Search

Measurements of the distribution of stochastic switching currents in homogeneous, ultra-narrow superconducting nanowires provide strong evidence that the low-temperature current-switching in such systems occurs through quantum phase slips—topological quantum fluctuations of the superconducting order parameter via which tunnelling occurs between current-carrying states.

Following the development of a scheme to bosonize and debosonize consistently [N. Shah and C.J. Bolech, Phys. Rev B 93, 085440 (2016); arXiv:1508.03078], we present in detail the Toulouse-point analytic solution of the two-lead Kondo junction model. The existence and location of the solvable point is not modified, but the calculational methodology and the final expressions for observable quantities change markedly as compared to the existent results. This solvable point is one of the remarkably few exact results for non-equilibrium transport in correlated systems. It yields relatively simple analytical expressions for the current in the full range of temperature, magnetic field and voltage. It also shows precisely, within the limitations of the Toulouse fine-tuning, how the transport evolves depending on the relative strengths of inter-lead and intra-lead Kondo exchange couplings ranging from weak to strong. Thus its improved understanding is an important stepping stone for future research., 15 pages, 6 figures

We critically reexamine the bosonization-debosonization procedure for systems including certain types of localized features (although more general scenarios are possible). By focusing on the case of a tunneling junction out of equilibrium, we show that the conventional approach gives results that are not consistent with the exact solution of the problem even at the qualitative level. We identify inconsistencies that can adversely affect the results of all types of calculations. We subsequently show a way to avoid these and proceed consistently. The extended framework we develop here should be widely applicable., 16 pages, 3 figures, 1 table

Electronic spin-orbit coupling (SOC) is essential for various newly discovered phenomena in condensed-matter systems. In particular, one-dimensional topological heterostructures with SOC have been widely investigated in both theory and experiment for their distinct transport signatures indicating the presence of emergent Majorana fermions. However, a general framework for the SOC-affected transport in superconducting heterostructures, especially with the consideration of interfacial effects, has not been developed even regardless of the topological aspects. We hereby provide one for an effectively one-dimensional superconductor-normal heterostructure with nonuniform magnitude and direction of both Rashba and Dresselhaus SOC as well as a spin-orbit-active interface. We extend the Blonder-Tinkham-Klapwijk treatment to analyze the current-voltage relation and obtain a rich range of transport behaviors. Our work provides a basis for characterizing fundamental physics arising from spin-orbit interactions in heterostructures and its implications for topological systems, spintronic applications, and a whole variety of experimental setups., Comment: 8 pages, 4 figures

Recently there has been a lot of excitement generated by the possibility of realizing and detecting Majorana fermions within the arena of condensed matter physics and its potential implication for topological quantum computing. In the pursuit of identifying and understanding the signatures of Majorana fermions in realistic systems, we go beyond the low-energy effective-model descriptions of Majorana bound states to derive non-equilibrium transport properties of a topological superconducting wire in the presence of arbitrarily large applied voltages. By virtue of a microscopic calculation we are able to model the tunnel coupling between the superconducting wire and the metallic leads realistically, study the role of high-energy non-topological excitations, predict how the behavior compares for an increasing number of odd versus even number of sites, and study the evolution across the topological quantum phase transition. We consider the Kitaev model as well as its specific realization in terms of a semicon...

We review current attempts to characterize the underlying nature of the hidden order in ${\mathrm{URu}}_{2}{\mathrm{Si}}_{2}.$ A wide variety of experiments point to the existence of two order parameters: a large primary order parameter of unknown character which co-exists with secondary antiferromagnetic order. Current theories can be divided into two groups determined by whether or not the primary order parameter breaks time-reversal symmetry. We propose a series of experiments designed to test the time-reversal nature of the underlying primary order in ${\mathrm{URu}}_{2}{\mathrm{Si}}_{2}$ and to characterize its local single-ion physics.

