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...

Topological superconductors can support localized Majorana states at their boundaries. These quasi-particle excitations have non-Abelian statistics that can be used to encode and manipulate quantum information in a topologically protected manner. While signatures of Majorana bound states have been observed in one-dimensional systems, there is an ongoing effort to find alternative platforms that do not require fine-tuning of parameters and can be easily scalable to large numbers of states. Here we present a novel experimental approach towards a two-dimensional architecture. Using a Josephson junction made of HgTe quantum well coupled to thin-film aluminum, we are able to tune between a trivial and a topological superconducting state by controlling the phase difference φ across the junction and applying an in-plane magnetic field. We determine the topological state of the induced superconductor *

The quantum Hall (QH) effect supports a set of chiral edge states at the boundary of a 2-dimensional electron gas (2DEG) system. A superconductor (SC) contacting these states can induce correlations of the quasi-particles in the dissipationless 1D chiral QH edge states. If the superconducting electrode is narrower than the superconducting coherence length, the incoming electron is correlated to the outgoing hole along the chiral edge state by the Andreev process 1-3 across the SC electrode. In order to realise this crossed Andreev conversion (CAC) 4-7 , it is necessary to fabricate highly transparent and nanometer-scale superconducting junctions to the QH system. Here we report the observation of CAC in a graphene QH system contacted with a nanostructured NbN superconducting electrode. The chemical potential of the edge states across the SC electrode exhibits a sign reversal, providing direct evidence of CAC. This hybrid SC/QH system is a novel route to create isolated non-Abelian anyonic zero modes, in resonance with the chiral QH edge 7-12 .Inducing superconducting correlations via the proximity effect into a 2DEG in the QH regime has been a long standing challenge and has attracted renewed attentions due to its promise for realising non-Abealian zero modes [13][14][15] . Unlike conventional conductors, the 2DEG can exhibit an insulating incompressible bulk electronic state under perpendicular quantizing magnetic fields. In this QH regime, the conduction of electric charge occurs only along the edges via 1D chiral edge states, which the SC can make contacts to. In order to realise the hybrid system of QH and SC, the upper critical field of the SC needs to be high enough such that Cooper pairs in the SC are correlated mostly to the quasiparticles in well-developed 1D QH edge states. The experimental realisation of such hybrid systems often encounters challenges in semiconductor 2DEGs due to the formation of large Schottky barriers at the SC/semiconductor interfaces 16 . Graphene is a compelling candidate for the SC/QH platform, since the zero-band gap of graphene ensures Ohmic contacts for most metals, including SCs with high upper critical fields. Highly transparent SC/graphene interfaces have been demonstrated with strong superconducting proximity interactions and Josephson couplings 15,[17][18][19][20][21][22][23] . In addition, high mobility hBN-encapsulated graphene channels exhibit integer and fractional QH effects 24,25 at much lower magnetic field than the upper critical field of a few select SCs.

