Supercurrent in atomic point contacts and andreev states

Application of Micro/Nanofabrication Techniques to On-Chip Molecular Electronics

Molecular electronics is a promising subject to overcome the size limitation of silicon-based electronic devices. In the past decades, various micro/nanofabrication techniques have been developed for constructing molecular junctions, and a number of breakthroughs are made in the characterizations and applications of the single-molecule device. The history and progress are reviewed in this article, laying emphasis on the recent works on the combination of micro/nanofabrication techniques with other techniques such as electrochemical deposition and surface-enhanced Raman spectroscopy (SERS). Some prototypical single-molecule devices such as molecular transistors are presented. Finally, the challenges and prospects in the fabrication of single-molecule devices are discussed.

Nonlocal Josephson Effect in Andreev Molecules

We propose the "Andreev molecule," an artificial quantum system composed of two closely spaced Josephson junctions. The coupling between Josephson junctions in an Andreev molecule occurs through the overlap and hybridization of the junction's "atomic" orbitals, Andreev Bound States. A striking consequence is that the supercurrent flowing through one junction depends on the superconducting phase difference across the other junction. Using the Bogolubiov-de-Gennes formalism, we derive the energy spectrum and nonlocal current-phase relation for arbitrary separation. We demonstrate the possibility of creating a φ-junction and propose experiments to verify our predictions. Andreev molecules may have potential applications in quantum information, metrology, sensing, and molecular simulation.

Role of Quasiparticles in an Electric Circuit with Josephson Junctions

Although Josephson junctions can be viewed as highly nonlinear impedances for superconducting quantum technologies, they also possess internal dynamics that may strongly affect their behavior. Here, we construct a computational framework that includes a microscopic description of the junction (full fledged treatment of both the superconducting condensate and the quasiparticles) in the presence of a surrounding electrical circuit. Our approach generalizes the standard resistor capacitor Josephson model to arbitrary junctions (including, e.g., multiterminal geometries and/or junctions that embed topological or magnetic elements) and arbitrary electric circuits treated at the classical level. By treating the superconducting condensate and quasiparticles on equal footings, we capture nonequilibrium phenomena such as multiple Andreev reflection. We show that the interplay between the quasiparticle dynamics and the electrical environment leads to the emergence of new phenomena. In a RC circuit connected to single channel Josephson junction, we find out-of-equilibrium current-phase relations that are strongly distorted with respect to the (almost sinusoidal) equilibrium one, revealing the presence of the high harmonic ac Josephson effect. In an RLC circuit connected to a junction, we find that the shape of the resonance is strongly modified by the quasiparticle dynamics: close to resonance, the current can be smaller than without the resonator. Our approach provides a route for the quantitative modeling of superconducting-based circuits.

Selective-Area Superconductor Epitaxy to Ballistic Semiconductor Nanowires

Semiconductor nanowires such as InAs and InSb are promising materials for studying Majorana zero modes and demonstrating non-Abelian particle exchange relevant for topological quantum computing. While evidence for Majorana bound states in nanowires has been shown, the majority of these experiments are marked by significant disorder. In particular, the interfacial inhomogeneity between the superconductor and nanowire is strongly believed to be the main culprit for disorder and the resulting "soft superconducting gap" ubiquitous in tunneling studies of hybrid semiconductor-superconductor systems. Additionally, a lack of ballistic transport in nanowire systems can create bound states that mimic Majorana signatures. We resolve these problems through the development of selective-area epitaxy of Al to InSb nanowires, a technique applicable to other nanowires and superconductors. Epitaxial InSb-Al devices generically possess a hard superconducting gap and demonstrate ballistic 1D superconductivity and near-perfect transmission of supercurrents in the single mode regime, requisites for engineering and controlling 1D topological superconductivity. Additionally, we demonstrate that epitaxial InSb-Al superconducting island devices, the building blocks for Majorana-based quantum computing applications, prepared using selective-area epitaxy can achieve micron-scale ballistic 1D transport. Our results pave the way for the development of networks of ballistic superconducting electronics for quantum device applications.

Nonlocal supercurrent of quartets in a three-terminal Josephson junction

A novel nonlocal supercurrent, carried by quartets, each consisting of four electrons, is expected to appear in a voltage-biased three-terminal Josephson junction. This supercurrent results from a nonlocal Andreev bound state (ABS), formed among three superconducting terminals. While in a two-terminal Josephson junction the usual ABS, and thus the dc Josephson current, exists only in equilibrium, the ABS, which gives rise to the quartet supercurrent, persists in the nonlinear regime. In this work, we report such resonance in a highly coherent three-terminal Josephson junction made in an InAs nanowire in proximity to an aluminum superconductor. In addition to nonlocal conductance measurements, cross-correlation measurements of current fluctuations provided a distinctive signature of the quartet supercurrent. Multiple device geometries had been tested, allowing us to rule out competing mechanisms and to establish the underlying microscopic origin of this coherent nondissipative current.

