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...

The hexatic fluid refers to a phase in between a solid and a liquid which 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 2-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 paper, using a combination of real space imaging and transport measurements we show that the 2dimensional vortex lattice in 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.

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.

We report the temperature dependence of resistivity ͑͒ and Hall coefficient ͑R H ͒ in the normal state of homogeneously disordered epitaxial NbN thin films with k F l ϳ 1.68-10.12. The superconducting transition temperature ͑T c ͒ of these films varies from 2.7 to 16.8 K. While our least disordered film displays usual metallic behavior, for all the films with k F l Յ 8.13, both d dT and dR H dT are negative up to 285 K. We observe that R H ͑T͒ varies linearly with ͑T͒ for all the films and ͓ R H ͑T͒−R H ͑285 K͒ R H ͑285 K͒ ͔ = ␥͓ ͑T͒−͑285 K͒ ͑285 K͒ ͔, where ␥ = 0.68Ϯ 0.11. Measurements performed on a 2-nm-thick Be film show similar behavior with ␥ = 0.69. This behavior is inconsistent with existing theories of localization and e-e interactions in a disordered metal.

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 aMoGe, 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.

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We investigate the evolution of superconductivity with decreasing film thickness in ultrathin amorphous MoGe (a-MoGe) films using a combination of sub-Kelvin scanning tunneling spectroscopy, magnetic penetration depth measurements and magneto-transport measurements. We observe that superconductivity is strongly affected by quantum and classical phase fluctuations for thickness below 5 nm. The superfluid density is strongly suppressed by quantum phase fluctuations at low temperatures and evolves towards a linear-T dependence at higher temperatures. This is associated with a rapid decrease in the superconducting transition temperature, Tc, and the emergence of a pronounced pseudogap above Tc. These observations suggest that at strong disorder the destruction of superconductivity follows a Bosonic route where the global superconducting state is destroyed by phase fluctuations even though the pairing amplitude remains finite.In the late fifties, Anderson 1 predicted that in an s-wave superconductor the attractive pairing interaction forming Cooper pairs would remain largely unaffected by the presence of non-magnetic impurities. This has been loosely interpreted to imply that the superconducting transition temperature, Tc will also not be strongly sensitive to disorder scattering. However, later experiments showed that this is valid only in the limit of weak disorder: In the presence of strong disorder, Tc gets gradually suppressed 2,3 and eventually the material is driven into a non-superconducting state. The mechanism driving the transition from a superconductor to an insulator or a metal has been a subject of considerable debate. In principle, the suppression of Tc with increase in disorder can happen from two origins. The first mechanism is through the loss of effective screening with increase in disorder that weakens the attractive pairing interaction, and thus suppresses the mean field transition temperature 4,5 . The second mechanism results from the decrease in superfluid density, ns, induced by disorder scattering, which renders the superconductor susceptible to phase fluctuations 6,7 . When ns is small, the phase coherent superconducting state can get destroyed due to strong phase fluctuations even when the pairing amplitude remains finite 8,9,10 .The superconductor to non-superconductor transition driven by these two mechanisms are often classified as the Fermionic and Bosonic routes respectively 11 . In the Fermionic route, the pairing attraction drops to zero at a critical disorder where superconductivity is destroyed. This non-superconducting state is either a bad metal or an Anderson insulator. In the Bosonic mechanism the pairing interaction remains finite and therefore signatures of Cooper pairing continue to survive even in the non-superconducting state.Experimentally, this manifests as a persistence of the superconducting gap in the electronic excitation spectrum, known as the pseudogap, even after the global superconducting state is destroyed 12,13,14,15 .However, recent studies indicate that th...