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A quantum dot coupled to a superconducting contact provides a tunable artificial analogue of a magnetic atom in a superconductor, a paradigmatic quantum impurity problem. We realize such a system with an InAs semiconductor nanowire contacted by an Al-based superconducting electrode. We use an additional normal-type contact as weakly coupled tunnel probe to perform tunneling spectroscopy measurements of the elementary sub-gap excitations, known as Andreev bound states or Yu-Shiba-Rusinov states. We demonstrate that the energy of these states, $\zeta$, scales with the ratio between the Kondo temperature, $T_K$, and the superconducting gap, $\Delta$. $\zeta$ vanishes for $T_K/\Delta \approx 0.6$, denoting a quantum phase transition between spin singlet and doublet ground states. By further leveraging the gate control over the quantum dot parameters, we determine the singlet-doublet phase boundary in the stability diagram of the system. Our experimental results show remarkable quantitative agreement with numerical renormalization group calculations., Comment: 5 pages, 5 figures

We have simultaneously measured conductance and thermoelectric power (TEP) of individual silicon and germanium/silicon core/shell nanowires in the field effect transistor device configuration. As the applied gate voltage changes, the TEP shows distinctly different behaviors while the electrical conductance exhibits the turn-off, subthreshold, and saturation regimes respectively. At room temperature, peak TEP value of $\sim 300 \mu$V/K is observed in the subthreshold regime of the Si devices. The temperature dependence of the saturated TEP values are used to estimate the carrier doping of Si nanowires., Comment: 4 pages, 3 figures

The hybrid combination of superconductors and low-dimensional semiconductors offers a versatile ground for novel device concepts, such as sources of spin-entangled electrons, nanoscale superconducting magnetometers, or recently proposed qubits based on topologically protected Majorana fermions. The underlying physics behind such hybrid devices ultimately rely on the magnetic properties of sub-gap excitations, known as Andreev levels. Here we report the Zeeman effect on the Andreev levels of a semiconductor nanowire quantum dot (QD) strongly coupled to a conventional superconductor. The combination of the large QD g-factor with the large superconductor critical magnetic field allows spin degeneracy to be lifted without suppressing superconductivity. We show that a Zeeman-split Andreev level crossing the Fermi energy signals a quantum phase transition in the ground state of the superconductivity-induced QD, denoting a change in the fermionic parity of the system. This transition manifests itself as a zero-bias conductance anomaly appearing at a finite magnetic field, with properties that resemble those expected for Majorana fermions in a topological superconductor. Although the herein reported zero-bias anomalies do not hold any relation with topological superconductivity, the observed parity transitions can be regarded as precursors of Majorana modes in the long-wire limit., Comment: 16 pages, 9 figures

We studied the low-energy states of spin-1/2 quantum dots defined in InAs/InP nanowires and coupled to aluminium superconducting leads. By varying the superconducting gap, \Delta, with a magnetic field, B, we investigated the transition from strong coupling, \Delta << T_{K}, to weak coupling, \Delta >> T_{K}, where T_{K} is the Kondo temperature. Below the critical field, we observe a persisting zero-bias Kondo resonance that vanishes only for low B or higher temperatures, leaving the room to more robust sub-gap structures at bias voltages between \Delta and 2\Delta. For strong and approximately symmetric tunnel couplings, a Josephson supercurrent is observed in addition to the Kondo peak. We ascribe the coexistence of a Kondo resonance and a superconducting gap to a significant density of intra-gap quasiparticle states, and the finite-bias sub-gap structures to tunneling through Shiba states. Our results, supported by numerical calculations, own relevance also in relation to tunnel-spectroscopy experiments aiming at the observation of Majorana fermions in hybrid nanostructures., Comment: 11 pages, 7 figures

Controlling decoherence is the most challenging task in realizing quantum information hardware. Single electron spins in gallium arsenide are a leading candidate among solid- state implementations, however strong coupling to nuclear spins in the substrate hinders this approach. To realize spin qubits in a nuclear-spin-free system, intensive studies based on group-IV semiconductor are being pursued. In this case, the challenge is primarily control of materials and interfaces, and device nanofabrication. We report important steps toward implementing spin qubits in a predominantly nuclear-spin-free system by demonstrating state preparation, pulsed gate control, and charge-sensing spin readout of confined hole spins in a one-dimensional Ge/Si nanowire. With fast gating, we measure T1 spin relaxation times in coupled quantum dots approaching 1 ms, increasing with lower magnetic field, consistent with a spin-orbit mechanism that is usually masked by hyperfine contributions.

