arXiv subjects

Nayana Shah

Publications and source records attributed to Nayana Shah.

18 recordsLinked to original sources

arXiv2026

Bosonization solution of the Kondo lattice in a Luttinger liquid

We address the physics of a regular arrangement of independent magnetic impurities embedded in a band of interacting electrons. We focus on the one-dimensional case that can be studied using bosonization and in which the electron bulk is described by a Luttinger liquid. The impurity spins interact with the electrons via magnetic exchange that introduces the possibility of Kondo and Ruderman-Kittel-Kasuya-Yosida (RKKY) physics. We find that for two special values of the interactions, the model can be refermionized as a noninteracting electron band hybridized with a regular array of resonant levels. These solvable limits provide access to impurity correlators that correspond to either extended algebraic order or local screening. A physical picture emerges of how the interelectron interactions can stabilize either Kondo or RKKY physics depending on the sign of the interaction.

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arXiv2024

Systematic compactification of the two-channel Kondo model. I. Consistent bosonization-debosonization approach and exact comparisons

Capitalizing on recent work, that clarifies the consistent use of bosonization-debosonization methods to study Kondo-type quantum impurity models even in nonequilibrium settings, we revisit the compactification procedure of the two-channel Kondo model (by which it is rewritten more ``compactly'' using the single-channel version of the model and exploiting separation and duality between spin and charge) and uncover some hidden approximations that could limit its range of validity. This complements and extends, for two or any even number of channels, beyond previous work on the Toulouse limit of these models, and reinforces the need for the use of an extended framework in these calculations. We carry out a number of exact comparisons between the different models, and show that keeping track of the, so-called, consistency factors leads to full agreement between the compactified and original versions of the model.

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arXiv2024

Systematic compactification of the two-channel Kondo model. II. Comparative study of scaling and universality

Following up on the systematic compactification of the two-channel Kondo model (and its multichannel extensions; arXiv:2308.03569 (companion paper I)) and the demonstration of its validity over the past proposal of compactification, we resort to a study of scaling using Anderson's simple poor man's procedure to carry out a comparative study of these two and the original model. By doing so we unveil a universal agreement among the three models in how they flow upon scaling, and suggest the general limits of such a concordance. In this way we further elucidate the conditions under which the standard simplifications implicit in many bosonization-based mappings (particularly of quantum impurity models) can be used reliably, and when the consistent bosonization-debosonization approach is needed.

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arXiv2024

Systematic compactification of the two-channel Kondo model. III. Extended field-theoretic renormalization group analysis

We carry out a field-theoretical renormalization group procedure based on the Callan-Symanzik equation to calculate the detailed flow for the (multi) two-channel Kondo model and its compactified versions. In doing so, we go beyond the universal terms in the beta function we obtained using poor man's scaling (see arXiv:2308.03590 (companion paper II)) and culminate our analysis of how the compactified versions of the model fare against the original one. Among other results, we explore the large-channel-number limit and extend our considerations to the finite temperature crossover region. Moreover, we gain insights into the contradistinction between the consistent vs. conventional bosonization-debosonization formalisms, thereby advancing our understanding on multiple fronts. In particular, we make use of renormalization-flow arguments to further justify the consistent refermionization of the parallel Kondo interaction we presented earlier (see arXiv:2308.03569 (companion paper I))

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arXiv2020

Accessing different topological classes and types of Majorana edge states in coupled superconducting platforms using perturbations

The study of topological classes and their associated edge states has been of ongoing interest. In one dimension, the standard platform of these studies has been the conventional Kitaev wire and its realizations. In this work, we study the edge states in coupled p-wave platforms in 1D, in the presence of experimentally relevant perturbations, like a Zeeman field and s-wave SC. Firstly, we show that the unperturbed coupled p-wave setup by itself can have two types of Majorana edge states, depending on the value of the effective onsite potential. We show that additional components like Zeeman field and s-wave term can cause transitions to different symmetry classes, both topologically trivial or non-trivial, and change the nature of these edge states. In the presence of the perturbations, we show that there are 3 symmetry classes when the effective p-wave pairing is equal between the spin species, and 6 for the second kind, when the pairing differs by a phase $π$ between the two. Some of these classes are topologically non-trivial. Further, we explore the nature of subgap states when we have a junction between two such topological setups and their corresponding behaviour with the phase of the p-wave order parameter. Our work provides a theoretical framework of the different ways to get non-trivial topological classes in coupled p-wave nanowire setup, using experimentally feasible perturbations, and the nature of subgap states across junctions of these platforms.

cond-mat.mes-hall↗

arXiv2016

Consistent bosonization-debosonization II: The two-lead Kondo problem and the fate of its non-equilibrium Toulouse point

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.