Transport regimes of a split gate superconducting quantum point contact in the two-dimensional LaAlO3/SrTiO3 superfluid

One of the hallmark experiments of quantum transport is the observation of the quantized resistance in a point contact in GaAs/AlGaAs heterostructures. Being formed with split gate technology, these structures represent in an ideal manner equilibrium reservoirs which are connected only through a few electron mode channel. It has been a long standing goal to achieve similar experimental conditions also in superconductors. Here we demonstrate the formation of a superconducting quantum point contact (SQPC) with split gate technology in a two-dimensional superconductor, utilizing the unique gate tunability of the superfluid at the LaAlO3/SrTiO3 interface. When the constriction is tuned through the action of metallic split gates we identify three regimes of transport: First, SQPC for which the supercurrent is carried only by a few quantum transport channels. Second, superconducting island strongly coupled to the equilibrium reservoirs. Third, charge island with a discrete spectrum weakly coupled to the reservoirs.

Tailoring supercurrent confinement in graphene bilayer weak links

The Josephson effect is one of the most studied macroscopic quantum phenomena in condensed matter physics and has been an essential part of the quantum technologies development over the last decades. It is already used in many applications such as magnetometry, metrology, quantum computing, detectors or electronic refrigeration. However, developing devices in which the induced superconductivity can be monitored, both spatially and in its magnitude, remains a serious challenge. In this work, we have used local gates to control confinement, amplitude and density profile of the supercurrent induced in one-dimensional nanoscale constrictions, defined in bilayer graphene-hexagonal boron nitride van der Waals heterostructures. The combination of resistance gate maps, out-of-equilibrium transport, magnetic interferometry measurements, analytical and numerical modelling enables us to explore highly tunable superconducting weak links. Our study opens the path way to design more complex superconducting circuits based on this principle, such as electronic interferometers or transition-edge sensors.

Superconducting properties of lithographic lead break junctions

We have fabricated mechanically controlled break junction samples made of lead (Pb) by means of state-of-the-art nanofabrication methods: electron beam lithography and physical vapour deposition. The electrical and magnetic properties were characterized in a [Formula: see text] cryostat and showed a hard superconducting gap. Temperature and magnetic field dependence of tunnel contacts were compared and quantitatively described by including either thermal broadening of the density of states or pair breaking in the framework of a Skalski model, respectively. We show point contact spectra of few-atom contacts and present tunneling spectra exhibiting a superconducting double-gap structure.

Quantum Brownian Motion at Strong Dissipation Probed by Superconducting Tunnel Junctions

We have investigated the phase dynamics of a superconducting tunnel junction at ultralow temperatures in the presence of high damping, where the interaction with environmental degrees of freedom represents the leading energy scale. In this regime, theory predicts the dynamics to follow a generalization of the classical Smoluchowski description, the quantum Smoluchowski equation, thus, exhibiting overdamped quantum Brownian motion characteristics. For this purpose, we have performed current-biased measurements on the small-capacitance Josephson junction of a scanning tunneling microscope placed in a low impedance environment at milli-Kelvin temperatures. We can describe our experimental findings with high accuracy by using a quantum phase diffusion model based on the quantum Smoluchowski equation. In this way we experimentally demonstrate that overdamped quantum systems follow quasiclassical dynamics with significant quantum effects as the leading corrections.

Two-terminal transport measurements with cold atoms

In recent years, the ability of cold atom experiments to explore condensed-matter-related questions has dramatically progressed. Transport experiments, in particular, have expanded to the point in which conductance and other transport coefficients can now be measured in a way that is directly analogous to solid-state physics, extending cold-atom-based quantum simulations into the domain of quantum electronic devices. In this topical review, we describe the transport experiments performed with cold gases in the two-terminal configuration, with an emphasis on the specific features of cold atomic gases compared to solid-state physics. We present the experimental techniques and the main experimental findings, focusing on-but not restricted to-the recent experiments performed by our group. We finally discuss the perspectives opened up by this approach, the main technical and conceptual challenges for future developments, and potential applications in quantum simulation for transport phenomena and mesoscopic physics problems.

