fixing procedure to implement the single occupancy constraint, we obtain the phase diagram of the model. We then show that it matches the exact results obtained earlier using the Majorana fermion representation. We also compute the spin-spin correlation in the gapless phase and show that it is a spin liquid. Finally, we map the one-dimensional model in terms of the slave fermions to the model of 1D p-wave superconducting model with complex parameters and show that the parameters of our model fall in the topological trivial regime and hence does not have edge Majorana modes.
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