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 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.

Spectroscopic evidence of mixed angular momentum symmetry in non-centrosymmetric Ru$$_7$$B$$_3$$

Superconducting crystals with a lack of inversion symmetry can potentially host unconventional pairing. However, till today, no direct conclusive experimental evidence of such unconventional order parameters in non-centrosymmetric superconductors has been reported. In this paper, through direct measurement of the superconducting energy gap by scanning tunnelling spectroscopy, we report the existence of both s-wave (singlet) and p-wave (triplet) pairing symmetries in non-centrosymmetric Ru$$_7$$ 7 B$$_3$$ 3 . Our temperature and magnetic field-dependent studies also indicate that the relative amplitudes of the singlet and triplet components change differently with temperature.

Holographic p-wave superconductivity from higher derivative theory

We construct a holographic SU(2) p-wave superconductor model with Weyl corrections. The high derivative (HD) terms do not seem to spoil the generation of the p-wave superconducting phase. We mainly study the properties of AC conductivity, which is absent in holographic SU(2) p-wave superconductor with Weyl corrections. The conductivities in superconducting phase exhibit obvious anisotropic behaviors. Along y direction, the conductivity $$\sigma _{yy}$$ σ yy is similar to that of holographic s-wave superconductor. The superconducting energy gap exhibits a wide extension. For the conductivity $$\sigma _{xx}$$ σ xx along x direction, the behaviors of the real part in the normal state are closely similar to that of $$\sigma _{yy}$$ σ yy . However, the anisotropy of the conductivity obviously shows up in the superconducting phase. A Drude-like peak at low frequency emerges in $$Re\sigma _{xx}$$ R e σ xx once the system enters into the superconducting phase, regardless of the behaviors in normal state.

Josephson Currents and Gap Enhancement in Graph Arrays of Superconductive Islands

Evidence is reported that topological effects in graph-shaped arrays of superconducting islands can condition superconducting energy gap and transition temperature. The carriers giving rise to the new phase are couples of electrons (Cooper pairs) which, in the superconducting state, behave as predicted for bosons in our structures. The presented results have been obtained both on star and double comb-shaped arrays and the coupling between the islands is provided by Josephson junctions whose potential can be tuned by external magnetic field or temperature. Our peculiar technique for probing distribution on the islands is such that the hopping of bosons between the different islands occurs because their thermal energy is of the same order of the Josephson coupling energy between the islands. Both for star and double comb graph topologies the results are in qualitative and quantitative agreement with theoretical predictions.

Superfluid density from magnetic penetration depth measurements in Nb–Cu 3D nano-composite films

Superconductivity in 3D Nb–Cu nanocomposite granular films have been studied with varying thickness for two different compositions, Nb rich with 88 at% of Nb and Cu rich with 46 at% of Nb. For both compositions, the superconducting transition temperature (Tc) decreases with decreasing film thickness. For any thickness, doubling the Cu content in the films decreases the Tc by about 2 K. To explore if phase fluctuations play any role in superconductivity in these 3D films, the superfluid stiffness (JS) of the films was measured using low frequency two-coil mutual inductance (M) technique. Interestingly, the measurement of M in magnetic fields showed two peaks in the imaginary component of M for both Nb rich and Cu rich films. The two peaks were associated with the pair-breaking effect of the magnetic field on the intra and inter-granular coupling in these films consisting of random network of superconductor (S) and normal metal (N) nano-particles. Furthermore, JS was seen to decrease with decreasing film thickness and increasing Cu content. However, for all films studied JS remained higher than the superconducting energy gap (∆) indicating that phase fluctuations do not play any role in superconductivity in the film thickness and composition range investigated. Our results indicate that an interplay of quantum size effects (QSE) and superconducting proximity effect (SPE) controls the Tc with composition in these 3D nano-composite films.

Thermionic junction devices utilizing phonon blocking

Electrothermal elements are used in various energy harvesters, coolers, and radiation detectors. The optimal operation of these elements relies on mastering two competing boundary conditions: the maximization of the electrothermal response and the blockade of lattice (phonon) thermal conduction. In this work, we propose and demonstrate that efficient electrothermal operation and phonon blocking can be achieved in solid-state thermionic junctions, paving the way for new phonon-engineered high-efficiency refrigerators and sensors. Our experimental demonstration uses semiconductor-superconductor (Sm-S) junctions where the electrothermal response arises from the superconducting energy gap and the phonon blocking results from the acoustic transmission bottleneck at the junction. We demonstrate a cooling platform where a silicon chip, suspended only from the Sm-S junctions, is cooled by ~40% from the bath temperature. We also show how the observed effect can be used in radiation detectors and multistage electronic refrigerators suitable for cooling of quantum technology devices.