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arXiv2016

Consistent bosonization-debosonization I: A resolution of the non-equilibrium transport puzzle

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.

cond-mat.str-el↗

arXiv2015

General framework for transport in spin-orbit-coupled superconducting heterostructures: Nonuniform spin-orbit coupling and spin-orbit-active interfaces

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.

cond-mat.supr-con↗

arXiv2013

Nature of the zero-bias conductance peak associated with Majorana bound states in topological phases of semiconductor-superconductor hybrid structures

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.

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arXiv2013

Transport in multi-terminal superconductor/ferromagnet junctions having spin-dependent interfaces

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.

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arXiv2012

Anomalous polarization-dependent transport in nanoscale double-barrier superconductor/ferromagnet/superconductor junctions

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.

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arXiv2012

Majorana fermions in an out-of-equilibrium topological superconducting wire: an exact microscopic transport analysis of a p-wave open chain coupled to normal leads

Topological superconductors are prime candidates for the implementation of topological-quantum-computation ideas because they can support non-Abelian excitations like Majorana fermions. We go beyond the low-energy effective-model descriptions of Majorana bound states (MBSs), to derive non-equilibrium transport properties of wire geometries of these systems in the presence of arbitrarily large applied voltages. Our approach involves quantum Langevin equations and non-equilibrium 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 non-topological excitations; predict how the behavior compares for increasing number of odd vs. 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.

cond-mat.mes-hall↗

arXiv2012

Dynamics of superconducting nanowires shunted with an external resistor

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.

cond-mat.mes-hall↗

arXiv2011

Cratered Lorentzian response of driven microwave superconducting nanowire-bridged resonators: oscillatory and magnetic-field induced stochastic states

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.

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arXiv2009

Stochastic dynamics of phase-slip trains and superconductive-resistive switching in current-biased nanowires

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.

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arXiv2008

Probing individual topological tunnelling events of a quantum field via their macroscopic consequences

Phase slips are topological fluctuation events that carry the superconducting order-parameter field between distinct current carrying states. Owing to these phase slips low-dimensional superconductors acquire electrical resistance. In quasi-one-dimensional nanowires it is well known that at higher temperatures phase slips occur via the process of thermal barrier-crossing by the order-parameter field. At low temperatures, the general expectation is that phase slips should proceed via quantum tunnelling events, which are known as quantum phase slips (QPS). Here we report strong evidence for individual quantum tunnelling events undergone by the superconducting order-parameter field in homogeneous nanowires.We accomplish this via measurements of the distribution of switching currents-the high-bias currents at which superconductivity gives way to resistive behaviour-whose width exhibits a rather counter-intuitive, monotonic increase with decreasing temperature. We outline a stochastic model of phase slip kinetics which relates the basic phase slip rates to switching rates. Comparison with this model indicates that the phase predominantly slips via thermal activation at high temperatures but at sufficiently low temperatures switching is caused by individual topological tunnelling events of the order-parameter field, i.e., QPS. Importantly, measurements on several wires show that quantum fluctuations tend to dominate over thermal fluctuations at larger temperatures in wires having larger critical currents. This fact provides strong supports the view that the anomalously high switching rates observed at low temperatures are indeed due to QPS, and not consequences of extraneous noise or hidden inhomogeneity of the wire.

cond-mat.supr-con↗

arXiv2007

Inherent stochasticity of superconductive-resistive switching in nanowires

Hysteresis in the current-voltage characteristic in a superconducting nanowire reflects an underlying bistability. As the current is ramped up repeatedly, the state switches from a superconductive to a resistive one, doing so at random current values below the equilibrium critical current. Can a single phase-slip event somewhere along the wire--during which the order-parameter fluctuates to zero--induce such switching, via the local heating it causes? We address 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. The model indicates that although, in general, several phase-slip events are necessary to induce switching, there is indeed a temperature- and current-range for which a single event is sufficient. It also indicates that the statistical distribution of switching currents initially broadens, as the temperature is reduced. Only at lower temperatures does this distribution show the narrowing with cooling naively expected for resistive fluctuations consisting of phase slips that are thermally activated.

cond-mat.supr-con↗

arXiv2007

Universal thermal and electrical transport near the superconductor-metal quantum phase transition in nanowires

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.

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