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

Exploring disorder correlations in superconducting systems: spectroscopic insights and matrix element effects

Understanding the intricate interplay between disorder and superconductivity has become a key area of research in condensed matter physics, with profound implications for materials science. Recent studies have shown that spatial correlations of disorder potential can improve superconductivity, prompting a re-evaluation of some theoretical models. This paper explores the influence of disorder correlations on the fundamental properties of superconducting systems, going beyond the traditional assumption of spatially uncorrelated disorder. In particular, we investigate the influence of disorder correlations on key spectroscopic superconductor properties, including the density of states, as well as on the matrix elements of the superconducting coupling constant and their impact on the localization length. Our findings offer valuable insights into the role of disorder correlations in shaping the behavior of superconducting materials.

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.

Role of non-linear effects and standing waves in microwave spectroscopy: Corbino measurements on superconductors and VO2

Broadband microwave spectroscopy can probe material properties in wide spectral and temperature ranges. The quality of such measurements crucially depends on the calibration, which also removes from the obtained spectra signatures of standing waves. Here we consider cryogenic Corbino-type reflection measurements on superconductors close to the critical temperature. We show that the non-linear sample response, which relates to sample heating, can lead to strong signatures of standing waves even in a well-calibrated Corbino spectrometer. We demonstrate our findings with microwave measurements as a function of frequency, power, and temperature and for different lengths of the microwave transmission line. Finally, we note such non-linear effects beyond the case of superconductors by probing a VO₂ thin film at the insulator-metal transition.

Critical exponents of dynamical conductivity in 2D percolative superconductor-insulator transitions: three universality classes

We simulate three types of random inductor-capacitor (LC) networks on [Formula: see text] square lattices. We calculate the dynamical conductivity using an equation-of-motion method in which timestep error is eliminated and windowing error is minimized. We extract the critical exponent a such that [Formula: see text] at low frequencies. The results suggest that there are three different universality classes. The [Formula: see text] model, with capacitances from each site to ground, has a  =  0.314(4). The [Formula: see text] model, with capacitances along bonds, has a  =  0. The [Formula: see text] model, with both types of capacitances, has a  =  0.304(1). This implies that classical percolative 2D superconductor-insulator transitions (SITs) generically have [Formula: see text] as [Formula: see text]. Therefore, any experiments that give a constant conductivity as [Formula: see text] must be explained in terms of quantum effects.

Critical properties of the superfluid-bose-glass transition in two dimensions

We investigate the superfluid (SF) to Bose-glass (BG) quantum phase transition using extensive quantum Monte Carlo simulations of two-dimensional hard-core bosons in a random box potential. T=0 critical properties are studied by thorough finite-size scaling of condensate and SF densities, both vanishing at the same critical disorder Wc=4.80(5). Our results give the following estimates for the critical exponents: z=1.85(15), ν=1.20(12), η=-0.40(15). Furthermore, the probability distribution of the SF response P(lnρSF) displays striking differences across the transition: while it narrows with increasing system sizes L in the SF phase, it broadens in the BG regime, indicating an absence of self-averaging, and at the critical point P(lnρSF+zlnL) is scale invariant. Finally, high-precision measurements of the local density rule out a percolation picture for the SF-BG transition.

Divergence of dynamical conductivity at certain percolative superconductor-insulator transitions

Random inductor–capacitor (LC) networks can exhibit percolative superconductor-insulator transitions (SITs). We use a simple and efficient algorithm to compute the dynamicalconductivity σ(ω,p) of one type of LC network on large (4000 × 4000) square lattices, where δ = p − p(c) is the tuning parameter for the SIT. We confirm that the conductivity obeys a scaling form, so that the characteristic frequency scales as∝|δ|(νz) with νz ≈ 1.91, the superfluid stiffness scales as ϒ∝|δ|(t) with t ≈ 1.3, and the electric susceptibility scales as χE∝|δ|(−s) with s = 2νz − t ≈ 2.52. In the insulating state, the low-frequency dissipative conductivity is exponentially small, whereas in the superconductor, it is linear in frequency.The sign of Im σ(ω) at small ω changes across the SIT. Most importantly, we find that right at the SIT Re σ(ω) ∝ ω(t/νz−1)∝ω(−0.32), so that the conductivity diverges in the DC limit, in contrast with most other classical and quantum models of SITs.

