Induced Superconducting Gap Research Articles

Spin-Orbit Protection of Induced Superconductivity in Majorana Nanowires.

Spin-orbit interaction (SOI) plays a key role in creating Majorana zero modes in semiconductor nanowires proximity coupled to a superconductor. We track the evolution of the induced superconducting gap in InSb nanowires coupled to a NbTiN superconductor in a large range of magnetic field strengths and orientations. Based on realistic simulations of our devices, we reveal SOI with a strength of 0.15-0.35eVÅ. Our approach identifies the direction of the spin-orbit field, which is strongly affected by the superconductor geometry and electrostatic gates.

Anomalous Low-Temperature Enhancement of Supercurrent in Topological-Insulator Nanoribbon Josephson Junctions: Evidence for Low-Energy Andreev Bound States.

We report anomalous enhancement of the critical current at low temperatures in gate-tunable Josephson junctions made from topological insulator BiSbTeSe_{2} nanoribbons with superconducting Nb electrodes. In contrast to conventional junctions, as a function of the decreasing temperature T, the increasing critical current I_{c} exhibits a sharp upturn at a temperature T_{*} around 20% of the junction critical temperature for several different samples and various gate voltages. The I_{c} vs T demonstrates a short junction behavior for T>T_{*}, but crosses over to a long junction behavior for T<T_{*} with an exponential T dependence I_{c}∝exp(-k_{B}T/δ), where k_{B} is the Boltzmann constant. The extracted characteristic energy scale δ is found to be an order of magnitude smaller than the induced superconducting gap of the junction. We attribute the long-junction behavior with such a small δ to low-energy Andreev bound states arising from winding of the electronic wave function around the circumference of the topological insulator nanoribbon.

Germanium Quantum-Well Josephson Field-Effect Transistors and Interferometers.

Hybrid superconductor-semiconductor structures attract increasing attention owing to a variety of potential applications in quantum computing devices. They can serve the realization of topological superconducting systems as well as gate-tunable superconducting quantum bits. Here, we combine a SiGe/Ge/SiGe quantum-well heterostructure hosting high-mobility two-dimensional holes and aluminum superconducting leads to realize prototypical hybrid devices, such as Josephson field-effect transistors (JoFETs) and superconducting quantum interference devices (SQUIDs). We observe gate-controlled supercurrent transport with Ge channels as long as one micrometer and estimate the induced superconducting gap from tunnel spectroscopy measurements. Transmission electron microscopy reveals the diffusion of Ge into the Al contacts, whereas no Al is detected in the Ge channel.

Effects of Gate-Induced Electric Fields on Semiconductor Majorana Nanowires

We study the effect of gate-induced electric fields on the properties of semiconductor-superconductor hybrid nanowires which represent a promising platform for realizing topological superconductivity and Majorana zero modes. Using a self-consistent Schr\"odinger-Poisson approach that describes the semiconductor and the superconductor on equal footing, we are able to access the strong tunneling regime and identify the impact of an applied gate voltage on the coupling between semiconductor and superconductor. We discuss how physical parameters such as the induced superconducting gap and Land\'e g-factor in the semiconductor are modified by redistributing the density of states across the interface upon application of an external gate voltage. Finally, we map out the topological phase diagram as a function of magnetic field and gate voltage for InAs/Al nanowires.

Inducing Strong Superconductivity in WTe2 by a Proximity Effect.

The search for proximity-induced superconductivity in topological materials has generated widespread interest in the condensed matter physics community. The superconducting states inheriting nontrivial topology at interfaces are expected to exhibit exotic phenomena such as topological superconductivity and Majorana zero modes, which hold promise for applications in quantum computation. However, a practical realization of such hybrid structures based on topological semimetals and superconductors has hitherto been limited. Here, we report the strong proximity-induced superconductivity in type-II Weyl semimetal WTe2, in a van der Waals hybrid structure obtained by mechanically transferring NbSe2 onto various thicknesses of WTe2. When the WTe2 thickness ( tWTe2) reaches 21 nm, the superconducting transition occurs around the critical temperature ( Tc) of NbSe2 with a gap amplitude (Δp) of 0.38 meV and an unexpected ultralong proximity length ( lp) up to 7 μm. With the thicker 42 nm WTe2 layer, however, the proximity effect yields Tc ≈ 1.2 K, Δp = 0.07 meV, and a short lp of less than 1 μm. Our theoretical calculations, based on the Bogoliubov-de Gennes equations in the clean limit, predict that the induced superconducting gap is a sizable fraction of the NbSe2 superconducting one when tWTe2 is less than 30 nm and then decreases quickly as tWTe2 increases. This agrees qualitatively well with the experiments. Such observations form a basis in the search for superconducting phases in topological semimetals.

