Proposal for the detection and braiding of Majorana fermions in a quantum spin Hall insulator

Abstract

We show how a quantum dot with a ballistic single-channel point contact to a superconductor can be created by means of a gate electrode at the edge of a quantum spin Hall insulator (such as an InAs/GaSb quantum well). A weak perpendicular magnetic field traps a Majorana zero mode, so that it can be observed in the gate-voltageaveraged differential conductance dI/dV as a 4e2 /h zero-bias peak above a ( 2 3 π 2 − 4)e 2 /h background. The one-dimensional edge does not permit the braiding of pairs of Majorana fermions, but this obstacle can be overcome by coupling opposite edges at a constriction, allowing for a demonstration of non-Abelian statistics. 4 The conducting edge of a quantum spin Hall (QSH) insulator seems like an ideal system to search for these elusive particles in a transport experiment: 5,6 Only a single mode propagates in each direction along the edge, unaffected by disorder since backscattering of these helical modes is forbidden by time-reversal symmetry. 7 The QSH edge is thus immune for the multimode and disorder effects that complicate the Majorana-fermion interpretation of transport experiments in semiconductor nanowires. 8,9 Andreev reflection at a superconducting interface has been reported in an InAs/GaSb quantum well, 10 which is a QSH insulator because of a band inversion and the appearance of edge states connecting conduction and valence bands. 11Similar experiments can be tried in HgTe/CdTe quantum wells, where the QSH effect was first discovered. 12,13 We expect a Majorana fermion to be present in these systems, delocalized along the edge connecting a normal and superconducting contact, but without a distinctive resonance in the electrical conductance. Andreev reflection of a helical edge mode doubles the current at all energies inside the band gap, so each edge contributes 2e 2 /h to the differential conductance irrespective of any midgap states.Here we present a method to restore the sensitivity of the conductance to the zero-mode resonance, by trapping the Majorana fermion near the superconducting interface. Only a minor modification of the existing experimental setup 10 is needed, essentially only a gate electrode at one of the edges, to locally push the conduction band through the Fermi level (see Fig. 1). The area under the gate then forms a two-dimensional metallic region, connected to the superconductor by the helical edge mode. Backscattering at this Andreev quantum dot in a weak magnetic field (one flux quantum or less through the dot) provides for an electrostatically tunable confinement of Majorana fermions. We discuss the detection of Majoranas as a short-term application, and braiding as a longer term perspective.There exists a variety of phase coherent backscattering mechanisms for helical edge modes, 14-20 based on different methods of time-reversal symmetry breaking to open a minigap in the edge state spectrum. A locally opened minigap forms a tunnel barrier for the edge modes and two tunnel barriers in series form a quantum dot at the QSH edge.19 For a robust Majoran...

Nonlinear spin-thermoelectric transport in two-dimensional topological insulators

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“…A feasible possibility is the application of local potentials to form quantum antidots. More generally, the presence of constrictions in two-dimensional topological insulators have been proposed to give rise to coherent oscillations [18], transformations between ordinary and topological regimes [19], peaks of noise correlations [20], metal-to-insulator quantum phase transitions [21], nonequilibrium fluctuation relations [22], braiding of Majorana fermions [23], competition between Fabry-Pérot and Mach-Zehnder processes [24], control of edge magnetization [25], and detection of Kondo clouds [26]. Interestingly, König et al have experimentally demonstrated [27] the local manipulation of helical states with back-gate electrodes.…”

Majorana braiding dynamics in nanowires

“…A recent proposed scheme to realize Majorana fermions by using the spin-orbit interaction and Zeeman field [10][11][12][13][14] was eventually applied to a one-dimensional nanowire with proximity induced swave pairing [15,16], which can be fabricated by the present experimental technique [17][18][19][20][21][22]. Furthermore, varieties of proposals exist in order to improve the experimental accessibility and controllability of Majorana modes [23][24][25][26][27][28][29][30][31][32][33][34][35].…”

Transport in superconductor–normal metal–superconductor tunneling structures: Spinful p -wave and spin-orbit-coupled topological wires

“…However, it can be effectively realized in spinful systems by a combination of spin-orbit coupling and explicitly lifting the Kramer's degeneracy of the electrons (e.g., by Zeeman spin splitting through an applied magnetic field). This idea has lead to a number of proposals for realizing topological superconductor in various hybrid structures with conventional s-wave superconductors [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] . There are, however, significant differences between a spinless p-wave superconductor and a spin-split s-wave superconductor with spin-orbit coupling although they both can have localized MZMs at the ends.…”