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Strongly Disordered Superconductors and Electronic Segregation
The search for macroscopic quantum tunneling in superconducting nanowires
I will make a brief introduction into the history of macroscopic quantum tunneling (MQT) in superconducting devices. Then I will present our results on MQT in superconducting nanowires. The superconductor-insulator transition will also be discussed.
Yuli V. Nazarov
Coherent quantum phase-slips
While incoherent slips of superconducting phase in quasi-1d wires are known for more than 50 years, the experimental evidence for coherent ones is just emerging. To facilitate experimental work in this direction, we consider simple "devices" where we account for coherent phase slips at phenomenological level. Interestingly, the phase slips provide isolation of charge in the wires, resulting in observable Coulomb blockade effects. The non-linearities found in an oscillator where superconducting inductance is subject to coherent phase slips, oscillate as a function of number of photons N with a period of the order of square root of N, which is the "width" of the coherent state. We prove that such non-linearities result in multiple metastable states encompassing few photons and study oscillatory dependence of various responses of the resonator. The experimental realization of our proposals can deliver an unambiguous verification of coherent quantum phase slips.
We also preview some new results concerning the better microscopic estimation of phase-slip amplitude and syncronization of charge and phase oscillations.
N. Peter Armitage
Overview of optical studies of disordered superconductors
The mean-field formalism of the electrodynamic response of superconductors has been in place almost as long as the BCS theory itself. It is believed to capture the physics of conventional superconductors quite accurately. In contrast, strongly disordered superconductors are dominated by order parameter fluctuations and inhomogeneity effects where the mean-field theory is only the roughest of guides. In this tutorial style talk I will review our understanding of the electrodynamic response of strongly disordered superconductors. I will start from the canonical mean-field response and then extend the treatment to strongly disordered systems. In particular I will concentrate on what we learn about fluctuation phenomena, the role of inhomogeneities, dissipation, and the role of coherence in these systems.
Oleg V. Astafiev
Phase-slip qubit realization efforts
Phase-slips in superconducting nano-wires have been studied for a long time. However, direct observation of quantum phase-slip is still a very challenging experimental task. One possibility to realize it is to make a superconducting loop with such a wire, which plays role of a coupler between two circulating currents. At the degeneracy point between the circulating currents, a finite phase-slip rate is expected to lift the degeneracy, forming a two-level system that is a phase-slip qubit. We work on fabrication and measurements of the phase-slip qubit and have observed its signature. Namely, transmission spectroscopy shows a weak signal from a two-level system dependent on magnetic field with expected energy dependence. The energy splitting at the degeneracy point is found to be approximately 3 GHz. Although the effect still has to be confirmed, the results require intensive scientific discussion.
O. Crauste, F. Couëdo, C. Marrache-Kikuchi, L. Bergé, L. Dumoulin
Disorder-induced Superconductor-to-Insulator Transition: three approaches
We report on the study of the Superconductor-to-Insulator Transition (SIT) in NbxSi1-x thin films induced by three different parameters, all related to the amount of disorder in the films : the Nb composition, the thickness and the annealing temperature. The annealing of the films does not modify their microscopic structure but slightly changes the quantum interference patterns. Our results show that the effect of the thickness on the destruction of superconductivity is very distinct from those of the composition or the annealing. The exact mechanism by which the disorder induces a SIT has thus yet to be understood.
Insulator to Superconductor Transitions Come in Multiple Flavors in Quench Condensed Films
Three qualitatively different Insulator to Superconductor Quantum Phase Transitions (ISTs) have been observed in ultrathin quench condensed film systems. Amorphous Bi films deposited onto Aluminum Oxide Nano-HoneyComb (NHC) substrates undergo an IST with increasing thickness that can be distinguished from the ISTs of quench condensed homogeneous and granular films on smooth substrates. Like the granular films, the NHC film insulator consists of localized Cooper pairs implying that superconducting order parameter phase fluctuations dominate these ISTs. The insulator of the homogeneous films, on the other hand, consists of unpaired electrons implying that fluctuations in the amplitude of the superconducting order parameter dominate near their IST. Unlike granular films, transport in NHC insulators is dominated by Cooper pair tunneling rather than quasi-particle tunneling. I will describe how morphological differences correlate with these 3 distinct IST behaviors. I will also describe how the magnetic field responses of both insulating and superconducting films vary with morphology.