On-chip Hybrid Superconducting-Semiconducting Quantum Circuit

In this paper, we experimentally demonstrate a hybrid superconducting-semiconducting circuit consisting of eight planar and ballistic Nb-In 0.75 Ga 0.25 As-Nb Josephson junctions. E-beam lithography was used to fabricate the Josephson junctions on an InGaAs chip. In contrast to our previous studies on long junctions that were fabricated by photolithography, in this study, we observe the induced superconductivity in an In 0.75 Ga 0.25 As quantum well at higher temperatures, between T = 0.3 and 1 K ( 3 He cryostat temperature range). The induced superconducting gap of Δ ind = 0.65 meV was measured at lowest base temperature T = 300 mK. The effect of temperature and magnetic fields B on the induced superconductivity are presented. Our results suggest that our In 0.75 Ga 0.25 As heterostructure is a promising scalable material system for quantum processing and computing applications.

Engineering hybrid epitaxial InAsSb/Al nanowires for stronger topological protection

The combination of strong spin-orbit coupling, large $g$-factors, and the coupling to a superconductor can be used to create a topologically protected state in a semiconductor nanowire. Here we report on growth and characterization of hybrid epitaxial InAsSb/Al nanowires, with varying composition and crystal structure. We find the strongest spin-orbit interaction at intermediate compositions in zincblende InAs$_{1-x}$Sb$_{x}$ nanowires, exceeding that of both InAs and InSb materials, confirming recent theoretical studies \cite{winkler2016topological}. We show that the epitaxial InAsSb/Al interfaces allows for a hard induced superconducting gap and 2$e$ transport in Coulomb charging experiments, similar to experiments on InAs/Al and InSb/Al materials, and find measurements consistent with topological phase transitions at low magnetic fields due to large effective $g$-factors. Finally we present a method to grow pure wurtzite InAsSb nanowires which are predicted to exhibit even stronger spin-orbit coupling than the zincblende structure.

Evolution of Nanowire Transmon Qubits and Their Coherence in a Magnetic Field.

We present an experimental study of flux- and gate-tunable nanowire transmons with state-of-the-art relaxation time allowing quantitative extraction of flux and charge noise coupling to the Josephson energy. We evidence coherence sweet spots for charge, tuned by voltage on a proximal side gate, where first order sensitivity to switching two-level systems and background 1/f noise is minimized. Next, we investigate the evolution of a nanowire transmon in a parallel magnetic field up to 70mT, the upper bound set by the closing of the induced gap. Several features observed in the field dependence of qubit energy relaxation and dephasing times are not fully understood. Using nanowires with a thinner, partially covering Al shell will enable operation of these circuits up to 0.5T, a regime relevant for topological quantum computation and other applications.

Proximity-effect-induced Superconducting Gap in Topological Surface States \u2013 A Point Contact Spectroscopy Study of NbSe2/Bi2Se3 Superconductor-Topological Insulator Heterostructures

Proximity-effect-induced superconductivity was studied in epitaxial topological insulator Bi2Se3 thin films grown on superconducting NbSe2 single crystals. A point contact spectroscopy (PCS) method was used at low temperatures down to 40 mK. An induced superconducting gap in Bi2Se3 was observed in the spectra, which decreased with increasing Bi2Se3 layer thickness, consistent with the proximity effect in the bulk states of Bi2Se3 induced by NbSe2. At very low temperatures, an extra point contact feature which may correspond to a second energy gap appeared in the spectrum. For a 16 quintuple layer Bi2Se3 on NbSe2 sample, the bulk state gap value near the top surface is ~159 μeV, while the second gap value is ~120 μeV at 40 mK. The second gap value decreased with increasing Bi2Se3 layer thickness, but the ratio between the second gap and the bulk state gap remained about the same for different Bi2Se3 thicknesses. It is plausible that this is due to superconductivity in Bi2Se3 topological surface states induced through the bulk states. The two induced gaps in the PCS measurement are consistent with the three-dimensional bulk state and the two-dimensional surface state superconducting gaps observed in the angle-resolved photoemission spectroscopy (ARPES) measurement.

Transport through a Majorana Island in the Strong Tunneling Regime.

