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We extract the vortex lattice parameters using low-frequency two-coil mutual inductance measurements in a 20-nm-thick superconducting a-MoGe thin film. We fit the temperature dependence of ac penetration depth in the mixed state using a model developed by Coffey and Clem and demonstrate a procedure for extracting vortex lattice parameters such as pinning constant, vortex lattice drag coefficient, and pinning potential barrier. We show that the extracted parameters follow the magnetic field variation expected for a weakly pinned 2-dimensional vortex lattice., 21 pages, 6 figures

Hybrid superconductor/graphene (SC/g) junctions are excellent candidates for investigating correlations between Cooper pairs and quantum Hall (QH) edge modes. Experimental studies are challenging as Andreev reflections are extremely sensitive to junction disorder and high magnetic fields are required to form QH edge states. We fabricated low-resistance SC/g interfaces, composed of graphene edge contacted with NbN with a barrier strength of $Z\approx 0.4$, that remain superconducting under magnetic fields larger than $18$ T. We establish the role of graphene's Dirac band structure on zero-field Andreev reflections and demonstrate dynamic tunability of the Andreev reflection spectrum by moving the boundary between specular and retro Andreev reflections with parallel magnetic fields. Through the application of perpendicular magnetic fields, we observe an oscillatory suppression of the 2-probe conductance in the $\nu = 4$ Landau level attributed to the reduced efficiency of Andreev processes at the NbN/g interface, consistent with theoretical predictions.

In a Type II superconductor, the vortex core behaves like a normal metal. Consequently, the single-particle density of states in the vortex core of a conventional Type II superconductor remains either flat or (for very clean single crystals) exhibits a peak at zero bias due to the formation of Caroli-de Gennes-Matricon bound state inside the core. Here we report an unusual observation from scanning tunneling spectroscopy measurements in a weakly pinned thin film of the conventional s-wave superconductor a-MoGe, namely, that a soft gap in the local density of states continues to exist even at the center of the vortex core. We ascribe this observation to rapid fluctuation of vortices about their mean position that blurs the boundary between the gapless normal core and the gapped superconducting region outside. Analyzing the data as a function of magnetic field we show that the variation of fluctuation amplitude as a function of magnetic field is consistent with quantum zero-point motion of vortices., arXiv admin note: substantial text overlap with arXiv:1905.01045

The highly convergent form of superfluid density in disordered conventional superconductors available in the literature and independently obtained by us following the approach of an earlier paper [Phys. Rev. B $\bm{102}$, 024514 (2020)] has been reformulated to separate out the generally used so-called `dirty-limit' term and an additional term. We use this new expression for making an extensive comparison with previously published experimental data and show that the former, generally used, term is {\em not} sufficient for analyzing these results. We point out that consequently, there is a large regime (disordered superconductors with moderate to no disorder) where theoretical predictions need to be confronted with experiment., Comment: 8 pages, 3 figures

In two-dimensional (2D) systems, the melting from a solid to an isotropic liquid can occur via an intermediate phase that retains orientational order. However, in 2D superconducting vortex lattices, the effect of orientational correlations on transport, and their interplay with disorder remain open questions. Here we study a 2D weakly pinned vortex system in amorphous MoGe films over an extensive range of temperatures ($\bm{T}$) and perpendicular magnetic fields ($\bm{H}$) using linear and nonlinear transport measurements. We find that, at low fields, the resistivity obeys the Vogel-Fulcher-Tamman (VFT) form, $\bm{\rho(T)\propto\exp[-{W}(H)/(T-T_0(H))]}$, characteristic of fragile glasses. As $\bm{H}$ increases, $\bm{T_0(H)}$ is suppressed to zero, and a standard vortex liquid behavior consistent with a $\bm{T=0}$ superconducting transition is observed. Our findings, supported also by simulations, suggest that the presence of orientational correlations gives rise to a heterogeneous dynamics responsible for the VFT behavior. The effects of quenched disorder become dominant at high $\bm{H}$, where a crossover to a strong-glass behavior is observed. This is a new insight into the dynamics of melting in 2D systems with competing orders., Comment: 16 pages, 12 figures