Liquid-gated interface superconductivity on an atomically flat film
Liquid/solid interfaces are attracting growing interest not only for applications in catalytic activities and energy storage, but also for their new electronic functions in electric double-layer transistors (EDLTs) exemplified by high-performance organic electronic field-induced electronic phase transitions, as well as superconductivity in SrTiO3. Broadening EDLTs to induce superconductivity within other materials is highly demanded for enriching the materials science of superconductors. However, it is severely hampered by inadequate choice of materials and processing techniques. Here we introduce an easy method using ionic liquids as gate dielectrics, mechanical micro-cleavage techniques for surface preparation, and report the observation of field- induced superconductivity showing a transition temperature Tc = 15.2 K on an atomically flat film of layered nitride compound, ZrNCl. The present result reveals that the EDLT is an extremely versatile tool to induce electronic phase transitions by electrostatic charge accumulation and provides new routes in the search for superconductors beyond those synthesized by traditional chemical methods.
A.Grockowiak, T.Klein, C.Marcenat, X.Blase, and D.Debarre.
Superconducting properties of Boron doped silicon
Short after the discovery of superconductivity in MgB2, a superconducting transition was established in Boron doped diamond and silicon showing that covalent semi-conductors could be a efficient starting point to obtain superconductivity. In diamond, superconductivity appears right at the (doping induced) metal-insulator transition (MIT) but the critical temperature (Tc) remains "abnormally" high down to the critical density. On the other hand, the onset of superconductivity in silicon occurs for Boron concentration several orders of magnitude above the critical value of the MIT but we show that that Tc smoothly decreases with doping and does not follow the exponential decay expected in a standard BCS model. On the contrary we show that Tc roughly scales as \lambda^2 where \lambda is the electron-pnonon coupling constant which can been deduced from ab-initio calculations.
Dr. Pratap Raychaudhuri
Phase fluctuations in 2D and 3D NbN thin films
In a conventional superconductor, it is normally believed that the transition from a superconducting to a normal state is caused by quasiparticle excitations alone and fluctuation is the phase of the order parameter plays a negligible role on the superconducting state. In this talk, I will review our experimental investigations using scanning tunneling spectroscopy, penetration depth and transport measurements, on two situations when phase fluctuations become important in a conventional superconductor. The first situation deals with very thin films of NbN, with thickness less than the superconducting coherence length. The superconducting transition is these 2-dimensional films are governed by the Kosterlitz-Thouless-Berizinski (KTB) transition, where the superconducting state is destroyed through a proliferation of vortex-antivortex pairs. I will show that while KTB theory provides a consistent description of the variation of superfluid density below TKTB, and resistivity above TKTB, the vortex core energy is different from the value given by the 2D-XY model, which is commonly invoked to understand this transition. The second situation deals with 3-dimensional NbN films when strong disorder is introduced in the form of defects in the crystalline lattice. In the presence of strong disorder we observe that the superconducting state become susceptible to phase fluctuations. Consequently, we observe a pronounced pseudogap state above Tc, where the signature of a gap in the electronic excitation spectrum persists up to a much higher temperature. I will describe the relevance of these measurements on the pseudogap state observed in cuprates (and more recently on pnictides).
1. A. Kamlapure et al., Appl. Phys. Lett. 96, 072509 (2010).
2. M. Mondal et al., Phys. Rev. Lett. 106, 047001 (2011).
Very Low Temperature STM: a powerful probe for inhomogeneous superconducting states (tutorial)
Scanning tunnelling microscopy and spectroscopy in the mK range give simultaneously access to very high spatial and energy resolution. This tool is therefore very well suited for studying any inhomogeneous superconducting states. Indeed, the spatial variation of the local density of states of a superconductor and its related superconducting gap can be measured at the mesoscopic scale and eventually down to the atomic scale. A brief introduction to this technique will be given and illustrated with the help of several different situations such as the superconducting proximity effect and the Abrikosov vortex array of superconductors in the mixed state. Highly disordered superconducting ultra-thin films provide another situation of inhomogeneous superconductivity which has been more recently unveiled. The case of TiN thin films close to the superconductor-insulator transition will be described and discussed in more details [1,2].
