Coupling and braiding Majorana bound states in networks defined in two-dimensional electron gases with proximity-induced superconductivity

Abstract

Two-dimensional electron gases with strong spin-orbit coupling covered by a superconducting layer offer a flexible and potentially scalable platform for Majorana networks. We predict Majorana bound states (MBSs) to appear for experimentally achievable parameters and realistic gate potentials in two designs: either underneath a narrow stripe of a superconducting layer (S-stripes) or where a narrow stripe has been removed from a uniform layer (N-stripes). The coupling of the MBSs can be tuned for both types in a wide range (< 1 neV to > 10 µeV) using gates placed adjacent to the stripes. For both types, we numerically compute the local density of states for two parallel Majorana-stripe ends as well as Majorana trijunctions formed in a tuning-fork geometry. The MBS coupling between parallel Majorana stripes can be suppressed below 1 neV for potential barriers in the meV range for separations of about 200 nm. We further show that the MBS couplings in a trijunction can be gate-controlled in a range similar to the intra-stripe coupling while maintaining a sizable gap to the excited states (tens of µeV). Altogether, this suggests that braiding can carried out on a time scale of 10-100 ns.PACS numbers: 71.10. Pm, 74.50.+r, Majorana bound states (MBSs) are quasiparticles in superconductors that are their own 'self-adjoints' [1][2][3][4]. This requires them to be an equal superposition of particles and holes and ties their energy to the middle of the superconducting gap. MBSs can appear in spatially separate pairs as, for example, at the opposite edges of a topological superconductor. This nonlocality may be utilized for storage and manipulation of quantum information in a topologically protected way [5][6][7]. However, the realization of MBSs requires superconducting p-wave pairing, which appears intrinsically only in exotic materials. Fortunately, p-wave pairing can also be engineered by combining s-wave superconductors with strong spin-orbit materials [8][9][10][11]. Based on this, experiments looked so far for evidence of MBSs in, for example, semiconducting nanowires [12][13][14][15][16][17][18][19], topological insulators [20], magnetic atom chains [21,22], and recently also twodimensional electron gases [23].This progress motivates further experiments that would be more conclusive than the 'local' Majorana features seen in tunneling spectroscopy so far. Theoretical proposals for probing their nonlocal properties range from interference experiments [24-31], teleportation [32], fusion-rule tests [33], coherence measurement of topological qubits [33], and ultimately to braiding [33][34][35][36][37][38][39][40][41][42][43]. The latter would unambiguously demonstrate non-Abelian exchange statistics. Realizing these proposals calls for a flexible platform for building complex and controllable Majorana devices. Such a Majorana platform should preferably also be scalable to build large-scale MBS networks later on as a central part of a topological quantum computer.A potential platform granting such flexibility and sca-FIG. ...

Evidence of topological superconductivity in planar Josephson junctions

“…The phase and magnetic field dependence of the zero-energy states is consistent with a model of Majorana zero modes in finite-size Josephson junctions. Besides providing experimental evidence of phase-tuned topological superconductivity, our devices are compatible with superconducting quantum electrodynamics architectures [11] and scalable to complex geometries needed for topological quantum computing [9,12].…”

Quantum Anomalous Vortex and Majorana Zero Mode in Iron-Based Superconductor Fe(Te,Se)

“…Furthermore, if the STM is used for both manipulating the excess Fe atoms (and the associated QAVs) and measuring the information in the MZMs, the tunneling current will introduce a source of dissipation and dephasing that put an upper bound for the adiabatic braiding time, accounting also for the extrinsic dissipation caused by the environment. This is also true when using techniques other than the STM, as well as using other platforms such as the Majorana nanowires [66]. Thus, in order to braid two MZMs successfully before the loss of coherence, the current associated with the STM needs to be sufficiently weak.…”

Floquet Majorana zero and π modes in planar Josephson junctions

“…The setting we choose for this synthesis is one that is well-characterized and has both practical and theoretical advantages [37][38][39][40][41][42][43][44][45][46]. In particular, we show how one may realize Floquet Majorana fermions in a readily accessible and realistic experimental setting via planar Josephson junctions fabricated from semiconductor heterostructures proximity coupled to superconducting Al [47][48][49][50][51]. * dillon.liu@nyu.edu [47][48][49][50][51].…”

“…In particular, we show how one may realize Floquet Majorana fermions in a readily accessible and realistic experimental setting via planar Josephson junctions fabricated from semiconductor heterostructures proximity coupled to superconducting Al [47][48][49][50][51]. * dillon.liu@nyu.edu [47][48][49][50][51]. A 2DEG with strong spin-orbit coupling is contacted to s-wave superconducting leads that have a phase difference φ.…”