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.

We present a phase diagram as a function of disorder in three-dimensional NbN thin films, as the system enters the critical disorder for the destruction of the superconducting state.The superconducting state is investigated using a combination of magnetotransport and tunneling spectroscopy measurements. Our studies reveal 3 different disorder regimes. At low disorder (k F l~10-4), the system follows the mean field Bardeen-Cooper-Schrieffer behavior where the superconducting energy gap vanishes at the temperature where electrical resistance appears. For stronger disorder ( k F l<4 ) a "pseudogap" state emerges where a gap in the electronic spectrum persists up to temperatures much higher than T c , suggesting that Cooper pairs continue to exist in the system even after the zero resistance state is destroyed. Finally, at even stronger disorder (k F l<1) the global superconducting ground state is completely destroyed, though superconducting correlations continue to survive as evidenced from a pronounced magnetoresistance peak at low temperatures. *

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.

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.

Abstract:We report the evolution of the magnetic penetration depth (λ) and superconducting energy gap (∆) in epitaxial NbN films with thickness (d) varying between 51-3nm. With decrease in film thickness T c and ∆(0) monotonically decreases, whereas λ(0) monotonically increases. Our results show that while the values of ∆(0) and λ(0) are well described by BardeenCooper-Schrieffer (BCS) theory, at elevated temperatures, films with d≤6.5nm show sudden drop in superfluid density associated with the Kosterlitz-Thouless-Berezinski (KTB) transition.We discuss the implication of these results on the time response of superconducting bolometers made out of ultrathin NbN films. * films with d>20nm, the thickness was measured using a stylus profilometer while for thinner films it was estimated from the time of deposition. λ was measured using a "two coil" mutual inductance technique operating at 60kHz. The main advantage of this technique is that it allows measurement of the absolute value of λ over the entire temperature range up to T c without any prior assumption about the temperature dependence of λ. In this technique, a 8mm diameter thin superconducting film is sandwitched between a quadrupole primary coil and a dipole secondary coil ( figure 1(a)). This technique operates on the principle that the thin superconducting film will partially shield the secondary coil from the magnetic field produced by the primary, the degree of shielding being dependent on λ. The mutual inductance between the primary and the secondary coil is measured as a function of temperature by passing a small a.c. excitation current (1mA) through the primary and measuring the in-phase and out-of-phase induced voltage in the secondary using a lock-in amplifier. λ is determined by evaluating the mutual inductance for different values of λ by numerically solving the Maxwell equations and comparing the measured value with the theoretically calculated value 10 . The quadrupole configuration of the primary coil ensures a fast radial decay of the magnetic field such that edge effects are minimized 11 . The excitation field was kept very low (~7mOe) and the cryostat was shielded from the earth's magnetic field using a mu-metal shield. ∆(Τ) was measured using a home built low temperature scanning tunneling microscope (STM) on freshly prepared NbN films using Pt-Ir tip. The show the tunneling spectra at various temperatures. ∆ is extracted by fitting these spectra to the tunneling equation,where,is the lifetime broadened BCS density of states. While the broadening parameter, ( ), formally incorporated 12 to take into account the lifetime (τ) of the quasiparticle, phenomenologically incorporates all sources of non-thermal broadening in the BCS DOS. We observe that the temperature dependence of ∆(Τ) (Fig. 2(c)-closely follows the BCS curve 13 within experimental accuracy.Figure 3(a) shows the temperature variation of λ −2 (Τ)∝n s (T) (where n s is the superfluid density). λ increases from 275nm to 529nm as the thickness decreases from 51nm to 3nm. The val...

We investigate theoretically and experimentally the statistical properties of the inhomogeneous order-parameter distribution (OPD) at the verge of the superconductor-insulator transition (SIT). We find within two prototype fermionic and bosonic models for disordered superconductors that one can identify a universal rescaling of the OPD. By performing scanning-tunneling microscopy experiments in three samples of NbN with increasing disorder we show that such a rescaling also describes the experimental data with excellent accuracy. These results can provide a breakthrough in our understanding of the SIT

We report directional point contact Andreev reflection (PCAR) measurements on high-quality single crystals of the noncentrosymmetric superconductor BiPd. The PCAR spectra measured on different crystallographic faces of the single crystal clearly show the presence of multiple superconducting energy gaps. For point contacts with low resistance, in addition to the superconducting gap feature, a pronounced zero-bias conductance peak is observed. These observations provide strong evidence for the presence of an unconventional order parameter in this material.

A magnetic atom in a superconducting host induces so-called Yu-Shiba-Rusinov (YSR) bound states inside the superconducting energy gap. By combining spin-resolved scanning tunneling spectroscopy with simulations we demonstrate that the pair of peaks associated with the YSR states of an individual Fe atom coupled to an oxygen-reconstructed Ta surface gets spin polarized in an external magnetic field. As theoretically predicted, the electron and hole parts of the YSR states have opposite signs of spin polarizations which keep their spin character when crossing the Fermi level through the quantum phase transition. The simulation of a YSR state right at the Fermi level reveals zero spin polarization which can be used to distinguish such states from Majorana zero modes in chains of YSR atoms. DOI: 10.1103/PhysRevLett.119.197002 Recent investigations of chains [1][2][3] and arrays [4,5] of magnetic atoms in contact with surfaces of s-wave superconductors in view of Majorana zero modes and topological superconductivity triggered renewed interest in the properties of the basic constituent of such systems, the individual magnetic adatom. Typically, such adatoms induce quasiparticle excitations inside the superconducting energy gap [6][7][8], referred to as Yu-Shiba-Rusinov (YSR) states, which hamper the identification of topologically nontrivial edge states [3,9], calling for a thorough characterization of all experimentally accessible properties of YSR states.Following the first experimental verification of YSR states of individual atoms using scanning tunneling spectroscopy (STS) [10], there were numerous experimental studies, focusing on orbital effects [11][12][13], magnetic anisotropy [14], effects of reduced dimensionality of the superconductor [15], effects of coupling [11,16], and the competition between Kondo screening and superconducting pairing [17,18]. However, the investigation of the spin polarization of the YSR state of individual atoms, which could serve as a fingerprint for the distinction from topological states [19], was so far restricted to theoretical predictions [6][7][8][20][21][22].Neglecting orbital effects or magnetic anisotropy, theory predicts one pair of spin-polarized states of a YSR atom, an electron (e − )-and a hole (h)-like part with opposite spin character, which are located at AEjεj from the Fermi level E F [20]. There is a pronounced asymmetry in spectral weight between the e − and h parts due to electron-hole asymmetry of the band structure [21,22] and/or a nonmagnetic scattering potential of the impurity [20,23]. With increasing exchange coupling J between the adatom and substrate, the binding energy ε decreases until the YSR states eventually cross E F through a quantum phase transition (QPT), accompanied by an inversion of the asymmetry in the e − − h spectral weight [17]. Most notably, since both parts of the YSR states keep their spin character, the spin polarization above and below E F is expected to invert [20] through the QPT. Here, we experimentally verify these prediction...