 B. Sacépé, et al., Physical Review Letters 101, 157006 (2008).
 B. Sacépé, et al., Nature. Commun. 1:140 doi: 10.1038/ncomms1140 (2010).
Condensation versus localization of preformed Cooper-pairs in disordered superconductors
The concept of localized Cooper pairs in disordered superconducting films close to the Superconductor-Insulator Transition (SIT) has intrigued scientists for several decades both theoretically and experimentally. Although the interplay of localization and superconductivity has been clearly evidenced on the macroscopic scale by transport measurements, very little is known about the microscopic details of the strong disorder limit. In this talk I will present tunneling measurements of the local density-of-states on amorphous indium oxide films close to the SIT . Our results show that disorder fluctuations lead to a mixture of superconducting and insulating regions that distinguish themselves by the presence or absence of coherence peaks at the gap edges. Besides, using our STM, we have continuously analyzed the local conductance between the tunneling regime and the point-contact regime. In the latter, Andreev-Sant-James spectroscopy reveals a new energy scale related to the superconducting coherence energy and independent from spatial fluctuations of the pairing energy. This finding as well as other striking anomalies will be discussed regarding recent theories of superconductivity close to the mobility edge that interpret such a gapped state without coherence peak as the spectral signature of localized Cooper pairs.
 B. Sacépé, et al. Nature Physics 7, 239 (2011)
Experimental situation for SIT in amorphous strongly disordered films (tutorial like)
The study of the superconductor-insulator transition has, in recent years, experienced a shift from the initial focus on the physics of the transition to a broader look at the properties of the insulator terminating superconductivity as well as superconductivity itself in the presence of strong disorder. I will attempt to review these developments focusing on results that are in common to more than one set of materials. I will also try to point out what I believe are the main open questions in our growing field.
Fractal and pseudogaped superconductivity: theoretical introduction
I will review basic point of the approach developed recently (Annals of Physics 325,1 (2010)) to describe Cooper pairing of electrons whose single-particle eigenstates
are nearly critical (in the sense of the Anderson transition), whereas Coulomb repulsion is assumed to be weak. Fractal nature of the eigenfunctions near Anderson mobility edge leads to strong spatial fluctuations of the order parameter and to increase of the transition temperature (at fixed coupling strength). Attraction between electrons populating localized eigenstates leads to development of a “pseudogap” whose width may strongly exceed superconductive transition temperature.
Superconductor-Insulator transition in Josephson junction arrays and films with preformed Cooper pairs.
I review the data and theoretical models of the disorder driven superconductor-insulator transition in which Cooper pairs remain intact in the insulating phase. I show that the remarkable feature of this transition is apparent inhomogeneity of the state even in homogeneously disordered materials. I discuss the properties of the insulating state appearing at the transition, I argue that this state is characterized by a small energy scale above which collective excitations are delocalized. As the disorder is increased, the energy scale is increased and eventually becomes infinite signaling the transition into the hard insulator.
A Pourret, P Spathis, H Aubin and K Behnia
Nernst signal generated by superconducting fluctuations in low-Tc disordered superconductors
In amorphous superconducting thin films of Nb0.15Si0.85  and InOx , a finite Nernst coefficient can be detected in a wide range of temperature and magnetic field. Due to the negligible contribution of normal quasi-particles, superconducting fluctuations easily dominate the Nernst response in the entire range of study. In the vicinity of the critical temperature and in the zero-field limit, the magnitude of the signal is in quantitative agreement with what is theoretically expected for the Gaussian fluctuations of the superconducting order parameter . Even at higher temperatures and finite magnetic field, the Nernst coefficient is set by the size of superconducting fluctuations. The Nernst coefficient emerges as a direct probe of the ghost critical field, the normal-state mirror of the upper critical field. Moreover, upon leaving the normal state with fluctuating Cooper pairs, we show that the temperature evolution of the Nernst coefficient is different whether the system enters a vortex solid, a vortex liquid or a phase-fluctuating superconducting regime.