A broadband microwave Corbino spectrometer at ³He temperatures and high magnetic fields

We present the technical details of a broadband microwave spectrometer for measuring the complex conductance of thin films covering the range from 50 MHz up to 16 GHz in the temperature range 300 mK-6 K and at applied magnetic fields up to 8 T. We measure the complex reflection from a sample terminating a coaxial transmission line and calibrate the signals with three standards with known reflection coefficients. Thermal isolation of the heat load from the inner conductor is accomplished by including a section of NbTi superconducting cable (transition temperature around 8-9 K) and hermetic seal glass bead adapters. This enables us to stabilize the base temperature of the sample stage at 300 mK. However, the inclusion of this superconducting cable complicates the calibration procedure. We document the effects of the superconducting cable on our calibration procedure and the effects of applied magnetic fields and how we control the temperature with great repeatability for each measurement. We have successfully extracted reliable data in this frequency, temperature, and field range for thin superconducting films and highly resistive graphene samples.

Specific heat measurement set-up for quench condensed thin superconducting films

We present a set-up designed for the measurement of specific heat of very thin or ultra-thin quench condensed superconducting films. In an ultra-high vacuum chamber, materials of interest can be thermally evaporated directly on a silicon membrane regulated in temperature from 1.4 K to 10 K. On this membrane, a heater and a thermometer are lithographically fabricated, allowing the measurement of heat capacity of the quench condensed layers. This apparatus permits the simultaneous thermal and electrical characterization of successively deposited layers in situ without exposing the deposited materials to room temperature or atmospheric conditions, both being irreversibly harmful to the samples. This system can be used to study specific heat signatures of phase transitions through the superconductor to insulator transition of quench condensed films.

Site-disorder driven superconductor-insulator transition: a dynamical mean field study

We investigate the effect of site disorder on the superconducting state in the attractive Hubbard model within the framework of dynamical mean field theory. For a fixed interaction strength (U), the superconducting order parameter decreases monotonically with increasing disorder (x), while the single-particle spectral gap decreases for small x, reaches a minimum and keeps increasing for larger x. Thus, the system remains gapped beyond the destruction of the superconducting state, indicating a disorder-driven superconductor-insulator transition. We investigate this transition in depth considering the effects of weak and strong disorder for a range of interaction strengths. In the clean case, the order parameter is known to increase monotonically with increasing interaction, saturating at a finite value asymptotically for U→∞. The presence of disorder results in destruction of superconductivity at large U, thus drastically modifying the clean case behaviour. A physical understanding of our findings is obtained by invoking particle-hole asymmetry and the probability distributions of the order parameter and spectral gap.

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, T_c, 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.

Pairing fluctuation ac conductivity of disordered thin films

We study temperature T and frequency ω dependence of the in-plane fluctuation conductivity of a disordered superconducting film above the critical temperature. Our calculation is based on the nonlinear sigma model within the Keldysh technique. The fluctuation contributions of different physical origin are found and analyzed in a wide frequency range. In the low-frequency range, ω ≪ T, we reproduce the known leading terms and find additional subleading ones in the Aslamazov-Larkin and the Maki-Thompson contributions to the ac conductivity. We also calculate the density of states ac correction. In the dc case these contributions logarithmically depend on the Ginzburg-Landau rate and are considerably smaller that the leading ones. However, in the ac case an external finite-frequency electromagnetic field strongly suppresses the known Aslamazov-Larkin and Maki-Thompson ac contributions, while the corresponding new terms and the density of states contribution are weakly suppressed and therefore become relevant at finite frequencies.