We explore the effects of sample dimensionality on vortex pinning in a type-II, low-$T_C$, s-wave superconductor, NbN, in the presence of a perpendicular magnetic field, $H$. We find significant differences in the phase diagrams in the magnetic field--temperature plane between 3-dimensional (3D) and 2-dimensional (2D) NbN films. The differences are most striking close to the normal-superconductor phase transition. We establish that these variances have their origin in the differing pinning properties in two different dimensions. We obtain the pinning strength quantitatively in both the dimensions from two independent transport measurements performed in two different regimes of vortex-motion -- (i) thermally assisted flux-flow (TAFF) regime and (ii) flux flow (FF) regime. Both the measurements consistently show that both the pinning potential and the zero-field free-energy barrier to depinning in the 3D superconductor are at least an order of magnitude stronger than that in the 2D superconductor. Further, we probed the dynamics of pinning in both 2D and 3D superconductor through voltage fluctuation spectroscopy. We find that the mechanism of vortex pinning-depinning is qualitatively similar for the 3D and 2D superconductors. The voltage-fluctuations arising from vortex-motion are found to be correlated only in the 2D superconductor. We establish this to be due to the presence of long-range phase fluctuations near the Berezinskii-Kosterlitz-Thouless (BKT) type superconducting transition in 2-dimensional superconductors.

Superconductivity occurs in metals when attractive interactions between electrons promote the formation of Cooper pairs which get locked in a phase-coherent state, leading to superfluid behavior. In situations where the phase stiffness falls below the pairing energy, the superconducting transition temperature ${T}_{c}$ is driven by phase fluctuations and pairing can continue to survive above ${T}_{c}$. Such a behavior has long been thought of as the hallmark of unconventional superconductivity. Here we combine sub-K scanning tunneling spectroscopy, magnetic penetration depth measurements, and magnetotransport measurements to show that in ultrathin amorphous MoGe ($a$-MoGe) films the superfluid density is strongly suppressed by quantum phase fluctuations at low temperatures for thickness below 5 nm. This is associated with a rapid decrease in the superconducting transition temperature ${T}_{c}$ and the emergence of a pronounced pseudogap above ${T}_{c}$. These observations suggest that even in conventional superconductors strong disorder and low dimensionality will ultimately trigger a Bosonic route for the destruction of superconductivity.

We report the growth, characterization and superconducting properties of a new amorphous superconductor, RexZr ( x ~ 6 ), in thin film form. Films were grown by pulsed laser deposition with the substrate kept at room temperature. Films with thickness larger than 40 nm showed a superconducting transition temperature (Tc) of 5.9 K. Superconducting properties were measured for films with varying thickness from 120 to 3 nm. The normal state resistance scales linearly with inverse of thickness. The transition temperature, critical field, coherence length, penetration depth and superconducting energy gap changes marginally with decreasing film thickness down to 8 nm. Scanning tunneling spectroscopy and penetration depth measurements provide evidence for a single gap strong coupling s-wave superconductor. Magneto-transport properties indicate a rich magnetic field-temperature phase diagram with the possibility of vortex liquid phases existing over a large fraction of the mixed state.

Recently, detailed real space imaging using scanning tunneling spectroscopy of the vortex lattice in a weakly pinned a-MoGe thin film revealed that the vortex lattice melts in two steps with temperature or magnetic field, going first from a vortex solid to a hexatic vortex fluid and then from a hexatic vortex fluid to an isotropic vortex liquid. In this paper, we show that the resistance in the vortex fluid states is extremely sensitive to radio-frequency electromagnetic perturbation. In the presence of very low-amplitude excitation above few kilohertz, the resistance increases by several orders of magnitude. On the other hand when the superconductor is well shielded from external electromagnetic radiation, the dissipation in the sample is very small and the resistance is below our detection limit., pdf file with figures

Pinning and creep determine the current--voltage characteristic of a type II superconductor and thereby its potential for technological applications. The recent development of strong pinning theory provides us with a tool to assess a superconductor's electric properties in a quantitative way. Motivated by the observation of typical excess-current characteristics and field-scaling of critical currents, here, we analyze current--voltage characteristics measured on 2H-NbSe$_2$ and $a$-MoGe type II superconductors within the setting provided by strong pinning theory. The experimentally observed shift and rounding of the voltage-onset is consistent with the predictions of strong pinning in the presence of thermal fluctuations. We find the underlying parameters determining pinning and creep and discuss their consistency.