Motivated by the recent progress in fabricating uniform and amorphous superconducting nanowires with diameter smaller than the coherence length, we theoretically study the transport behavior of such wires in the vicinity of a pair-breaking quantum phase transition. Such a realization of a superconductor quantum critical point is amenable to theoretical as well as experimental analysis. We construct a comprehensive theory in the entire neighborhood by combining the strengths of microscopic and effective approaches and analyze the Wiedemann–Franz law by using the effective quantum critical theory.

Rashba spin-orbit coupled semiconductor-superconductor hybrid structures in the presence of Zeeman splitting have emerged as the first experimentally realizable topological superconductor supporting zero-energy Majorana bound states. However, recent experimental studies in these hybrid structures are not in complete agreement with the theoretical predictions, for example, the observed height of the zero-bias conductance peak (ZBCP) associated with the Majorana bound states is less than 10% of the predicted quantized value 2e^2/h. We try to understand the sources of various discrepancies between the recent experiments and the earlier theories by starting from a microscopic theory and studying non-equilibrium transport in these systems at arbitrary temperatures and applied bias voltages. Our approach involves quantum Langevin equations and non-equilibrium Green's functions. Here we are able to model the tunnel coupling between the one-dimensional semiconductor-superconductor hybrid structure and the metallic leads realistically; study the role of tunnel coupling on the height of the ZBCP and the subgap conductance; predict the nature of the splitting of the ZBCP with an increasing magnetic field beyond the critical field; show the behavior of the ZBCP with an increasing gate-controlled onsite potential; and study the evolution of the full differential conductance across the topological quantum phase transition. When the applied magnetic field is quite large compared to the Rashba splitting and the bulk energy gap is much reduced, we find the ZBCP even for an onsite potential much larger than the applied magnetic field. The height of the corresponding ZBCP depends on the tunnel coupling even at zero temperature and can be much smaller than 2e^2/h.

We study electronic transport in junctions consisting of a superconductor electrode and two ferromagnet (F) leads in which crossed Andreev reflections (CAR) and elastic cotunnelings are accommodated. We model the system using an extended Blonder-Tinkham-Klapwijk treatment with a key modification that accounts for spin-dependent interfacial barriers (SDIB). We compute current-voltage relations as a function of parameters characterizing the SDIB, magnetization in the F leads, geometry of the junction, and temperature. Our results reveal a rich range of significantly altered physics due to a combination of interfering spin-dependent scattering processes and population imbalance in the ferromagnets, such as a significant enhancement in CAR current and a sign change in the relative difference between resistance of two cases having a antiparallel or parallel alignment of the magnetization in the F leads, respectively. Our model accounts for the surprising experimental findings of positive relative resistance by M. Colci et al. [Phys. Rev. B 85, 180512(R) (2012)] as well as previously measured negative relative resistance results, both within sufficiently large parameter regions., Comment: 12 pages, 10 figures

Topological superconductors are prime candidates for the implementation of topological-quantum-computation ideas because they can support non-Abelian excitations such as Majorana fermions. We go beyond the low-energy effective-model descriptions of Majorana bound states (MBSs) to derive nonequilibrium transport properties of wire geometries of these systems in the presence of arbitrarily large applied voltages. Our approach involves quantum Langevin equations and nonequilibrium Green's functions. By virtue of a full microscopic calculation we are able to model the tunnel coupling between the superconducting wire and the metallic leads realistically, study the role of high-energy nontopological excitations, predict how the behavior compares for an increasing number of odd versus even number of sites, and study the evolution across the topological quantum phase transition (QPT). We find that the normalized spectral weight in the MBSs can be remarkably large and goes to zero continuously at the topological QPT. Our results have concrete implications for the experimental search and study of MBSs.