Mapping out spin and particle conductances in a quantum point contact

We study particle and spin transport in a single-mode quantum point contact, using a charge neutral, quantum degenerate Fermi gas with tunable, attractive interactions. This yields the spin and particle conductance of the point contact as a function of chemical potential or confinement. The measurements cover a regime from weak attraction, where quantized conductance is observed, to the resonantly interacting superfluid. Spin conductance exhibits a broad maximum when varying the chemical potential at moderate interactions, which signals the emergence of Cooper pairing. In contrast, the particle conductance is unexpectedly enhanced even before the gas is expected to turn into a superfluid, continuously rising from the plateau at [Formula: see text] for weak interactions to plateau-like features at nonuniversal values as high as [Formula: see text] for intermediate interactions. For strong interactions, the particle conductance plateaus disappear and the spin conductance gets suppressed, confirming the spin-insulating character of a superfluid. Our observations document the breakdown of universal conductance quantization as many-body correlations appear. The observed anomalous quantization challenges a Fermi liquid description of the normal phase, shedding new light on the nature of the strongly attractive Fermi gas.

Ultimately short ballistic vertical graphene Josephson junctions

Much efforts have been made for the realization of hybrid Josephson junctions incorporating various materials for the fundamental studies of exotic physical phenomena as well as the applications to superconducting quantum devices. Nonetheless, the efforts have been hindered by the diffusive nature of the conducting channels and interfaces. To overcome the obstacles, we vertically sandwiched a cleaved graphene monoatomic layer as the normal-conducting spacer between superconducting electrodes. The atomically thin single-crystalline graphene layer serves as an ultimately short conducting channel, with highly transparent interfaces with superconductors. In particular, we show the strong Josephson coupling reaching the theoretical limit, the convex-shaped temperature dependence of the Josephson critical current and the exceptionally skewed phase dependence of the Josephson current; all demonstrate the bona fide short and ballistic Josephson nature. This vertical stacking scheme for extremely thin transparent spacers would open a new pathway for exploring the exotic coherence phenomena occurring on an atomic scale.

The functionality of Josephson junctions—a thin insulating layer between two superconducting regions—is greatly enhanced by using hybrid material systems. Here, the authors incorporate graphene into a Josephson junction and demonstrate ballistic transport through the atom-thick layer.

Andreev bound-state dynamics in quantum-dot Josephson junctions: a washing out of the 0-π transition

We consider a Josephson junction formed by a quantum dot connected to two bulk superconductors in the presence of Coulomb interaction and coupling to both an electromagnetic environment and a finite density of electronic quasiparticles. In the limit of a large superconducting gap we obtain a Born-Markov description of the relevant Andreev bound-states dynamics. We calculate the current-phase relation and we find that the experimentally unavoidable presence of quasiparticles can dramatically modify the 0-π standard transition picture. We show that photon-assisted quasiparticle absorption allows the dynamic switching from the 0 to the π state and vice versa, washing out the 0-π transition predicted by purely thermodynamic arguments. Spectroscopic signatures of Andreev bound-states broadening are investigated by considering microwave irradiation.

Crossover from Josephson to multiple Andreev reflection currents in atomic contacts

The basic current-carrying mechanism through a superconducting weak link embedded in a resistive environment undergoes a continuous crossover, as the voltage increases, from Josephson Cooper pair transfer exciting electromagnetic modes in the environment to multiple Andreev reflections leading to the creation of quasiparticles. We corroborate these ideas through measurements of the dc current-voltage characteristics of superconducting atomic contacts containing channels of arbitrary and adjustable transmission. We present a simple model, in the spirit of the classical resistively shunted junction model, that accounts well for the observed characteristics.

Superconducting atomic contacts under microwave irradiation

We have measured the effect of microwave irradiation on the dc current-voltage characteristics of superconducting atomic contacts. The interaction of the external field with the ac supercurrents leads to replicas of the supercurrent peak, the well-known Shapiro resonances. The observation of supplementary fractional resonances for contacts containing highly transmitting conduction channels reveals their nonsinusoidal current-phase relation. The resonances sit on a background current which is itself deeply modified, as a result of photon-assisted multiple Andreev reflections. The results provide firm support for the full quantum theory of transport between two superconductors based on the concept of Andreev bound states.