Within the Bardeen–Cooper–Schrieffer (BCS) theory, superconductivity is entirely governed by the pairing energy scale, which gives rise to the superconducting energy gap, Δ. However, another important energy scale, the superfluid phase stiffness, J, which determines the resilience of the superconductor to phase-fluctuations is normally ignored. The spectacular success of BCS theory owes to the fact that in conventional superconductors J is normally several orders of magnitude larger than Δ and thus an irrelevant energy scale. However, in certain situations such as in the presence of low carrier density, strong disorder, at low-dimensions or in granular superconductors, J can drastically come down and even become smaller than Δ. In such situations, the temperature and magnetic field evolution of superconducting properties is governed by phase fluctuations, which gives rise to novel electronic states where signatures of electronic pairing continue to exist even when the zero resistance state is destroyed. In this article, we will review the recent experimental developments on the study of phase fluctuations in conventional superconductors.

We investigate the magnetic field variation of the thermally activated flux flow resistivity, ρ TAFF and flux flow critical current density, J c, in a weakly pinned thin film of the amorphous superconductor a-MoGe, where vortices are in a fluid state over a large range of magnetic fields. We show that both quantities can be understood within the framework of collective pinning theory. In particular, our results demonstrate that a 'peak effect' can arise at the order-disorder transition of the vortex lattice even when both the ordered and disordered states are vortex fluids, such as the boundary between a hexatic vortex fluid and an isotropic vortex liquid.

One of the hallmarks of the Berezinskii-Kosterlitz-Thouless (BKT) transition in two-dimensional superconductors is the universal jump of the superfluid density that can be indirectly probed via the nonlinear exponent of the current-voltage $I\text{\ensuremath{-}}V$ characteristics. Here, we compare the experimental measurements of $I\text{\ensuremath{-}}V$ characteristics in two cases, namely NbN thin films and ${\mathrm{SrTiO}}_{3}$-based interfaces. While the former display a paradigmatic example of BKT-like nonlinear effects, the latter do not seem to justify a BKT analysis. Rather, the observed $I\text{\ensuremath{-}}V$ characteristics can be well reproduced theoretically by modeling the effect of mesoscopic inhomogeneity of the superconducting state. Our results offer an alternative perspective on the spontaneous fragmentation of the superconducting background in confined two-dimensional systems.

We investigate the magnetic field evolution of the superconducting state in a strongly disordered NbN thin film which exhibits a magnetic field tuned superconductor to insulator-like transition, employing low temperature scanning tunneling spectroscopy (STS). Transport measurements of the sample reveals a characteristic magnetic field, which separates the low field state where resistance decreases with decreasing temperature, i.e. dR/dT > 0 and a high-field state where dR/dT < 0. However, STS imaging of the superconducting state reveals a smooth evolution across this field and the presence of a robust pseudogap on both sides of this characteristic field. Our results suggest that the superconductor-insulator transition might be a percolative transition driven by the shrinking of superconducting fraction with magnetic field., 22 pages, 8 figures including supplementary material

${\mathrm{CeMnNi}}_{4}$ exhibits an unusually large spin polarization, but its origin has baffled researchers for more than a decade. We use bulk sensitive hard x-ray photoelectron spectroscopy (HAXPES) and density functional theory based on the Green's function technique to demonstrate the importance of electron-electron correlations of both the Ni $3d$ (${U}_{\text{Ni}}$) and Mn $3d$ (${U}_{\text{Mn}}$) electrons in explaining the valence band of this multiply correlated material. We show that Mn-Ni antisite disorder as well as ${U}_{\text{Ni}}$ play a crucial role in enhancing its spin polarization: Antisite disorder broadens a Ni $3d$ minority-spin peak close to the Fermi level (${E}_{F}$), while an increase in ${U}_{\text{Ni}}$ shifts it toward ${E}_{F}$, both leading to a significant increase of minority-spin states at ${E}_{F}$. Furthermore, the rare occurrence of a valence state transition between the bulk and the surface is demonstrated highlighting the importance of HAXPES in resolving the electronic structure of materials unhindered by surface effects.