We present the first study of superconducting nanowires shunted with an external resistor, geared towards understanding and controlling coherence and dissipation in nanowires. The dynamics is probed by measuring the evolution of the V-I characteristics and the distributions of switching and retrapping currents upon varying the shunt resistor and temperature. Theoretical analysis of the experiments indicates that as the value of the shunt resistance is decreased, the dynamics turns more coherent presumably due to stabilization of phase-slip centers in the wire and furthermore the switching current approaches the Bardeen's prediction for equilibrium depairing current. By a detailed comparison between theory and experimental, we make headway into identifying regimes in which the quasi-one-dimensional wire can effectively be described by a zero-dimensional circuit model analogous to the RCSJ (resistively and capacitively shunted Josephson junction) model of Stewart and McCumber. Besides its fundamental significance, our study has implications for a range of promising technological applications., Comment: 15 pages, 14 figures

Microwave Fabry-Perot resonators containing nonlinear mesoscopic elements (such as superconducting nanowires) can be used to explore many-body circuit QED. Here, we report on observations of a superconductor-normal pulsing regime in microwave (GHz) coplanar waveguide resonators consisting of superconducting MoGe films interrupted by a gap that is bridged by one or more suspended superconducting nanowires. This regime, which involve MHz-frequency oscillations in the amplitude of the supercurrent in the resonator, are achieved when the steady-state amplitude of the current in the driven resonator exceeds the critical current of the nanowires. Thus we are able to determine the temperature dependence of the critical current, which agrees well with the corresponding Bardeen formula. The pulsing regime manifests itself as an apparent "crater" on top of the fundamental Lorentzian peak of the resonator. Once the pulsing regime is achieved at a fixed drive power, however, it remains stable for a range of drive frequencies corresponding to subcritical steady state currents in the resonator. We develop a phenomenological model of resonator-nanowire systems, from which we are able to obtain a quantitative description of the amplitude oscillations and also, inter alia, to investigate thermal relaxation processes in superconducting nanowires. For the case of resonators comprising two parallel nanowires and subject to an external magnetic field, we find field-driven oscillations of the onset power for the amplitude oscillations, as well as the occurrence (for values of the magnetic field that strongly frustrate the nanowires) of a distinct steady state in which the pulsing is replaced by stochastic amplitude-fluctuations. We conclude by giving a brief discussion of how circuit-QED-based systems have the potential to facilitate understanding of quantum phase-slips in superconducting nanowires., Comment: 40 pages, 20 figures

We study the transport properties of nanoscale superconducting (S) devices in which two superconducting electrodes are bridged by two parallel ferromagnetic (F) wires, forming an SFFS junction with a separation between the two wires less than the superconducting coherence length. This allows crossed Andreev reflection to take place. We find that the resistance as a function of temperature exhibits behavior reminiscent of the re-entrant effect and, at low temperatures and excitation energies below the superconducting gap, the resistance corresponding to antiparallel alignment of the magnetization of the ferromagnetic wires is higher than that of parallel alignment, in contrast to the behavior expected from crossed Andreev reflection. We present a model based on spin-dependent interface scattering that explains this surprising result and demonstrates the sensitivity of the junction transport properties to interfacial parameters., Comment: 5 pages, 3 figures

Superconducting nanowires fabricated via carbon-nanotube-templating can be used to realize and study quasi-one-dimensional superconductors. However, measurement of the linear resistance of these nanowires have been inconclusive in determining the low-temperature behavior of phase-slip fluctuations, both quantal and thermal. Thus, we are motivated to study the nonlinear current-voltage characteristics in current-biased nanowires and the stochastic dynamics of superconductive-resistive switching, as a way of probing phase-slip events. In particular, we address the question: Can a single phase-slip event occurring somewhere along the wire--during which the order-parameter fluctuates to zero--induce switching, via the local heating it causes? We explore this and related issues by constructing a stochastic model for the time-evolution of the temperature in a nanowire whose ends are maintained at a fixed temperature. We derive the corresponding master equation as tool for evaluating and analyzing the mean switching time at a given value of current. The model indicates that although, in general, several phase-slip events are necessary to induce switching via a thermal runaway, there is indeed a regime of temperatures and currents in which a single event is sufficient. We carry out a detailed comparison of the results of the model with experimental measurements of the distribution of switching currents, and provide an explanation for the counter-intuitive broadening of the distribution width that is observed upon lowering the temperature. Moreover, we identify a regime in which the experiments are probing individual phase-slip events, and thus offer a way for exploring the physics of nanoscale quantum tunneling of the superconducting order parameter., 21 pages, 15 figures