Dynamical coulomb blockade of multiple Andreev reflections

We analyze the dynamical Coulomb blockade of multiple Andreev reflections (MAR) in a superconducting quantum point contact coupled to a macroscopic impedance. We find that at very low transmission the blockade scales as n2 with n = Int(2delta/eV), where V is the bias voltage and delta is the superconducting gap, as it would correspond to the occurrence of shots of charge ne. For higher transmission the blockade is reduced because of both the Pauli principle and the elastic renormalization of the MAR probability, and for certain voltage regions it may even become an anti-blockade; i.e., the current is enhanced due to the coupling with the electromagnetic environment.

Decoherence in josephson phase qubits from junction resonators

Although Josephson junction qubits show great promise for quantum computing, the origin of dominant decoherence mechanisms remains unknown. Improving the operation of a Josephson junction based phase qubit has revealed microscopic two-level systems or resonators within the tunnel barrier that cause decoherence. We report spectroscopic data that show a level splitting characteristic of coupling between a two-state qubit and a two-level system. Furthermore, we show Rabi oscillations whose "coherence amplitude" is significantly degraded by the presence of these spurious microwave resonators. The discovery of these resonators impacts the future of Josephson qubits as well as existing Josephson technologies.

Andreev level qubit

We investigate the dynamics of a two-level Andreev bound state system in a transmissive quantum point contact embedded in an rf SQUID. Coherent coupling of the Andreev levels to the circulating supercurrent allows manipulation and readout of the level states. The two-level Hamiltonian for the Andreev levels is derived, and the effect of interaction with the quantum fluctuations of the induced flux is studied. We also consider an inductive coupling of qubits and discuss the relevant SQUID parameters for qubit operation and readout.

Spontaneous formation of a pi soliton in a superconducting wire with an odd number of electrons

We consider a one-dimensional superconducting wire where the total number of electrons can be controlled in the Coulomb blockade regime. We predict that a pi soliton (kink) will spontaneously form in the system when the number of electrons is odd, because this configuration has a lower energy. If the wire with an odd number of electrons is closed in a ring, the phase difference on the two sides of the soliton will generate a supercurrent detectable by a SQUID. The two degenerate states with the current flowing clockwise or counterclockwise can be utilized as a qubit.

Subharmonic shapiro steps and assisted tunneling in superconducting point contacts

We analyze the current in a superconducting point contact of arbitrary transmission in the presence of a microwave radiation. The interplay between the ac Josephson current and the microwave signal gives rise to Shapiro steps at voltages V = (m/n)h(omega)(r)/2e, where n,m are integer numbers and omega(r) is the radiation frequency. The subharmonic steps (n not equal 1) are a consequence of multiple Andreev reflections (MAR) and provide a signature of the peculiar ac Josephson effect at high transmission. Moreover, the dc current exhibits a rich subgap structure due to photon-assisted MARs.

Coherent low-energy charge transport in a diffusive S-N-S junction

We have studied the current-voltage characteristics of diffusive mesoscopic Nb-Cu-Nb Josephson junctions with highly transparent Nb-Cu interfaces. We consider the low-voltage and high-temperature regime eV < epsilon(c) < k(B)T, where epsilon(c) is the Thouless energy. The observed excess current as well as the observed subharmonic Shapiro steps under microwave irradiation suggest the occurrence of low-energy coherent multiple Andreev reflection.

Direct link between Coulomb blockade and shot noise in a quantum-coherent structure

We analyze the current-voltage characteristic of a quantum conduction channel coupled to an electromagnetic environment with arbitrary frequency-dependent impedance. In the weak blockade regime the correction to the Ohmic behavior is directly related to the channel current fluctuations, vanishing at perfect transmission in the same way as shot noise. This relation can be generalized to describe the environmental Coulomb blockade in a generic mesoscopic conductor coupled to an external impedance, as the response of the latter to the current fluctuations in the former.

Multiple-charge-quanta shot noise in superconducting atomic contacts

We have measured shot noise in aluminum atomic point contacts containing a small number of conduction channels of known transmissions. In the normal state, we find that the noise power is reduced from its Poissonian value and reaches the partition limit, as calculated from the transmissions. In the superconducting state, the noise reveals the large effective charge associated with each elementary transfer process, in excellent agreement with the predictions of the quantum theory of multiple Andreev reflections.

Multiple Andreev reflections revealed by the energy distribution of quasiparticles

We have performed the tunnel spectroscopy of the energy distribution function of quasiparticles in 5-microm-long silver wires connected to superconducting reservoirs biased at different potentials. The distribution function f(E) presents several steps, which are manifestations of multiple Andreev reflections at the NS interfaces. The rounding of the steps is well explained by electron-electron interactions.