In the presence of Rashba spin-orbit coupling, a magnetic field can drive a proximitized nanowire into a topological superconducting phase [R. M. Lutchyn, J. D. Sau, and S. Das Sarma, Phys. Rev. Lett. 105, 077001 (2010).PRLTAO0031-900710.1103/PhysRevLett.105.077001 and Y. Oreg, G. Refael, and F. von Oppen, Phys. Rev. Lett. 105, 177002 (2010).PRLTAO0031-900710.1103/PhysRevLett.105.177002]. We study the transport properties of such nanowires in the Coulomb blockade regime. The associated with topological superconductivity Majorana modes significantly modify transport and lead to single-electron coherent transmission through the nanowire-a nonlocal signature of topological superconductivity. In this Letter, we focus on the case of strong hybridization of the Majorana modes with normal leads. The induced by hybridization broadening of the Majorana zero-energy states competes with the charging energy, leading to a considerable modification of the Coulomb blockade in a nanowire contacted by two normal leads. We evaluate the two-terminal conductance as a function of the gate voltage, junctions transmission coefficients, and the geometric capacitance of and the induced superconducting gap in the nanowire.

High-Transparency Al/Bi2Te3Double-Barrier Heterostructures

We have fabricated highly transparent Al/Bi2Te3/Al superconductor/normal metal/superconductor double-barrier heterostructures. Transport measurements reveal the presence of multiple Andreev reflections related to two distinct energy gaps that we identify as the induced superconducting gap in the two electrodes. The realization of high-transparency Josephson junctions with topological insulators is an important step towards the study of topological superconductivity and Majorana fermions.

Induced spectral gap and pairing correlations from superconducting proximity effect

We theoretically consider superconducting proximity effect, using the Bogoliubov-de Gennes theory, in heterostructure sandwich-type geometries involving a normal s-wave superconductor and a non-superconducting material with the proximity effect being driven by Cooper pairs tunneling from the superconducting slab to the non-superconducting slab. Applications of the superconducting proximity effect may rely on an induced spectral gap or induced pairing correlations without any spectral gap. We clarify that in a non-superconducting material the induced spectral gap and pairing correlations are independent physical quantities arising from the proximity effect. This is a crucial issue in proposals to create topological superconductivity through the proximity effect. Heterostructures of 3D topological insulator (TI) slabs on conventional s-wave superconductor (SC) substrates provide a platform, with proximity-induced topological superconductivity expected to be observed on the "naked" top surface of a thin TI slab. We theoretically study the induced superconducting gap on this naked surface. In addition, we compare against the induced spectral gap in heterostructures of SC with a normal metal or a semiconductor with strong spin orbit coupling and a Zeeman splitting potential (another platform for topological superconductivity). We find that for any model for the non-SC metal (including metallic TI) the induced spectral gap on the naked surface decays as $L^{-3}$ as the thickness ($L$) of the non-SC slab is increased in contrast to the slower $1/L$ decay of the pairing correlations. Our distinction between proximity-induced spectral gap (with its faster spatial decay) and pairing correlation (with its slower spatial decay) has important implications for the currently active search for topological superconductivity and Majorana fermions in various superconducting heterostructures.

Effects of large induced superconducting gap on semiconductor Majorana nanowires

With the recent achievement of extremely high-quality epitaxial interfaces between InAs nanowires and superconducting Al shells with strong superconductor-semiconductor tunnel coupling, a new regime of proximity-induced superconductivity in semiconductors can be explored where the induced gap may be similar in value to the bulk Al gap (large gap) with negligible subgap conductance (hard gap). We propose several experimentally relevant consequences of this large-gap strong-coupling regime for tunneling experiments, and we comment on the prospects of this regime for topological superconductivity. In particular, we show that the advantages of having a strong spin-orbit coupling and a large spin g-factor in the semiconductor nanowire may both be compromised in this strongly coupled limit, and somewhat weaker interface tunneling may be necessary for achieving optimal proximity superconductivity in the semiconductor nanowire. We derive a minimal, generic theory for the strong-coupling hard-gap regime obtaining good qualitative agreement with the experiment and pointing out future directions for further progress toward Majorana nanowires in hybrid semiconductor-superconductor structures.

Epitaxy of semiconductor-superconductor nanowires.

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.