We study the stochastic dynamics of superconductive-resistive switching in hysteretic current-biased superconducting nanowires undergoing phase-slip fluctuations. We evaluate the mean switching time using the master-equation formalism, and hence obtain the distribution of switching currents. We find that as the temperature is reduced this distribution initially broadens; only at lower temperatures does it show the narrowing with cooling naively expected for phase slips that are thermally activated. We also find that although several phase-slip events are generally necessary to induce switching, there is an experimentally accessible regime of temperatures and currents for which just one single phase-slip event is sufficient to induce switching, via the local heating it causes.

A microscopic analysis of the superconducting quantum critical point realized via a pair-breaking quantum phase transition is presented. Finite temperature crossovers are derived for the electrical conductivity, which is a key probe of superconducting fluctuations. By using the diagrammatic formalism for disordered systems, we are able to incorporate the interplay between fluctuating Cooper pairs and electrons, that is outside the scope of a time-dependent Ginzburg Landau or effective bosonic action formalism. It is essential to go beyond the standard approximation in order to capture the zero temperature correction which results purely from the (dynamic) quantum fluctuations and dictates the behavior of the conductivity in an entire low temperature quantum regime. All dynamic contributions are of the same order and conspire to add up to a negative total, thereby inhibiting the conductivity as a result of superconducting fluctuations. On the contrary, the classical and the intermediate regimes are dominated by the positive bosonic channel. Our theory is applicable in one, two and three dimensions and is relevant for experiments on superconducting nanowires, doubly-connected cylinders, thin films and bulk in the presence of magnetic impurities, magnetic field or other pair-breakers. A window of non-monotonic behavior is predicted to exist as either the temperature or the pair-breaking parameter is swept., 20 pages, 9 figures

In chiral ferromagnets, weak spin-orbit interactions twist the ferromagnetic order into spirals, leading to helical order. We investigate an extended Ginzburg-Landau theory of such systems where the helical order is destabilized in favor of crystalline phases. These crystalline phases are based on periodic arrangements of double-twist cylinders and are strongly reminiscent of blue phases in liquid crystals. We discuss the relevance of such blue phases for the phase diagram of the chiral ferromagnet MnSi., Comment: 6 pages, 5 figures (published version)

We describe the thermal and electrical conductivities of quasi-one dimensional wires, across a quantum phase transition from a superconductor to a metal induced by pairbreaking perturbations. Fluctuation corrections to BCS theory motivate a field theory for quantum criticality. We describe deviations in the Wiedemann-Franz ratio from the Lorenz number, which can act as sensitive tests of the theory. We also describe the crossovers out of the quantum critical region into the metallic and superconducting phases., Comment: 4 pages, 1 figure

We study the low temperature magnetoresistance of dirty thin films and quantum wires close to a quantum phase transition from a superconducting to normal state, induced by applying a parallel magnetic field. We find that the different corrections (Aslamazov-Larkin, density of states and Maki-Thompson) to the normal state conductivity, coming from the superconducting pair fluctuations, are of the same order at zero temperature. There are three regimes at finite temperatures. In the "quantum" regime, which essentially shows a zero-temperature-like behavior we find a negative magnetoresistance. Since in the "classical" regime the correction is positive, we predict a non-monotonic magnetoresistance at higher temperatures., Comment: Proceedings for SCES conference (2004)

We propose a set-up to realize two-channel Kondo physics using quantum dots. We discuss how the charge fluctuations on a small dot can be accessed by using a system of two single electron transistors arranged in parallel. We derive a microscopic Hamiltonian description of the set-up that allows us to make connection with the two-channel Anderson model (of extended use in the context of heavy-Fermion systems) and in turn make detailed predictions for the differential capacitance of the dot. We find that its lineshape, which we determined precisely, shows a robust behavior that should be experimentally verifiable., Comment: 4 pages, 3 figures