We investigate the performance of niobium nitride superconducting coplanar waveguide resonators towards hybrid quantum devices with magnon-photon coupling. We find internal quality factors ~ 20000 at 20 mK base temperature, in zero magnetic field. We find that by reducing film thickness below 100 nm internal quality factor greater than 1000 can be maintained up to parallel magnetic field of ~ 1 T and perpendicular magnetic field of ~ 100 mT. We further demonstrate strong coupling of microwave photons in these resonators, with magnons in chromium trichloride, a van der Waals antiferromagnet, which shows that these cavities serve as a good platform for studying magnon-photon coupling in 2D magnonics based hybrid quantum systems. We demonstrate strong magnon-photon coupling for both optical and acoustic magnon modes of an antiferromagnet., 15 pages, 14 figures

The proposals for realizing exotic particles through coupling of quantum Hall effect to superconductivity involve spatially non-uniform magnetic fields. As a step toward that goal, we study, both theoretically and experimentally, a system of Dirac electrons exposed to an Abrikosov flux lattice. We theoretically find that the non-uniform magnetic field causes a carrier-density–dependent reduction of the Hall conductivity. Our studies show that this reduction originates from a rather subtle effect: a levitation of the Berry curvature within Landau levels broadened by the non-uniform magnetic field. Experimentally, we measure the magneto-transport in a monolayer graphene-hexagonal boron nitride-niobium diselenide (NbSe2) heterostructure, and find a density-dependent reduction of the Hall resistivity of graphene as the temperature is lowered from above the superconducting critical temperature of NbSe2, when the magnetic field is uniform, to below, where the magnetic field bunches into an Abrikosov flux lattice.

In this article, we present evidence for the existence of vortex-solid/glass (VG) to vortex-fluid (VF) transition in a type-II superconductor (SC), NbN. We probed the VG to VF transition in both 2D and 3D films of NbN through studies of magnetoresistance and current-voltage characteristics. The dynamical exponents corresponding to this phase transition were extracted independently from the two sets of measurements. The $H$-$T$ phase diagram for the 2D and 3D SC are found to be significantly different near the critical point. In the case of 3D SC, the exponent values obtained from the two independent measurements show excellent match. On the other hand, for the 2D SC, the exponents obtained from the two experiments were significantly different. We attribute this to the fact that the characteristic length scale diverges near the critical point in a 2D SC in a distinctly different way from its 3D counterpart form scaling behaviour.

Superconductivity and the quantum Hall effect are distinct states of matter occurring in apparently incompatible physical conditions. Recent theoretical developments suggest that the coupling of the quantum Hall effect with a superconductor can provide fertile ground for realizing exotic topological excitations such as non-Abelian Majorana fermions or Fibonacci particles. As a step toward that goal, we report observation of Andreev reflection at the junction of a quantum Hall edge state in a single layer graphene and a quasi-two-dimensional niobium diselenide (${\mathrm{NbSe}}_{2}$) superconductor. Our principal finding is the observation of an anomalous finite-temperature conductance peak located precisely at the Dirac point, providing a definitive evidence for inter-Landau-level Andreev reflection in a quantum Hall system. Our observations are well supported by detailed numerical simulations, which offer additional insight into the role of the edge states in Andreev physics. This study paves the way for investigating analogous Andreev reflection in a fractional quantum Hall system coupled to a superconductor to realize exotic quasiparticles.

The hexatic fluid refers to a phase in between a solid and a liquid that has short-range positional order but quasi-long-range orientational order. In the celebrated theory of Berezinskii, Kosterlitz, and Thouless and subsequently refined by Halperin, Nelson, and Young, it was predicted that a two-dimensional hexagonal solid can melt in two steps: first, through a transformation from a solid to a hexatic fluid, which retains quasi-long-range orientational order; and then from a hexatic fluid to an isotropic liquid. In this Letter, using a combination of real space imaging and transport measurements, we show that the two-dimensional vortex lattice in an a-MoGe thin film follows this sequence of melting as the magnetic field is increased. Identifying the signatures of various transitions on the bulk transport properties of the superconductor, we construct a vortex phase diagram for a two-dimensional superconductor.