 A. Pourret et al., Nature Physics 2, 683 - 686 (2006)
 A. Pourret et al., Phys. Rev. B. 76, 214504 (2007)
 P. Spathis et al., Europhys. Lett. 83, 57005 (2008)
 A. Pourret et al., New Journal of Physics 11, 055071 (2009)
 I. Ussishkin, S. L. Sondhi and D. A. Huse, Phys. Rev. Lett. 89, 287001 (2002)
Electron cooling rate in amorphous films near SIT: puzzles from the giant I-V jumps experiments
We analyze the recent experiments on giant I-V jumps in amorphous films of InO from the viewpoint of the model of overheated electrons. The electron cooling rate in the localized regime and its dependence on magnetic field and temperature is discussed.
Minsoo Kim, Tailung Wu and Sambandamrthy Ganapathy
Angle-dependent transport behavior across the superconductor-insulator transition in amorphous indium oxide films
We present experimental results from transport studies on amorphous indium oxide films that are driven through a superconductor-insulator transition by applying a pair-breaking magnetic field. The direction of the magnetic field is varied continuously from being perpendicular to the film plane to parallel to the film plane and we identify four distinct transport regimes when the film is rotated in a magnetic field. We also study the evolution of these transport regimes as a function of the disorder in the samples. Implications for our current understanding of the 2D superconductor - insulator transition will be presented.
Dynamical study of phase fluctuations and their critical slowing down in amorphous superconducting films
We report a comprehensive study of the complex ac conductance of amorphous superconducting InOx thin films. We measure the explicit frequency dependency of the complex conductance and the phase stiffness over a range from 0.21 to 15 GHz at temperatures down to 350 mK using a novel broadband microwave Corbino spectrometer. The dynamic ac measurements are sensitive to the temporal correlations of the superconducting order parameter in the fluctuation range above Tc. Among other aspects, we explicitly demonstrate the critical slowing down of the characteristic fluctuation rate on the approach to the superconducting state and show that its behavior is consistent with vortex-like phase fluctuations and a phase-ordering scenario of the transition. If time allows I will discuss our very recent results concerning microwave measurements across the 2D superconductor insulator quantum phase transition.
J. Paramanandam, M. Bell, L.B. Ioffe, and M.E. Gershenson
Magnetic-field-driven phase transitions in unconventional Josephson arrays
We have studied the phase transitions induced by the magnetic field B in arrays of Josephson junctions over a wide range of EJ/EC (EJ is the Josephson energy, EC is the charging energy). These unconventional arrays are characterized by a large number of nearest-neighbor junctions connected to a single superconducting island (typically 10). Due to the commensurability effects, the arrays demonstrated several quantum phase transitions at different critical values of B, which is in line with earlier observations. The critical resistance RC for these transitions varied between 3 kΩ and 20 kΩ. The transitions observed for RC < 5 kΩ were consistent with the “dirty boson” scenario of the superconductor-to-insulator transition (SIT). However, the duality was lacking for the transitions observed at larger RC. The activation energy E0, extracted from the Arrhenius fitting of R(T) in the “insulating” regime, has been compared with the quantity eVt, where Vt is the “offset” voltage corresponding to the onset of a strong non-linearity of the current-voltage characteristics (IVCs). Interestingly, we observed that E0 ≈ eVt for the arrays with sufficiently small values of E0. At a large current bias, the IVCs demonstrate voltage steps 2/e indicating the onset of quasiparticle generation in the arrays. The critical power corresponding to the threshold for quasiparticle generation is temperature-independent below ~ 200 mK and weakly dependent on the zero-bias resistance.
M. A. Skvortsov, M. V. Feigel'man
Spontaneous inhomogeneity in disordered superconducting films
Various sample characteristics are known to exhibit mesoscopic fluctuations. In disordered superconductors, the value of the local pairing field fluctuates across the sample which smears the BCS peak in the density of states. We calculate the smearing of the peak and show that it is enhanced by Coulomb repulsion, leading to strong fluctuations in the vicinity of the quantum critical point where superconductivity is totally suppressed by the “fermionic mechanism”.