Coupled electron spins in semiconductor double quantum dots hold promise as the basis for solid-state qubits. To date, most experiments have used III-V materials, in which coherence is limited by hyperfine interactions. Ge/Si heterostructure nanowires seem ideally suited to overcome this limitation: the predominance of spin-zero nuclei suppresses the hyperfine interaction and chemical synthesis creates a clean and defect-free system with highly controllable properties. Here we present a top gate-defined double quantum dot based on Ge/Si heterostructure nanowires with fully tunable coupling between the dots and to the leads. We also demonstrate a novel approach to charge sensing in a one-dimensional nanostructure by capacitively coupling the double dot to a single dot on an adjacent nanowire. The double quantum dot and integrated charge sensor serve as an essential building block required to form a solid-state spin qubit free of nuclear spin., Comment: Related work at http://marcuslab.harvard.edu and http://cmliris.harvard.edu

The controlled growth of nanowires (NWs) with dimensions comparable to the Fermi wavelengths of the charge carriers allows fundamental investigations of quantum confinement phenomena. Here, we present studies of proximity-induced superconductivity in undoped Ge/Si core/shell NW heterostructures contacted by superconducting leads. By using a top gate electrode to modulate the carrier density in the NW, the critical supercurrent can be tuned from zero to greater than 100 nA. Furthermore, discrete sub-bands form in the NW due to confinement in the radial direction, which results in stepwise increases in the critical current as a function of gate voltage. Transport measurements on these superconductor-NW-superconductor devices reveal high-order (n = 25) resonant multiple Andreev reflections, indicating that the NW channel is smooth and the charge transport is highly coherent. The ability to create and control coherent superconducting ordered states in semiconductor-superconductor hybrid nanostructures allows for new opportunities in the study of fundamental low-dimensional superconductivity.

We analyze the performance of a recently reported Ge/Si core/shell nanowire transistor using a semiclassical, ballistic transport model and an sp3s*d5 tight-binding treatment of the electronic structure. Comparison of the measured performance of the device with the effects of series resistance removed to the simulated result assuming ballistic transport shows that the experimental device operates between 60 to 85% of the ballistic limit. For this ~15 nm diameter Ge nanowire, we also find that 14-18 modes are occupied at room temperature under ON-current conditions with ION/IOFF=100. To observe true one dimensional transport in a <110> Ge nanowire transistor, the nanowire diameter would have to be much less than about 5 nm. The methodology described here should prove useful for analyzing and comparing on common basis nanowire transistors of various materials and structures.

We demonstrate that semiconductor nanowires measuring just a few nanometers in diameter can be translated, rotated, cut, fused and organized into nontrivial structures using holographic optical traps. The holographic approach to nano-assembly allows for simultaneous independent manipulation of multiple nanowires, including relative translation and relative rotation., Comment: 5 pages, 5 figures

