Topological insulators are a newly discovered phase of matter characterized by a gapped bulk surrounded by novel conducting boundary states [1,2,3]. 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 [4,5]. 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 [6]. 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 dC = 6.3 nm [7]. 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.Topological superconductors, like topological insulators, possess a bulk energy gap and gapless surface states. In a topological superconductor, the surface states are predicted to manifest as zero-energy Majorana fermions, fractionalized modes which pair to form conventional fermions. Due to their non-Abelian braiding statistics, achieving control of these Majorana modes is desirable both fundamentally and for [9], and on their direct engineering using s-wave superconductors combined with topological insulators or semiconductors [10,11]. Particularly appealing are implementations in one-dimensional (1D) systems, where Majorana modes would be localized to the ends of a wire. In such a 1D system, restriction to a single spin degree of freedom combined with proximity to an s-wave superconductor would provide the basis for topological superconductivity [12]. Effort in this direction has been advanced by studies of nanowire systems [13,14,15,16,17,18] and by excess current measurements on InAs/GaSb devices [19]. Given the wide interest in Majorana fermions in one dimension, it is essential to expand the search to other systems whose properties are suited toward their control.An attractive route toward a 1D topological superconductor uses as its starting point the twodimensional (2D) quantum spin Hall (QSH) insulator. This topological phase of matter was recently predicted [20,21] and observed [22,23] in HgTe/HgCdTe quantum wells thicker than a critical thickness d C = 6...

The realization of quantum spin Hall effect in HgTe quantum wells is considered a milestone in the discovery of topological insulators. Quantum spin Hall states are predicted to allow current flow at the edges of an insulating bulk, as demonstrated in various experiments. A key prediction yet to be experimentally verified is the breakdown of the edge conduction under broken time-reversal symmetry. Here we first establish a systematic framework for the magnetic field dependence of electrostatically gated quantum spin Hall devices. We then study edge conduction of an inverted quantum well device under broken time-reversal symmetry using microwave impedance microscopy, and compare our findings to a non-inverted device. At zero magnetic field, only the inverted device shows clear edge conduction in its local conductivity profile, consistent with theory. Surprisingly, the edge conduction persists up to 9 T with little change. This indicates physics beyond simple quantum spin Hall model, including material-specific properties and possibly many-body effects.

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We study the weak antilocalization (WAL) effect in the magnetoresistance of narrow HgTe wires fabricated in quantum wells with normal and inverted band ordering. Measurements at different gate voltages indicate that the WAL is only weakly affected by Rashba spin-orbit splitting and persists when the Rashba splitting is about zero. The WAL amplitude in wires with normal band ordering is an order of magnitude smaller than for wires with an inverted band structure. These observations are attributed to the Dirac-like dispersion of the energy bands in HgTe quantum wells. From the magnetic-field and temperature dependencies we extract the dephasing lengths and band Berry phases. The weaker WAL for samples with a normal band structure can be explained by a nonuniversal Berry phase which always exceeds π, the characteristic value for gapless Dirac fermions.