Summary: Quantum dots, used as local thermometers, detect upstream heat transport in a ν = 2/3 fractional quantum Hall edge state, even when the state is carrying no net charge. AbstractA system of electrons in two dimensions and strong magnetic fields can be tuned to create a gapped 2D system with one dimensional channels along the edge. Interactions among these edge modes can lead to independent transport of charge and heat, even in opposite directions. Measuring the chirality and transport properties of these charge and heat modes can reveal otherwise hidden structure in the edge. Here, we heat the outer edge of such a quantum Hall system using a quantum point contact. By placing quantum dots upstream and downstream along the edge of the heater, we can measure both the chemical potential and temperature of that edge to study charge and heat transport, respectively. We find that charge is transported exclusively downstream, but heat can be transported upstream when the edge has additional structure related to fractional quantum Hall physics.When a two-dimensional electron system (2DES) is subject to a strong perpendicular magnetic field and tuned such that the ratio of electrons to magnetic flux quanta in the system (ν) is near certain integer or fractional values, the bulk of the system develops a gap due to either quantization of kinetic energy (the integer quantum Hall, or IQH, effect) or strong correlations arising from non-perturbative Coulomb interactions (the fractional quantum Hall, or FQH, effect) [1]. While the bulk (2D) is gapped and incompressible, the edge (1D) of the system contains compressible regions with gapless excitations that carry charge chirally around the system, in a direction determined by the external magnetic field. Compressible edge states have gained more attention recently due to their ability to serve as a bus for quasiparticles that exist in exotic FQH phases [2,3]. These edges, however, can have considerable internal structure that is not apparent from bulk transport measurements.The spatial structure of edges is dictated by the interplay between the external confining potential which defines the edge, an additional harmonic confinement from the magnetic field, and Coulomb interactions. It was predicted [4] and verified [5, 6, 7] that for a smooth, topgate-defined confining potential, it is energetically favorable for the electron density to redistribute slightly to create alternating compressible and incompressible strips. This has the effect of spatially separating edges corresponding to different filling factors. Such an effect is not present in sharper edges [8].Perhaps more surprising than this spatial structure is the possibility of modes that carry energy (or heat) upstream, even as the magnetic field carries the injected charge downstream. The edge of the ν = 2/3 FQH state was originally predicted to consist of a ν = 1 edge of electrons going downstream with a ν = 1/3 edge of holes going upstream [9,10] would be allowed to travel diffusively upstream and downstream, l...

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...

Recent experiments with metallic nanowires devices seem to indicate that superconductivity can be controlled by the application of electric fields. In such experiments, critical currents are tuned and eventually suppressed by relatively small voltages applied to nearby gate electrodes, at odds with current understanding of electrostatic screening in metals. We investigate the impact of gate voltages on superconductivity in similar metal nanowires. Varying materials and device geometries, we study the physical mechanism behind the quench of superconductivity. We demonstrate that the transition from superconducting to resistive state can be understood in detail by tunneling of high-energy electrons from the gate contact to the nanowire, resulting in quasiparticle generation and, at sufficiently large currents, heating. Onset of critical current suppression occurs below gate currents of 100fA, which are challenging to detect in typical experiments.

Nanowires can serve as flexible substrates for hybrid epitaxial growth on selected facets, allowing for design of heterostructures with complex material combinations and geometries. In this work we report on hybrid epitaxy of semiconductor -ferromagnetic insulator -superconductor (InAs/EuS/Al) nanowire heterostructures. We study the crystal growth and complex epitaxial matching of wurtzite InAs / rock-salt EuS interfaces as well as rock-salt EuS / face-centered cubic Al interfaces. Because of the magnetic anisotropy originating from the nanowire shape, the magnetic structure of the EuS phase are easily tuned into single magnetic domains. This effect efficiently ejects the stray field lines along the nanowires. With tunnel spectroscopy measurements of the density of states, we show the material has a hard induced superconducting gap, and magnetic hysteretic evolution which indicates that the magnetic exchange fields are not negligible. These hybrid nanowires fulfil key material requirements for serving as a platform for spin-based quantum applications, such as scalable topological quantum computing.

Gate-tunable semiconductor-superconductor nanowires with superconducting leads form exotic Josephson junctions that are a highly desirable platform for two types of qubits: those with topological superconductivity (Majorana qubits) and those based on tunable anharmonicity (gatemon qubits). Controlling their behavior, however, requires understanding their electrostatic environment and electronic structure. Here we study gated InAs nanowires with epitaxial aluminum shells. By measuring current-phase relations (CPR) and comparing them with analytical and numerical calculations, we show that we can tune the number of modes, determine the transparency of each mode, and tune into regimes in which electron-electron interactions are apparent, indicating the presence of a quantum dot. To take into account electrostatic and geometrical effects, we perform microscopic self-consistent Schrodinger-Poisson numerical simulations, revealing the energy spectrum of Andreev states in the junction as well as their spatial distribution. Our work systematically demonstrates the effect of device geometry, gate voltage and phase bias on mode behavior, providing new insights into ongoing experimental efforts and predictive device design. 1 arXiv:1902.07804v1 [cond-mat.mes-hall]