Why Shot Noise Does Not Generally Detect Pairing in Mesoscopic Superconducting Tunnel Junctions.

The shot noise in tunneling experiments reflects the Poissonian nature of the tunneling process. The shot-noise power is proportional to both the magnitude of the current and the effective charge of the carrier. Shot-noise spectroscopy thus enables us, in principle, to determine the effective charge q of the charge carriers of that tunnel. This can be used to detect electron pairing in superconductors: In the normal state, the noise corresponds to single electron tunneling (q=1e), while in the paired state, the noise corresponds to q=2e. Here, we use a newly developed amplifier to reveal that in typical mesoscopic superconducting junctions, the shot noise does not reflect the signatures of pairing and instead stays at a level corresponding to q=1e. We show that transparency can control the shot noise, and this q=1e is due to the large number of tunneling channels with each having very low transparency. Our results indicate that in typical mesoscopic superconducting junctions, one should expect q=1e noise and lead to design guidelines for junctions that allow the detection of electron pairing.

Andreev Reflections in NbN/Graphene Junctions under Large Magnetic Fields.

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 ≈ 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 ν = 4 Landau level attributed to the reduced efficiency of Andreev processes at the NbN/g interface, consistent with theoretical predictions.

Melting of the Vortex Lattice through Intermediate Hexatic Fluid in an a-MoGe Thin Film.

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.

Inter-Landau-level Andreev Reflection at the Dirac Point in a Graphene Quantum Hall State Coupled to a NbSe_{2} 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.

Quantum Phase Transition in Few-Layer NbSe_{2} Probed through Quantized Conductance Fluctuations.

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}.

Correlated conductance fluctuations close to the Berezinskii-Kosterlitz-Thouless transition in ultrathin NbN films.

We probe the presence of long-range correlations in phase fluctuations by analyzing the higher-order spectrum of resistance fluctuations in ultrathin NbN superconducting films. The non-Gaussian component of resistance fluctuations is found to be sensitive to film thickness close to the transition, which allows us to distinguish between mean field and Berezinskii-Kosterlitz-Thouless (BKT) type superconducting transitions. The extent of non-Gaussianity was found to be bounded by the BKT and mean field transition temperatures and depends strongly on the roughness and structural inhomogeneity of the superconducting films. Our experiment outlines a novel fluctuation-based kinetic probe in detecting the nature of superconductivity in disordered low-dimensional materials.

Superfluid density in conventional superconductors: from clean to strongly disordered.

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 (Mandal and Ramakrishnan 2020Phys. Rev.B102024514) 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 isnotsufficient 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.

Phase fluctuations in a strongly disordered s-wave NbN superconductor close to the metal-insulator transition.

We explore the role of phase fluctuations in a three-dimensional s-wave superconductor, NbN, as we approach the critical disorder for destruction of the superconducting state. Close to critical disorder, we observe a finite gap in the electronic spectrum which persists at temperatures well above T(c). The superfluid density is strongly suppressed at low temperatures and evolves towards a linear-T variation at higher temperatures. These observations provide strong evidence that phase fluctuations play a central role in the formation of a pseudogap state in a disordered s-wave superconductor.

Role of the vortex-core energy on the Berezinskii-Kosterlitz-Thouless transition in thin films of NbN.

We analyze the occurrence of the Berezinskii-Kosterlitz-Thouless (BKT) transition in thin films of NbN at various film thickness, by probing the effect of vortex fluctuations on the temperature dependence of the superfluid density below T(BKT) and of the resistivity above T(BKT). By direct comparison between the experimental data and the theory, we show the crucial role played by the vortex-core energy in determining the characteristic signatures of the BKT physics, and we estimate its dependence on the disorder level. Our work provides a paradigmatic example of BKT physics in a quasi-two-dimensional superconductor.

Phase fluctuations in conventional superconductors.

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 superconductorsJis 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,Jcan 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.

Collective flux pinning in hexatic vortex fluid in a-MoGe thin film.

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.

Competing effects of surface phonon softening and quantum size effects on the superconducting properties of nanostructured Pb.

The superconducting transition temperature (T(C)) in nanostructured Pb decreases from 7.24 to 6.4 K as the particle size is reduced from 65 to 7 nm, below which superconductivity is lost rather abruptly. In contrast, there is a large enhancement in the upper critical field (H(C2)) in the same size regime. We explore the origin of the unusual robustness of T(C) over such a large particle size range in nanostructured Pb by measuring the temperature dependence of the superconducting energy gap in planar tunnel junctions of Al/Al(2)O(3)/nano-Pb. We show that below 22 nm, the electron-phonon coupling strength increases monotonically with decreasing particle size, and almost exactly compensates for the quantum size effect, which is expected to suppress T(C).

