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...

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The quantum spin Hall (QSH) state is a state of matter characterized by a non-trivial topology of its band structure, and associated conducting edge channels. The QSH state was predicted and experimentally demonstrated to be realized in HgTe quantum wells. The existence of the edge channels has been inferred from local and non-local transport measurements in sufficiently small devices. Here we directly confirm the existence of the edge channels by imaging the magnetic fields produced by current flowing in large Hall bars made from HgTe quantum wells. These images distinguish between current that passes through each edge and the bulk. On tuning the bulk conductivity by gating or raising the temperature, we observe a regime in which the edge channels clearly coexist with the conducting bulk, providing input to the question of how ballistic transport may be limited in the edge channels. Our results represent a versatile method for characterization of new QSH materials systems.

Frequency analysis of the rf emission of oscillating Josephson supercurrent is a powerful passive way of probing properties of topological Josephson junctions. In particular, measurements of the Josephson emission enables to detect the expected presence of topological gapless Andreev bound states that give rise to emission at half the Josephson frequency f J , rather than conventional emission at f J . Here we report direct measurement of rf emission spectra on Josephson junctions made of HgTe-based gate-tunable topological weak links. The emission spectra exhibit a clear signal at half the Josephson frequency f J /2. The linewidths of emission lines indicate a coherence time of 0.3−4 ns for the f J /2 line, much shorter than for the f J line (3−4 ns). These observations strongly point towards the presence of topological gapless Andreev bound states, and pave the way for a future HgTe-based platform for topological quantum computation.

Conventional s-wave superconductivity is understood to arise from singlet pairing of electrons with opposite Fermi momenta, forming Cooper pairs whose net momentum is zero [1]. Several recent studies have focused on structures where such conventional s-wave superconductors are coupled to systems with an unusual configuration of electronic spin and momentum at the Fermi surface. Under these conditions, the nature of the paired state can be modified and the system may even undergo a topological phase transition [2,3]. Here we present measurements and theoretical calculations of several HgTe quantum wells coupled to either aluminum or niobium superconductors and subject to a magnetic field in the plane of the quantum well. By studying the oscillatory response of Josephson interference to the magnitude of the in-plane magnetic field, we find that the induced pairing within the quantum well is spatially varying. Cooper pairs acquire a tunable momentum that grows with magnetic field strength, directly reflecting the response of the spin-dependent Fermi surfaces to the in-plane magnetic field. In addition, in the regime of high electron density, nodes in the induced superconductivity evolve with the electron density in agreement with our model based on the Hamiltonian of Bernevig, Hughes, and Zhang [4]. This agreement allows us to quantitatively extract the value ofg/vF , whereg is the effective g-factor and vF is the Fermi velocity. However, at low density our measurements do not agree with our model in detail. Our new understanding of the interplay between spin physics and superconductivity introduces a way to spatially engineer the order parameter, as well as a general framework within which to investigate electronic spin texture at the Fermi surface of materials.1 arXiv:1509.02940v1 [cond-mat.mes-hall] Sep 2015Below a critical temperature and magnetic field, certain materials undergo a phase transition to the superconducting state. Macroscopically identified through effects such as zero resistivity and the Meissner effect [5], superconductors may further be understood microscopically as arising due to pairing of electrons occupying opposite points on the Fermi surface and having opposite spin. Within a conventional setting this interaction results in Cooper pairs with zero net momentum. However, in certain materials the presence of both magnetic order and superconductivity can lead to intrinsically nonzero pairing momentum as the system enters the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state [6,7]. Studies of both CeCoIn 5 and κ-(BEDT-TTF) 2 Cu(NCS) 2 under large external magnetic fields found evidence for coupled magnetic order and superconductivity, although in each material the field strength needed was in excess of 10 T [8,9].Exotic superconductivity has recently come under additional investigation through the goal of combining s−wave superconductors with materials whose properties are rarely found among the conventional superconductors. For example, inducing the singlet pairing of an s-wave supercon...