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.

The concept of mass-generation via the Higgs mechanism was strongly inspired by earlier works on the Meissner-Ochsenfeld effect in superconductors. In quantum field theory, the excitations of longitudinal components of the Higgs field manifest as massive Higgs bosons. The analogous Higgs mode in superconductors has not yet been observed due to its rapid decay into particle-hole pairs. Following recent theories, however, the Higgs mode should decrease below the pairing gap 2∆ and become visible in two-dimensional systems close to the superconductor-insulator transition (SIT). For experimental verification, we measured the complex terahertz transmission and tunneling density of states (DOS) of various thin films of superconducting NbN and InO close to criticality. Comparing both techniques reveals a growing discrepancy between the finite 2∆ and the threshold energy for electromagnetic absorption which vanishes critically towards the SIT. We identify the excess absorption below 2∆ as a strong evidence of the Higgs mode in two dimensional quantum critical superconductors.The Higgs mechanism, which has great implications to recent developments in particle physics [1], originates in Anderson's pioneering work on symmetry breaking with gauge fields in superconductors [2]. A superconductor spontaneously breaks continuous U (1) symmetry and acquires the well-known Mexican hat potential with a degenerate circle of minima described by the order parameter Ψ = Ae iϕ , see Fig. 1a. Excitations from the ground state can be classified as transverse Nambu-Goldstone (phase) modes and massive longitudinal Higgs (amplitude) modes (see blue and red lines in Fig. 1a). In particle physics, the latter manifest themselves as the Higgs boson which was recently discovered at CERN [3]. Indications of a Higgs mode in correlated many-body systems have been found in one-dimensional charge-densitywave systems [4], quantum antiferromagnets [5] and twodimensional superfluid to Mott transition in cold atoms [6]. An amplitude mode, also named Higgs mode, was theoretically predicted for superconductors [7] and recently reported to be measured by pump-probe spectroscopy [8]. This amplitude mode describes pairing fluctuations, which are qualitatively distinct from the purely bosonic mode expected from the O(2) field theory. The Higgs-amplitude mode analogous to the highenergy Higgs Boson has not yet been observed in superconductors. A partial reason is that in homogeneous, BCS superconductors the Higgs mode is short-lived and decays to particle hole (Bogoliubov) pairs [9,10]. Nevertheless, collective modes were recently predicted to be significant in strongly disordered superconductors [11], and, in particular it was shown [12][13][14] that the Higgs mode softens but remains sufficiently sharp near a quantum critical point (QCP) in two dimensions since it is found to be a critical energy scale of the quantum phase transition. Hence, the Higgs mass can be reduced below twice the pairing gap, 2∆, making this mode experimentally visible. Such a critical...

We have measured the magnetotransport properties and Hall effect of a series of epitaxial NbN films grown on (100) oriented single crystalline MgO substrate under different conditions using reactive magnetron sputtering. Hall effect measurements reveal that the carrier density in NbN thin films is sensitive to the growth condition. The carrier density increases by a factor of 3 between the film with highest normal state resistivity (ρ n~3 .83µΩ-m) and lowest transition temperature (T c~9 .99K) and the film with lowest normal state resistivity (ρ n~0 .94µΩm) and highest transition temperature (T c~1 6.11K) while the mobility of carriers does not change significantly. Our results show that the T c of NbN is governed primarily by the carrier density rather than disorder scattering. By varying the carrier concentration during growth we can vary the effective disorder (k F l) from the moderately clean limit to the dirty limit which makes this system ideal to study the interplay of carrier density and disorder on the superconducting properties of an 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. *

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...