Superconductivity and the quantum Hall effect are distinct states of matter occurring in apparently incompatible physical conditions. Recent theoretical developments suggest that the coupling of the quantum Hall effect with a superconductor can provide fertile ground for realizing exotic topological excitations such as non-Abelian Majorana fermions or Fibonacci particles. As a step toward that goal, we report observation of Andreev reflection at the junction of a quantum Hall edge state in a single layer graphene and a quasi-two-dimensional niobium diselenide (NbSe_{2}) superconductor. Our principal finding is the observation of an anomalous finite-temperature conductance peak located precisely at the Dirac point, providing a definitive evidence for inter-Landau-level Andreev reflection in a quantum Hall system. Our observations are well supported by detailed numerical simulations, which offer additional insight into the role of the edge states in Andreev physics. This study paves the way for investigating analogous Andreev reflection in a fractional quantum Hall system coupled to a superconductor to realize exotic quasiparticles.

We present the first observation of dynamically modulated quantum phase transition between two distinct charge density wave (CDW) phases in two-dimensional $2H\text{\ensuremath{-}}{\mathrm{NbSe}}_{2}$. There is recent spectroscopic evidence for the presence of these two quantum phases, but its evidence in bulk measurements remained elusive. We studied suspended, ultrathin $2H\text{\ensuremath{-}}{\mathrm{NbSe}}_{2}$ devices fabricated on piezoelectric substrates---with tunable flakes thickness, disorder level, and strain. We find a surprising evolution of the conductance fluctuation spectra across the CDW temperature: the conductance fluctuates between two precise values, separated by a quantum of conductance. These quantized fluctuations disappear for disordered and on-substrate devices. With the help of mean-field calculations, these observations can be explained as to arise from dynamical phase transition between the two CDW states. To affirm this idea, we vary the lateral strain across the device via piezoelectric medium and map out the phase diagram near the quantum critical point. The results resolve a long-standing mystery of the anomalously large spectroscopic gap in ${\mathrm{NbSe}}_{2}$.

In contrast to the seminal weak localization prediction of a non-critical Hall constant ($R_{H}$) at the Anderson metal-insulator transition (MIT), $R_{H}$ in quite a few real disordered systems exhibits both, a strong $T$-dependence and critical scaling near their MIT. Here, we investigate these issues in detail within a non-perturbative "strong localization" regime using cluster-dynamical mean field theory (CDMFT). We uncover $(i)$ clear and unconventional quantum-critical scaling of the $\gamma$-function, finding that $\gamma(g_{xy})\simeq$ log$(g_{xy})$ over a wide range spanning the continuous MIT, very similar to that seen for the longitudinal conductivity, $(ii)$ strongly $T$-dependent and clear quantum critical scaling in both transverse conductivity and $R_{H}$ at the MIT. We find that these surprising results are in comprehensive and very good accord with signatures of a novel kind of localization in disordered NbN near the MIT, providing substantial support for our "strong" localization view., Comment: 6 pages, 8 figures

When a magnetic field is applied, the mixed state of a conventional Type II superconductor gets destroyed at the upper critical field Hc2, where the normal vortex cores overlap with each other. Here, we show that in the presence weak and homogeneous disorder the destruction of superconductivity with field follows a different route. Starting with a weakly disordered NbN thin film ( Tc ~ 9K ), we show that under the application of magnetic field the superconducting state becomes increasingly granular, where lines of vortices separate the superconducting islands. Consequently, phase fluctuations between these islands give rise to a field induced pseudogap phase, which has a gap in the electronic density of states but where the global zero resistance state is destroyed., Comment: New data added in this version

We present the first observation of dynamically modulated quantum phase transition between two distinct charge density wave (CDW) phases in two-dimensional 2H-NbSe_{2}. There is recent spectroscopic evidence for the presence of these two quantum phases, but its evidence in bulk measurements remained elusive. We studied suspended, ultrathin 2H-NbSe_{2} devices fabricated on piezoelectric substrates-with tunable flakes thickness, disorder level, and strain. We find a surprising evolution of the conductance fluctuation spectra across the CDW temperature: the conductance fluctuates between two precise values, separated by a quantum of conductance. These quantized fluctuations disappear for disordered and on-substrate devices. With the help of mean-field calculations, these observations can be explained as to arise from dynamical phase transition between the two CDW states. To affirm this idea, we vary the lateral strain across the device via piezoelectric medium and map out the phase diagram near the quantum critical point. The results resolve a long-standing mystery of the anomalously large spectroscopic gap in NbSe_{2}.