Synthesis of nanodimensional TiO2 thin films.

Nanodimensional TiO2 has wide application in the field of photocatalysis, photovoltaic and photochromic devices. In present investigation TiO2 thin films deposited by pulsed laser deposition method are irradiated by 100 MeV Ag ion beam to achieve growth of nanophases. The nanostructure evolution is characterized by atomic force microscopy (AFM). The phases of TiO2 formed after irradiation are identified by glancing angle X-ray diffraction and Raman spectroscopy. The particle radius estimated by AFM varies from 10-13 nm. Anatase phase of TiO2 is formed after irradiation. The blue shift observed in UV-VIS absorption spectra indicates the nanostructure formation. The shape and size of nanoparticles formed due to high electronic excitation depend upon thickness of the film.

Orientational coupling between the vortex lattice and the crystalline lattice in a weakly pinned Co(0.0075)NbSe2 single crystal.

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. When the magnetic field is applied along the six-fold symmetric c-axis of the NbSe2 crystal, the basis vectors of the vortex lattice are 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. This orientational 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. Our results underpin the importance of crystal lattice symmetry on the vortex state phase diagram of weakly pinned type II superconductors.

Disordering of the vortex lattice through successive destruction of positional and orientational order in a weakly pinned Co0.0075NbSe2 single crystal.

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 Co(0.0075)NbSe(2) 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.

Enhancement of the finite-frequency superfluid response in the pseudogap regime of strongly disordered superconducting films.

The persistence of a soft gap in the density of states above the superconducting transition temperature Tc, the pseudogap, has long been thought to be a hallmark of unconventional high-temperature superconductors. However, in the last few years this paradigm has been strongly revised by increasing experimental evidence for the emergence of a pseudogap state in strongly-disordered conventional superconductors. Nonetheless, the nature of this state, probed primarily through scanning tunneling spectroscopy (STS) measurements, remains partly elusive. Here we show that the dynamic response above Tc, obtained from the complex ac conductivity, is highly modified in the pseudogap regime of strongly disordered NbN films. Below the pseudogap temperature, T*, the superfluid stiffness acquires a strong frequency dependence associated with a marked slowing down of critical fluctuations. When translated into the length-scale of fluctuations, our results suggest a scenario of thermal phase fluctuations between superconducting domains in a strongly disordered s-wave superconductor.

Emergence of nanoscale inhomogeneity in the superconducting state of a homogeneously disordered conventional superconductor.

The notion of spontaneous formation of an inhomogeneous superconducting state is at the heart of most theories attempting to understand the superconducting state in the presence of strong disorder. Using scanning tunneling spectroscopy and high resolution scanning transmission electron microscopy, we experimentally demonstrate that under the competing effects of strong homogeneous disorder and superconducting correlations, the superconducting state of a conventional superconductor, NbN, spontaneously segregates into domains. Tracking these domains as a function of temperature we observe that the superconducting domains persist across the bulk superconducting transition, Tc, and disappear close to the pseudogap temperature, T*, where signatures of superconducting correlations disappear from the tunneling spectrum and the superfluid response of the system.

A 350 mK, 9 T scanning tunneling microscope for the study of superconducting thin films on insulating substrates and single crystals.

We report the construction and performance of a low temperature, high field scanning tunneling microscope (STM) operating down to 350 mK and in magnetic fields up to 9 T, with thin film deposition and in situ single crystal cleaving capabilities. The main focus lies on the simple design of STM head and a sample holder design that allows us to get spectroscopic data on superconducting thin films grown in situ on insulating substrates. Other design details on sample transport, sample preparation chamber, and vibration isolation schemes are also described. We demonstrate the capability of our instrument through the atomic resolution imaging and spectroscopy on NbSe2 single crystal and spectroscopic maps obtained on homogeneously disordered NbN thin film.

Mechanism of the size dependence of the superconducting transition of nanostructured Nb.

A direct measurement of the superconducting energy gap by point contact spectroscopy in nanostructured Nb films shows that the gap decreases with a reduction in the average particle size. The superconducting T(c), obtained from transport and magnetic measurements, also decreases with size and scales with the energy gap. The size dependence of the superconducting properties in this intermediate coupling type II superconductor is therefore governed by changes in the electronic density of states rather than by phonon softening. Consistent with the Anderson criterion, no T(c) was observed for sizes below 8 nm.