Momentum-resolved superconducting energy gaps of Sr2RuO4 from quasiparticle interference imaging

Sr2RuO4 has long been the focus of intense research interest because of conjectures that it is a correlated topological superconductor. It is the momentum space (k-space) structure of the superconducting energy gap Δi(k) on each band i that encodes its unknown superconducting order parameter. However, because the energy scales are so low, it has never been possible to directly measure the Δi(k) of Sr2RuO4. Here, we implement Bogoliubov quasiparticle interference (BQPI) imaging, a technique capable of high-precision measurement of multiband Δi(k). At T = 90 mK, we visualize a set of Bogoliubov scattering interference wavevectors qj:j=1−5 consistent with eight gap nodes/minima that are all closely aligned to the (±1,±1) crystal lattice directions on both the α and β bands. Taking these observations in combination with other very recent advances in directional thermal conductivity [E. Hassinger et al., Phys. Rev. X 7, 011032 (2017)], temperature-dependent Knight shift [A. Pustogow et al., Nature 574, 72–75 (2019)], time-reversal symmetry conservation [S. Kashiwaya et al., Phys. Rev B, 100, 094530 (2019)], and theory [A. T. Rømer et al., Phys. Rev. Lett. 123, 247001 (2019); H. S. Roising, T. Scaffidi, F. Flicker, G. F. Lange, S. H. Simon, Phys. Rev. Res. 1, 033108 (2019); and O. Gingras, R. Nourafkan, A. S. Tremblay, M. Côté, Phys. Rev. Lett. 123, 217005 (2019)], the BQPI signature of Sr2RuO4 appears most consistent with Δi(k) having dx2−y2(B1g) symmetry.

Higher derivatives driven symmetry breaking in holographic superconductors

In this paper, we construct a novel holographic superconductor from higher derivative (HD) gravity involving a coupling between the complex scalar field and the Weyl tensor. This HD coupling term provides a near horizon effective mass squared, which can violates IR Breitenlohner–Freedman (BF) bound by tuning the HD coupling and induces the instability of black brane such that the superconducting phase transition happens. We also study the properties of the condensation and the conductivity in the probe limit. We find that a wider extension of the superconducting energy gap ranging from 4.6 to 10.5 may provide a novel platform to model and interpret the phenomena in the real materials of high temperature superconductor.

Generalized Anderson’s theorem for superconductors derived from topological insulators

A well-known result in unconventional superconductivity is the fragility of nodal superconductors against nonmagnetic impurities. Despite this common wisdom, Bi2Se3-based topological superconductors have recently displayed unusual robustness against disorder. Here, we provide a theoretical framework that naturally explains what protects Cooper pairs from strong scattering in complex superconductors. Our analysis is based on the concept of superconducting fitness and generalizes the famous Anderson’s theorem into superconductors having multiple internal degrees of freedom with simple assumptions such as the Born approximation. For concreteness, we report on the extreme example of the Cux(PbSe)5(BiSe3)6 superconductor. Thermal conductivity measurements down to 50 mK not only give unambiguous evidence for the existence of nodes but also reveal that the energy scale corresponding to the scattering rate is orders of magnitude larger than the superconducting energy gap. This provides the most spectacular case of the generalized Anderson’s theorem protecting a nodal superconductor.

Analytical Study of the Holographic Superconductor from Higher Derivative Theory

In this paper, we analytically study the holographic superconductor models with the high derivative (HD) coupling terms. Using the Sturm-Liouville (S-L) eigenvalue method, we perturbatively calculate the critical temperature. The analytical results are in good agreement with the numerical results. It confirms that the perturbative method in terms of the HD coupling parameters is available. Along the same line, we analytically calculate the value of the condensation near the critical temperature. We find that the phase transition is second order with mean field behavior, which is independent of the HD coupling parameters. Then, in the low-temperature limit, we also calculate the conductivity, which is qualitatively consistent with the numerical one. We find that the superconducting energy gap is proportional to the value of the condensation. But we note that since the condensation changes with the HD coupling parameters, as the function of the HD coupling parameters, the superconducting energy gap follows the same change trend as that of the condensation.