We simulate a rotating 2D BEC to study the melting of a vortex lattice in presence of random impurities. Impurities are introduced either through a protocol in which vortex lattice is produced in an impurity potential or first creating the vortex lattice in the absence of random pinning and then cranking up the (co-rotating) impurity potential. We find that for a fixed strength, pinning of vortices at randomly distributed impurities leads to the new states of vortex lattice. It is unearthed that the vortex lattice follow a two-step melting via loss of positional and orientational order. Also, the comparisons between the states obtained in two protocols show that the vortex lattice states are metastable states when impurities are introduced after the formation of an ordered vortex lattice. We also show the existence of metastable states which depend on the history of how the vortex lattice is created., Comment: Accepted in Euro. Phys. Lett

Despite extensive search for about a decade, specular Andreev reflection (SAR) has only recently been realized in the bilayer graphene-superconductor interface. The experimental observation of retro to specular Andreev reflection is not only fundamentally important, but also has potential application in quantum computing, etc. Here we have carried out the transport measurements at the van der Waals interface of single-layer graphene and ${\mathrm{NbSe}}_{2}$ superconductor. We investigate the Andreev reflection near the Dirac point by measuring the differential conductance as a function of Fermi energy and bias energy. We find that the normalized conductance (${G}_{Tl{T}_{c}}/{G}_{TgTc}$) becomes suppressed as we pass through the Dirac cone, which manifests the transition from retro to nonretro-type Andreev reflection. The suppression indicates the blockage of Andreev reflection beyond a critical angle (${\ensuremath{\theta}}_{c}$) of the incident electron with respect to the normal between the single-layer graphene and the superconductor junction. However, the observation of SAR was restricted due to the finite Fermi-energy broadening. The results are compared with a theoretical model of the corresponding setup.

Disorder induced melting, where the increase in positional entropy created by random pinning sites drives the order-disorder transition in a periodic solid, provides an alternate route to the more conventional thermal melting. Here, using real space imaging of the vortex lattice through scanning tunneling spectroscopy, we show that in the presence of weak pinning, the vortex lattice in a type II superconductor disorders through two distinct topological transitions. Across each transition, we separately identify metastable states formed through superheating of the low temperature state or supercooling of the high temperature state. Comparing crystals with different levels of pinning we conclude that the two-step melting is fundamentally associated with the presence of random pinning which generates topological defects in the ordered vortex lattice.

We report experimental evidence of strong orientational coupling between the crystal lattice and the vortex lattice in a weakly pinned Co-doped NbSe2 single crystal through direct imaging using low temperature scanning tunneling microscopy/spectroscopy. At low fields, when the magnetic field is applied along the six-fold symmetric c-axis of the NbSe2 crystal, the equilibrium configuration of the vortex lattice is preferentially aligned along the basis vectors of the crystal lattice. The orientational coupling between the vortex lattice and crystal lattice becomes more pronounced as the magnetic field is increased. We show that this coupling enhances the stability of the orientational order of the vortex lattice, which persists even in the disordered state at high fields where dislocations and disclinations have destroyed the topological order., Comment: Expanded with additional data

The vortex lattice in a Type II superconductor provides a versatile model system to investigate the order-disorder transition in a periodic medium in the presence of random pinning. Here, using scanning tunnelling spectroscopy in a weakly pinned Co0.0075NbSe2 single crystal, we show that the vortex lattice in a 3-dimensional superconductor disorders through successive destruction of positional and orientational order, as the magnetic field is increased across the peak effect. At the onset of the peak effect, the equilibrium quasi-long range ordered state transforms into an orientational glass through the proliferation of dislocations. At a higher field, the dislocations dissociate into isolated disclination giving rise to an amorphous vortex glass. We also show the existence of a variety of additional non-equilibrium metastable states, which can be accessed through different thermomagnetic cycling.