Field-enhanced conductivity in electron-glasses
The conductance of electron-glasses may be enhanced when exposed to sufficiently strong electro-magnetic (EM) fields. In the microwaves (MW) regime, this enhancement is an adiabatic effect. Data taken on several systems will be shown to illustrate that this effect is generic and is closely related to the non-ohmic feature commonly found in the dc transport regime. However, in contrast with the lack of heating in the MW regime, applying a large dc field exhibits a non-adiabatic component. A systematic study of these effects as function of the EM frequency reveals a crossover at a surprisingly low frequency. Possible implications of these results to the issue of many-body-localization will be discussed.
Superinductance: implementation and experimental techniques to characterize it
Superinductance is a quantum circuit element defined by its two key properties. First, it must superconduct direct current (DC). Second, it must present to an alternating current (AC) the impedance of a frequency-independent inductance L with sufficiently small stray capacitance Cs, such that (L/Cs)1/2>RQ, where RQ=h/(2e)²≃6.5 kΩ is the superconducting impedance quantum. The amount of dissipation to the alternating current determines the quality of the superinductance, the weaker the dissipation the better the quality. On the technical side, since quantum circuits operate in the microwave frequency range, the maximum operating frequency of the superinductance, which is for instance limited by the self resonance frequency (LCs)-1/2, should exceed at least 10 GHz. This latter condition translates into the following numerical estimate for the required magnitude of the inductance: L>6.5 kΩ/2π×10 GHz≃100 nH.
Remarkably, the experimental implementation and testing of a superinductance goes far beyond the scope of radio-engineering. For instance, attempting to wind a regular wire, or even a bulk superconducting wire, into a conventional coil will result in a failure, which could be traced back to the small value of the fine structure constant. Alternative attempts to increase the specific inductance by turning to highly disordered superconductors would be limited by the quantum phase-slip and eventually by some kind of superconductor-to-insulator transition. Furthermore, in order to fully test a superinductance against various failure modes, it is crucial to develop a setup to measure the superinductance with both DC and microwave excitations.
Our implementation of a superinductance consists of an array of Josephson tunnel junctions with properly chosen parameters. Such array may be viewed as a special case of a highly disordered but structurally continuous superconducting wire. We have developed two types of measurement techniques to characterize our array-based superinductances, which should be applicable to any other implementation.
In the first technique we use the superinductance as a semi-transparent "mirror" of a superconducting Fabry-Perot resonator, made of a conventional low kinetic inductance superconductor. The quality factor of the resonance translates directly into the value of the superinductance at the resonance frequency, provided the internal dissipation inside the Fabry-Perot is negligible. This technique is nearly insensitive to the dissipation inside the superinductance. In the second technique we use a superinductance as a key element of a superconducting fluxonium qubit and measure its transition frequencies and decoherence times. The former allows precise determination of superinductance magnitude, while the latter reveals information about the dissipation inside the superinductance as well as the coherent quantum phase-slip frequency.
Our techniques may prove useful in characterizing highly disordered superconductors on the superconducting side of the superconductor to insulator transition.
Flash presentations and posters
Enhancement of superconductivity by Anderson localization
Influence of disorder on the temperature of superconding transition (Tc) is studied within the sigma-model renormalization group framework. Electron-electron interaction in particle-hole and Cooper channels is taken into account and assumed to be short-range.
Two-dimensional systems in the weak localization and antilocalization regime, as well as systems near mobility edge are considered. It is shown that in all these regimes the Anderson localization leads to strong enhancement of Tc related to the multifractal character of wave functions.
Superfluid density and phase relaxation in superconductors with strong disorder
As a prototype of disordered superconductor we consider the attractive Hubbard model with on site disorder. We solve the Bogoljubov-de-Gennes equations on two-dimensional finite clusters at zero temperature and we evaluate the electromagnetic response to a vector potential. We find that the standard decoupling between transverse and longitudinal response does not apply in the presence of disorder and that the superfluid density is strongly reduced by the relaxation of the phase of the order parameter already at mean-field level when disorder is large. We also find that the anharmonicity of the phase fluctuations increases by increasing disorder. Going beyond mean-field, this provides an enhancement of quantum fluctuations in producing a zero-temperature transition to a non-superconducting phase. In the large U limit, near half-filling, this transition is towards a phase of disordered preformed pairs. Finally, by analyzing the distribution of the on-site order parameter in the superconducting phase at large U we find anomalous tails like those of a glassy (replica-symmetry breaking) phase recently suggested by Ioffe and Mezard for disorder superconductors using a cavity method approach.