Two-dimensional electron and hole gas systems, enabled through band structure design and epitaxial growth on planar substrates, have served as key platforms for fundamental condensed matter research and high performance devices. The analogous development of one-dimensional (1D) electron or hole gas systems through controlled growth on 1D nanostructure substrates, which could open up opportunities beyond existing carbon nanotube and nanowire systems, has not been realized. Here we report the synthesis and transport studies of a 1D hole gas system based on a free-standing germanium/silicon (Ge/Si) core/shell nanowire heterostructure. Room temperature electrical transport measurements show clearly hole accumulation in undoped Ge/Si nanowire heterostructures, in contrast to control experiments on single component nanowires. Low-temperature studies show well controlled Coulomb blockade oscillations when the Si shell serves as a tunnel barrier to the hole gas in the Ge channel. Transparent contacts to the hole gas also have been reproducibly achieved by thermal annealing. In such devices, we observe conductance quantization at low temperatures, corresponding to ballistic transport through 1D subbands, where the measured subband energy spacings agree with calculations for a cylindrical confinement potential. In addition, we observe a 0.7 structure, which has been attributed to spontaneous spin polarization, suggesting the universality of this phenomenon in interacting 1D systems. Lastly, the conductance exhibits little temperature dependence, consistent with our calculation of reduced backscattering in this 1D system, and suggests that transport is ballistic even at room temperature., Comment: 17 pages, 5 figures

We report low-temperature electrical transport studies of molecule-scale silicon nanowires. Individual nanowires exhibit well-defined Coulomb blockade oscillations characteristic of charge addition to a single nanostructure with length scales up to at least 400 nm. Further studies demonstrate coherent charge transport through discrete single particle quantum levels extending the whole device, and show that the ground state spin configuration follows the Lieb-Mattis theorem. In addition, depletion of the nanowires suggests that phase coherent single-dot characteristics are accessible in a regime where correlations are strong., Comment: 4 pages and 4 figures

The mechanism of lasing in single cadmium sulfide (CdS) nanowire cavities was elucidated by temperature-dependent and time-resolved photoluminescence (PL) measurements. Temperature-dependent PL studies reveal rich spectral features and show that an exciton-exciton interaction is critical to lasing up to 75 K, while an exciton-phonon process dominates at higher temperatures. These measurements together with temperature and intensity dependent life-time and threshold studies suggest that lasing is due to formation of excitons, and moreover, have implications for the design of efficient, low-threshold nanowire lasers., Comment: 4 figures

We characterized the energy band dispersion near the Fermi level in single-walled carbon nanotubes using low-temperature scanning tunneling microscopy. Analysis of energy dependent standing wave oscillations, which result from quantum interference of electrons resonantly scattered by defects, yield a linear energy dispersion near EF, and indicate the importance of parity in scattering for armchair single-walled carbon nanotubes. Additionally, these data provide values of the tight-binding overlap integral and Fermi wavevector in good agreement with previous work, but indicate that the electron coherence length is substantially shortened., Comment: 5 pages, 3 figures

Dislocation-free decoration images containing up to 80,000 vortices have been obtained on high quality Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$ superconducting single crystals. The observed flux line lattices are in the random manifold regime with a roughening exponent of 0.44 for length scales up to 80-100 lattice constants. At larger length scales, the data exhibit nonequilibrium features that persist for different cooling rates and field histories., Comment: 4 pages, 3 gif images, to appear in PRB rapid communication

The electronic density of states of atomically resolved single-walled carbon nanotubes have been investigated using scanning tunneling microscopy. Peaks in the density of states due to the one-dimensional nanotube band structure have been characterized and compared with the results of tight-binding calculations. In addition, tunneling spectroscopy measurements recorded along the axis of an atomically-resolved nanotube exhibit new, low-energy peaks in the density of states near the tube end. Calculations suggest that these features arise from the specific arrangement of carbon atoms that close the nanotube end., Comment: 4 pages including 4 eps figures, to apear in Phys. Rev. Lett

The positions of columnar pins and magnetic flux lines determined from a decoration experiment on BSCCO were used to calculate the single--particle density of states at low temperatures in the Bose glass phase. A wide Coulomb gap is found, with gap exponent $s \approx 1.2$, as a result of the long--range interaction between the vortices. As a consequence, the variable--range hopping transport of flux lines is considerably reduced with respect to the non--interacting case, the effective Mott exponent being enhanced from $p_0 = 1/3$ to $p_{\rm eff} \approx 0.5$ for this specific experiment., Comment: 10 pages, Revtex, 4 figures appended as uu-encoded postscript files, also available as hardcopies from tauber@cmt.harvard.edu