The conductance and thermoelectric power (TEP) of graphene is simultaneously measured using a microfabricated heater and thermometer electrodes. The sign of the TEP changes across the charge neutrality point as the majority carrier density switches from electron to hole. The gate dependent conductance and TEP exhibit a quantitative agreement with the semiclassical Mott relation. In the quantum Hall regime at a high magnetic field, quantized thermopower and Nernst signals are observed and are also in agreement with the generalized Mott relation, except for strong deviations near the charge neutrality point.

Controlling the properties of semiconductor/metal interfaces is a powerful method for designing functionality and improving the performance of electrical devices. Recently semiconductor/superconductor hybrids have appeared as an important example where the atomic scale uniformity of the interface plays a key role in determining the quality of the induced superconducting gap. Here we present epitaxial growth of semiconductor-metal core-shell nanowires by molecular beam epitaxy, a method that provides a conceptually new route to controlled electrical contacting of nanostructures and the design of devices for specialized applications such as topological and gate-controlled superconducting electronics. Our materials of choice, InAs/Al grown with epitaxially matched single-plane interfaces, and alternative semiconductor/metal combinations allowing epitaxial interface matching in nanowires are discussed. We formulate the grain growth kinetics of the metal phase in general terms of continuum parameters and bicrystal symmetries. The method realizes the ultimate limit of uniform interfaces and seems to solve the soft-gap problem in superconducting hybrid structures.

Many present and future applications of superconductivity would benefit from electrostatic control of carrier density and tunnelling rates, the hallmark of semiconductor devices. One particularly exciting application is the realization of topological superconductivity as a basis for quantum information processing. Proposals in this direction based on the proximity effect in semiconductor nanowires are appealing because the key ingredients are currently in hand. However, previous instances of proximitized semiconductors show significant tunnelling conductance below the superconducting gap, suggesting a continuum of subgap states--a situation that nullifies topological protection. Here, we report a hard superconducting gap induced by the proximity effect in a semiconductor, using epitaxial InAs-Al semiconductor-superconductor nanowires. The hard gap, together with favourable material properties and gate-tunability, makes this new hybrid system attractive for a number of applications, as well as fundamental studies of mesoscopic superconductivity.

Quasiparticle excitations can compromise the performance of superconducting devices, causing high frequency dissipation, decoherence in Josephson qubits [1][2][3][4][5][6], and braiding errors in proposed Majorana-based topological quantum computers [7][8][9]. Quasiparticle dynamics have been studied in detail in metallic superconductors [10][11][12][13][14] but remain relatively unexplored in semiconductor-superconductor structures, which are now being intensely pursued in the context of topological superconductivity. To this end, we introduce a new physical system comprised of a gate-confined semiconductor nanowire with an epitaxially grown superconductor layer, yielding an isolated, proximitized nanowire segment. We identify Andreev-like bound states in the semiconductor via bias spectroscopy, determine the characteristic temperatures and magnetic fields for quasiparticle excitations, and extract a parity lifetime (poisoning time) of the bound state in the semiconductor exceeding 10 ms.Semiconductor-superconductor hybrids have been investigated for many years [15][16][17][18][19], but recently have received renewed interest in the context of topological superconductivity, motivated by the realization that combining spin-orbit interaction, Zeeman splitting and proximity coupling to a conventional s-wave superconductor provides the necessary ingredients to create Majorana modes at the ends of a one-dimensional (1D) wire. Such modes are expected to show nonabelian statistics, allowing, in principle, topological encoding of quantum information [20][21][22] among other interesting effects [23,24].Transport experiments on semiconductor nanowires proximitized by a grounded superconductor have recently revealed characteristic features of Majorana modes [25][26][27][28]. Semiconductor quantum dots with superconducting leads have also been explored experimentally [29][30][31][32], and have been proposed as a basis for Majorana chains [33][34][35]. Here, we expand the geometries investigated in this context by creating an isolated semiconductorsupercondutor hybrid quantum dot (HQD) connected to normal leads. The device forms the basis of an isolated * These authors contributed equally to this work.Majorana system with protected total parity, where both the semiconductor nanowire and the metallic superconductor are mesoscopic [36,37].The measured device consists of an InAs nanowire with epitaxial superconducting Al on two facets of the hexagonal wire, with Au ohmic contacts (Figs. 1a,b). Four devices showing similar behavior have been measured. The InAs nanowire was grown without stacking faults using molecular beam epitaxy with Al deposited in situ to ensure high-quality proximity effect [38,39]. Differential conductance, g, was measured in a dilution refrigerator with base electron temperature T ∼ 50 mK using standard ac lock-in techniques. Local side gates, patterned with electron beam lithography, and a global back gate were adjusted to form an Al-InAs HQD in the Coulomb blockade regime, with gate-controlled weak tun...