L.Benfatto, G.Seibold, J.Lorenzana, and C.Castellani, “Superfluid density and phase relaxation in superconductors with strong disorder ”, submitted to PRL.
P.C.J.J. Coumou, E.F.C. Driessen, R.R. Tromp, P.J. de Visser, A. Endo, M.R. Zuiddam and T.M. Klapwijk
Electrodynamics of strongly disordered superconducting TiN films
We study the electrodynamics of atomic layer deposited and sputter deposited TiN films with varying disorder. The films have kFℓ values between 2.6 and 11 characterizing the disorder. We measure the electromagnetic response of these films using microwave resonators. The internal quality factor and the shift in the resonance frequency as a function of temperature are probes for the real and imaginary part of the complex conductivity. The response of the films with low disorder can be described in the framework of Mattis-Bardeen, provided that a broadening of the BCS density of states is introduced. For increasing disorder, the needed broadening parameter is observed to increase. This suggests that the stronger the disorder, the larger the deviation from the conventional Mattis-Bardeen / BCS theory.
A.M. Hriscu and Yu.V. Nazarov
Quantum Phase-Slip Devices
We theoretically propose novel devices to illustrate the coherent quantum phase-slips (QPS): the QPS oscillator, the QPS-box and QPS-transistor.
The QPS oscillator can be realized on the basis of a thin superconducting wire or a chain of Josephson junctions1. It proves that the experimental detection of quantum phase slips is achievable for small phase slip amplitudes, contrary to what is usually assumed. The responses of this damped-driven oscillator exhibit a cosine dependence on the charge induced by a gate electrode and very unusual oscillatory dependence on the drive/frequency.
The QPS-box and the QPS-transistor are derived from the Cooper-pair box and Cooper-pair transistor2. They exhibit sensitivity to a charge induced by a gate electrode, this being the main signature of Coulomb blockade. Experimental realization of such devices will prove the Coulomb blockade as an effect of coherence of QPS processes.
1A.M. Hriscu, Y.V. Nazarov, Phys. Rev. Lett. 106, 0
Cooper pair insulator in amorphous films induced by nanometer-scale thickness variations
Ultrathin films near the quantum Insulator-Superconductor Transition (IST) can exhibit Cooper pair transport in their insulating state. This Cooper Pair Insulator (CPI) state is achieved in amorphous Bi films evaporated onto substrates with a topography varying on lengths slightly greater than the superconducting coherence length. We present evidence that this topography induces film thickness and corresponding superconducting coupling constant variations that promote Cooper pair island formation. Analyses of many thickness-tuned ISTs show that weak links between superconducting islands dominate the transport. In particular, the IST occurs when the link resistance approaches the resistance quantum for pairs. These results support conjectures that the CPI is an inhomogeneous state of matter.
E.F.C. Driessen, H.L. Hortensius, N. Vercruyssen, K.K. Berggren, T. Zijlstra, and T.M. Klapwijk
The Superconducting Transition in Highly Resistive NbTiN Nanowires.
Superconducting thin-_lm materials with a high normal-state resistivity are of interest as building blocks for quantum devices and radiation detectors. However, the very disordered nature of these materials gives rise to a strong competition between electron localization and superconductivity, leading to a superconductor-insulator transition with increasing disorder1. Prior to this transition the electronic properties are expected to become inhomogeneous even for uniform structural disorder. This leads to the question how superconductivity manifests itself in these resistive materials. We present measurements of the normal-to-superconducting transition of NbTiN nanowires, with a thick- ness of 8 nm, widths varying from 50 nm to 400 nm, and a normal-state resistivity of _ 160 _cm. Each width shows a smooth superconductive transition at Tc = 10:5 K, consistent with the Aslamazov-Larkin theory for two-dimensional wires. Close to Tc however, measurements of the critical current and the critical magnetic _eld of the nanowires reveal that the resistive state is reached in a series of steps, each adding a typical resistance of 5 10 k to the wire. Moreover, from the critical currents we obtain a higher critical temperature than observed in the zero-bias resistive transition. From this, we conclude that in a certain temperature regime the wire is resistive while localized superconductivity is still present.