Exporting superconductivity across the gap: Proximity effect for semiconductor valence-band states due to contact with a simple-metal superconductor

The proximity effect refers to the phenomenon whereby superconducting properties are induced in a normal conductor that is in contact with an intrinsically superconducting material. In particular, the combination of nano-structured semiconductors with bulk superconductors is of interest because these systems can host unconventional electronic excitations such as Majorana fermions when the semiconductor's charge carriers are subject to a large spin-orbit coupling. The latter requirement generally favors the use of hole-doped semiconductors. On the other hand, basic symmetry considerations imply that states from typical simple-metal superconductors will predominantly couple to a semiconductor's conduction-band states and, therefore, in the first instance generate a proximity effect for band electrons rather than holes. In this article, we show how the superconducting correlations in the conduction band are transferred also to hole states in the valence band by virtue of inter-band coupling. A general theory of the superconducting proximity effect for bulk and low-dimensional hole systems is presented. The interplay of inter-band coupling and quantum confinement is found to result in unusual wave-vector dependencies of the induced superconducting gap parameters. One particularly appealing consequence is the density tunability of the proximity effect in hole quantum wells and nanowires, which creates new possibilities for manipulating the transition to nontrivial topological phases in these systems.

Superconducting proximity effect in semiconductor nanowires

We theoretically consider the proximity effect in semiconductor-superconductor hybrid nanostructures, which are being extensively studied in the context of the ongoing search for non-Abelian Majorana fermions in solid state systems. Specifically, we consider the dependence on the thickness of the semiconductor in the direction normal to the interface, a physical effect that has been uncritically neglected in prior work on the subject. Quite surprisingly, we find the unanticipated result that increasing the semiconductor thickness leads to a suppression of the induced superconducting gap due to proximity-induced interband coupling. As a result, in the limit of strong semiconductor-superconductor coupling, the proximity-induced gap becomes much smaller than the bulk superconductor gap and depends weakly on the interface transparency.

Proximity-induced high-temperature superconductivity in the topological insulators Bi2Se3 and Bi2Te3

Interest in the superconducting proximity effect has been reinvigorated recently by novel optoelectronic applications as well as by the possible emergence of the elusive Majorana fermion at the interface between topological insulators and superconductors. Here we produce high-temperature superconductivity in Bi(2)Se(3) and Bi(2)Te(3) via proximity to Bi(2)Sr(2)CaCu(2)O(8+δ), to access higher temperature and energy scales for this phenomenon. This was achieved by a new mechanical bonding technique that we developed, enabling the fabrication of high-quality junctions between materials, unobtainable by conventional approaches. We observe proximity-induced superconductivity in Bi(2)Se(3) and Bi(2)Te(3) persisting up to at least 80 K-a temperature an order of magnitude higher than any previous observations. Moreover, the induced superconducting gap in our devices reaches values of 10 mV, significantly enhancing the relevant energy scales. Our results open new directions for fundamental studies in condensed matter physics and enable a wide range of applications in spintronics and quantum computing.

Majorana Edge States in Interacting One-Dimensional Systems

We show that one-dimensional electron systems in the proximity of a superconductor that support Majorana edge states are extremely susceptible to electron-electron interactions. Strong interactions generically destroy the induced superconducting gap that stabilizes the Majorana edge states. For weak interactions, the renormalization of the gap is nonuniversal and allows for a regime in which the Majorana edge states persist. We present strategies of how this regime can be reached.

Self-consistent superconducting proximity effect at the quantum spin Hall edge

We study self-consistently a microscopic interface between a quantum spin Hall insulator (QSHI) and a superconductor (SC), focusing on properties related to Majorana fermion creation. For an $s$-wave SC we show that odd-in-momentum, or $p$-wave, order parameters exist for all doping levels of the QSHI and that they can be related to different spinless Cooper pair amplitudes. Despite this, the induced superconducting gap in the QSHI always retains its $s$-wave character, validating the commonly used effective model for superconductivity in a topological insulator. For a ${d}_{\mathit{xy}}$-wave SC, we show that a Majorana mode is only created at finite doping and that there is no excitation gap protecting this mode.

Electron-correlation effects on the properties of LaxSr1-xTiO3.

A theoretical study of the electron-correlation effects on the properties of ${\mathrm{La}}_{\mathit{x}}$${\mathrm{Sr}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{TiO}}_{3}$ is presented. Using a single band repulsive Hubbard model employing the Gutzwiller approximation we study the effect of electron correlations on the effective-mass, band narrowing, plasma frequency, and spin susceptibility. The doping dependence of these properties are found to be qualitatively in agreement with recent experimental studies on ${\mathrm{La}}_{\mathit{x}}$${\mathrm{Sr}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{TiO}}_{3}$. We have also proposed a possibility for inducing superconductivity using the idea of proximity effect. The induced superconducting gap in ${\mathrm{La}}_{\mathit{x}}$${\mathrm{Sr}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{TiO}}_{3}$ is predicted to be maximum near the half-filling of the Ti 3d band.