We calculate the fluctuation correction to the normal state conductivity in the vicinity of a quantum phase transition from a superconducting to normal state, induced by applying a magnetic field parallel to a dirty thin film or a nanowire with thickness smaller than the superconducting coherence length. We find that at zero temperature, where the correction comes purely from quantum fluctuations, the positive Aslamazov-Larkin contribution, the negative density of states contribution, and the Maki-Thompson interference contribution, are all of the same order and the total correction is negative. Further we show that based on how the quantum critical point is approached, there are three regimes that show different temperature and field dependencies which should be experimentally accessible., 4 pages, 3 figures

We study theoretically the dynamics of an ``xxz'' spin necklace coupled to a conduction electron sea, a model system for a nanostructure in a dissipative environment. We extract the long-time behavior via a mapping to a multichannel Coulomb gas problem followed by a scaling analysis. The strong quantum fluctuations of the necklace cause a nontrivial dependence of couplings on system size which we extract via an analysis involving the ``boundary condition changing operator'', and confirm via a detailed numerical evaluation of one case., 4 pages, 4 figures

We use a recently proposed model of the interplane conductivity of high temperature superconductors to investigate the `scattering rate sum-rule' introduced by Basov and co-workers. We present a new derivation of the sum-rule. The quantal and thermal fluctuations of the order parameter which have been argued to produce the observed pseudogap behavior are shown to increase the total integrated `scattering rate' but may either increase or decrease the `quasiparticle' contribution from frequencies greater than twice the superconducting gap., 4 pages, 5 figures, revised

We present a theory of the interplane conductivity of bilayer high temperature superconductors, focusing on the effect of quantal and thermal fluctuations on the oscillator strengths of the superfluid stiffness and the bilayer plasmon. We find that the opening of the superconducting gap and establishment of superconducting phase coherence each lead to redistribution of spectral weight over wide energy scales. The factor-of-two relation between the superfluid stiffness and the change below $T_c$ in the oscillator strength of the absorptive part of the conductivity previously derived for single-layer systems, is found to be substantially modified in bilayer systems., Comment: 11 pages, 14 figures

Phase slips are topological fluctuation events that carry the superconducting order-parameter field between distinct current carrying states and impart a non-zero resistance to superconducting nanowires. They play a fundamental role in determining the fate of superconductivity in nanowires. Conversely, superconducting nanowires provide an ideal setting for accessing non-trivial fluctuations driven by thermal activation and—at low temperatures—by quantum tunneling of a one-dimensional field. However, this potential has not been fully realized because resistance measurements, on the one hand, are capable of capturing only the averaged phase-slip behavior, and on the other hand, are incapable of pinning down the low temperature phase-slip behavior, as the measured resistance values drop below the noise floor. On going beyond the linear-response regime, the I-V characteristics show a hysteretic behavior. As the current is ramped up repeatedly, the state switches from a superconductive to a resistive one, doing so at somewhat random current values below the depairing critical current. The distribution of these switching currents was studied recently. I will report on the rather counter-intuitive temperature dependence of the distribution and its theoretical understanding via a stochastic model. It will be shown that although, in general, several phase-slip events are necessary to induce switching, there is an experimentally accessible temperature- and current-range for which a single phase-slip event is sufficient to switch the wire to the normal (resistive) state. I will conclude by arguing that switching-current statistics provide an effective probe to resolve individual phase-slip events and in addition offer unprecedented access to quantum phase-slip tunneling events.

Phase-slip fluctuations play a central role in a variety of systems and are responsible for dissipation via a loss of coherence. By virtue of these fluctuations, quasi-one-dimensional superconductors acquire a non-zero resistance unlike the bulk superconductors in which the resistance drops to zero upon entering the superconducting phase. The present generation of experiments on superconducting nanowires are capable of characterizing non only the thermally activated phase slips in detail, but also the quantum phase slip processes as well as the crossover from thermal to quantal. The proceeding will report on the recent progress made towards achieving this goal by studying the dynamics of current-induced transitions from superconductive to resistive state and analyzing the switching statistics.