1For example Sacépé et al, Nature Physics 7, 239 (2011)
A Theory of Quantum Phase-slips in One-dimensional Superconductors Based on
In this presentation I will describe a new theory of quantum phase-slips in1D superconducting wires. This theory takes as its starting point the hypothesis advanced by Mooij and Nazarov [Nat. Phys. 2, 169 - 2006] that quantum phase-slips (tunneling of fluxoid quanta through narrow superconducting wires) and Josephson tunneling of Cooper pairs are related through electromagnetic duality. Just as Cooper pairs can tunnel through an energy barrier due to the zero-point fluctuations associated with their finite mass (kinetic inductance), I postulate that tunneling of fluxoid quanta through an energy barrier (a narrow superconducting wire) arises due to a mass associated with their electromagnetic momentum. The resulting kinetic energy is associated with an electric field, effectively generated by moving flux, which must charge up a capacitance. In this picture, the "kinetic capacitance" (dual of the kinetic inductance) postulated by Mooij and Nazarov can be connected directly with the real part of the electric permittivity (geometric series capacitance) of the wire. Building on this basic microscopic picture of quantum phase-slips, I will describe a model for an extended nanowire where polarization charge of the wire is dual to magnetic flux through a JJ barrier, and quantum phase-slips occur coherently along the entire wire, just as Cooper pairs tunnel coherently through the entire barrier of a JJ. This model predicts a new type of secondary quantum macroscopic effect, which I call a type-II phase slip (intimately related to a vortex in a type-II superconductor), that in very short 1D wires is dual to the well-known Bloch oscillation in a Josephson junction. Excitation of these type-II phase slips may provide a new explanation for phenomena that have previously been identified with quantum phase slips in 1D superconducting wires. The model also connects to the well-known LAMH model of thermal phase slips near the critical temperature, and it provides a simple and intuitive means to calculate the attempt rate for these phase slips. I will discuss what this theory, if correct, would imply for the future prospects of observing quantum phase-slips and for new types of superconducting electronic devices.
Fluctuating Hall effect and nonlinear fluctuating conductivity of the dirty superconductor
We consider fluctuation phenomena in dirty superconductors on the basis of the superconducting sigma model [1, 2]. To begin, we reproduce well-known results for longitudal fluctuational conductivity. Next, we consider this effects in the out-of-equilibrium conditions, and calculate fluctuating Hall effect, extending existing theory  for arbitrary temperatures and magnetic fields.
 A. Levchenko, A. Kamenev, Keldysh Ginzburg-Landau action of
fluctuating superconductors. Phys. Rev. B76 094518.
R.R. Tromp, E.F.C. Driessen, P.C.J.J. Coumou, T. Zijlstra, and T.M. Klapwijk
Interplay of superconducting fluctuations and localization in TiN films with increasing disorder
Localization effects on superconducting fluctuations are investigated for 200-400 nm thick TiN films as a function of disorder. The disorder is characterized with the product kFℓ, which is determined from measurements of the resistivity and Hall effect at different temperatures in magnetic fields up to 13 T. For films with kFℓ between 2.6 and 11.1, it is found that the resistivity increases and the free electron density decreases with increasing disorder.
Measurements on the superconducting transition at zero magnetic field show that the resistivity is affected by superconducting fluctuations up to 2Tc, signaling the presence of 3D Aslamazov-Larkin paraconductivity. The superconducting transition becomes more gradual with increasing disorder.
When a magnetic field is applied, the fluctuations are increasingly suppressed, leading to an increased resistivity. At large fields the resistivity saturates, sign of a characteristic field required to suppress fluctuation effects. The width of the suppression region is constant with sample temperature, but increases with disorder from about 0.6 T for kFℓ = 11.1 to 1.9 T for kFℓ = 3.7 at temperatures 0.1 K above Tc. Together with the superconducting transition in zero field, this signals a relation between fluctuation effects and disorder in TiN films.