We show that under an a.c. magnetic field excitation the vortex lattice in a superconductor with periodic array of holes can undergo a transition from a Mott-like state where each vortex is localized in a hole, to a metal-like state where the vortices get delocalized. The vortex dynamics is studied through the magnetic shielding response which is measured using a low frequency two-coil mutual inductance technique on a disordered superconducting NbN film having periodic array of holes. We observe that the shielding response of the vortex state is strongly dependent on the amplitude of the a.c. magnetic excitation. At low amplitude the shielding response varies smoothly with excitation amplitude, corresponding to elastic deformation of the vortex lattice. However, above a threshold value of excitation the response shows a series of sharp jumps, signaling the onset of the Mott to metal transition. Quantitative analysis reveals that this is a collective phenomenon which depends on the filling fraction of vortices in the antidot lattice., Comment: Significantly modified version

Superconductivity in disordered systems close to an incipient localization transition has been an area of investigation for many years. It has been noted that in such highly disordered superconductors, anomalous spectral weight develops in their conductivity near and below the superconducting gap energy. In this work we investigate the low frequency conductivity in disordered superconducting NbN thin films close to the localization transition with time-domain terahertz spectroscopy. In the normal state, strong deviations from the Drude form due to incipient localization are found. In the superconducting state we find substantial spectral weight at frequencies well below the superconducting gap scale derived from tunneling. We analyze this spectral weight in the context of a model of disorder induced broadening of the quasiparticle density of states and effective pair-breaking. We find that although aspects of the optical and tunneling data can be consistently modeled in terms of this effect of mesoscopic disorder, the optical conductivity returns to the normal state value much faster than any model predicts. This points to the non-trivial interplay of superconductivity and disorder close to localization., 5 pages, 3 figures in main text; 7 pages, 4 figures in SI

The vortex lattice in a Type II superconductor provides a versatile model system to investigate the order-disorder transition in a periodic medium in the presence of random pinning. Here, using scanning tunnelling spectroscopy in a weakly pinned Co0.0075NbSe2 single crystal, we show that the vortex lattice in a 3-dimensional superconductor disorders through successive destruction of positional and orientational order, as the magnetic field is increased across the peak effect. At the onset of the peak effect, the equilibrium quasi-long range ordered state transforms into an orientational glass through the proliferation of dislocations. At a higher field, the dislocations dissociate into isolated disclination giving rise to an amorphous vortex glass. We also show the existence of a variety of additional non-equilibrium metastable states, which can be accessed through different thermomagnetic cycling.

We have studied resistance fluctuations in two different types of two-dimensional superconductors near to the Bcrczinskii-Kostcrlitz-Thoulcss (BKT) transition. The power spectral density of the resistance fluctuations was seen to deviate from 1/f as transition temperature is approached. We find that the shape of the spectrum can not be explained by a model for local defect fluctuations. Probability distribution function(PDF) and voltage-voltage auto-correlation functions provides evidence of the non-Gaussian nature of the resistance fluctuations near the BKT transition.

We present a quantitative comparison between the measurements of the complex conductance at low [kilohertz (kHz)] and high [gigahertz (GHz)] frequency in a thin superconducting film of NbN and the theoretical predictions of the dynamical Berezinksii-Kosterlitz-Thouless theory. While the data in the GHz regime can be well reproduced by extending the standard approach to the realistic case of a inhomogeneous sample, the low-frequency measurements present an anomalously large dissipative response around ${T}_{c}$. This anomaly can only be accounted for by assuming a strong slowing down of the vortex diffusion in the kHz regime, or analogously a strong reduction of the length scale probed by the incoming finite-frequency field. This effect suggests the emergence of an intrinsic length scale for the vortex motion that coincides with the typical size of inhomogeneity probed by STM measurements in disordered NbN films.

We report the superconducting properties of immiscible Nb–Cu nanocomposite films with varying compositions. The microstructure of the films revealed the presence of phase separated, closely spaced, nano-grains of Nb and Cu whose sizes changed marginally with composition. In all films we observe two resistive transitions. Analysis of the superconducting phase transition from temperature dependences of DC resistivity and AC susceptibility and comparison of the superconducting transition temperatures with that in nanoparticles of pure Nb with different particle sizes permit us to make a conclusion about a possible establishment of a global phase coherence in Nb–Cu system. The temperature variation of the critical current fits well with the Ambegaokar-Baratoff theory and this agreement suggests that our thick Nb–Cu films possibly behave like a random 3D network of Josephson junctions.