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Typically the superconducting phase weakens at several points with the increase in disorder before it is distroyed in the 2d-thin films. This may lead to an inhomogeneous superconducting state without a continuous phase. Here we present scanning tunneling spectroscopy measurements at 0.1 K in the disordered polycrystalline film of TiN describing the nanoscale size features of the superconducting state. The imaging shows imcommensurate charge density modulations, originating at the crystalline bounadries, and intercepted on large scale by the beat patterns in the regions of overlap. Electronic coherence is maintained over length scale minimum of crystalline sizes, and suffers scattering across low angle crystalline boundaries. The superconducting state fluctuates at the positions of the charge density modulations and zones of the weak phase appear in the vicinity of the beats. Our data shows that the BCS-like behavior evolves into the V-shaped density of states in such inhomogeneous regions as a result of the competition between the superconducting correlations with that of the strong electron-electron repulsive interactions assisted by the inelastic scattering at the crystalline boundaries., Comment: 38 pages, 8 figures

We report in this paper the temperature and mangetic field dependence of the conductance in the polycrystalline film of titanium nitride, before and after heating at ambient conditions. The difference between the two films is the room temperature sheet resistance which remains within 15 percent and both the films show superconducting transition at lower temperatures. The zero field and the high field data, respectively, corresponds to the superconducting and the normal states. Both the films display Atshuler-Aronov zero bias anamoly in their normal states, and the superconducting gap openeing up at low fields. However the heated film has a smaller gap owing to more pronounced zero bias suppression of the density of states. The normal states in both the films are similar to the quasi-2d-disordered metal and its behavior is studied with temperature. Our data suggests that the zero bias anamoly suppresses the superconducting gap with increase in the disorder., Comment: 5 pages, 7 figures

We present in this paper the conductance maps at 100 mK in the disordered polycrystalline film of titanium nitride (TiN). At 5 nm, the film is close to quasi-two dimensional limit and exhibits features pertaining to the superconductor to insulator transition. We measured conductance maps at zero field and at 4 T, which represent the superconducting and the normal phase, respectively. The conductance map at 4 T is uniform, in which the conductance behavior, with logarithmic variation, resembles to the disorder enhanced electron-electron interaction in the two dimensional metallic phase. At low fields we observe the spatial variations of the conductance in the superconducting phase. At several places the superconducting energy gap fluctuates to an extent that the quasi-particle peaks are absent in the conductance curves. The conductance map over a region encompassing only few crystallites suggests that the inhomogeneities in the superconducting phase related to the spatial variations of the electronic density are across the crystalline boundaries., Comment: 5 pages, 7 figures

We investigate transition to the superconducting state in the ultrathin titanium nitride films on approach to superconductor-insulator transition. Building on the complete account of quantum contributions to conductivity, we demonstrate that the resistance of thin superconducting films exhibits a non-monotonic temperature behaviour due to the competition between weak localization, electron-electron interaction, and superconducting fluctuations. We show that superconducting fluctuations give rise to an appreciable decrease in the resistance even at temperatures well exceeding the superconducting transition temperature, T_c, with this decrease being dominated by the Maki-Thompson process.The transition to a global phase-coherent superconducting state occurs via the Berezinskii-Kosterlitz-Thouless (BKT) transition, which we observe both by power-law behaviour in current-voltage characteristics and by flux flow transport in the magnetic field. The ratio T_{BKT}/T_c follows the universal Beasley-Mooij-Orlando relation. Our results call for revisiting the past data on superconducting transition in thin disordered films., Comment: 6 pages, 4 figures

We present the intrinsic optical properties over a broad spectral range of TiN thin films deposited on a Si/SiO$_2$ substrate. We analyze the measured reflectivity spectra of the film-substrate multilayer structure within a well-establish procedure based on the Fresnel equation and extract the real part of the optical conductivity of TiN. We identify the metallic contribution as well as the finite energy excitations and disentangle the spectral weight distribution among them. The absorption spectrum of TiN bears some similarities with the electrodynamic response observed in the normal state of the high-temperature superconductors. Particularly, a mid-infrared feature in the optical conductivity is quite reminiscent of a pseudogap-like excitation.

A superconducting state is characterized by the gap in the electronic density of states which vanishes at the superconducting transition temperature Tc. It was discovered that in high temperature superconductors a noticeable depression in the density of states still remains even at temperatures above Tc; this feature being called pseudogap. Here we show that a pseudogap exists in a conventional superconductor: ultrathin titanium nitride films over a wide range of temperatures above Tc. Our study reveals that this pseudogap state is induced by superconducting fluctuations and favored by two-dimensionality and by the proximity to the transition to the insulating state. A general character of the observed phenomenon provides a powerful tool to discriminate between fluctuations as the origin of the pseudogap state, and other contributions in the layered high temperature superconductor compounds., Comment: 26 pages, 4 figures

We investigate the insulating phase that forms in a titanium nitride film in a close vicinity of the disorder-driven superconductor-insulator transition. In zero magnetic field the temperature dependence of the resistance reveals a sequence of distinct regimes upon decreasing temperature crossing over from logarithmic to activated behavior with the variable-range hopping squeezing in between. In perpendicular magnetic fields below 2 T, the thermally activated regime retains at intermediate temperatures, whereas at ultralow temperatures, the resistance increases faster than that of the thermally activated type. This indicates a change of the mechanism of the conductivity. We find that at higher magnetic fields the thermally activated behavior disappears and the magnetoresistive isotherms saturate towards the value close to quantum resistance h/e^2., Comment: revtex4 file, 6 pages, 4 figures (published)

Scanning tunneling spectroscopy at very low temperature on homogeneously disordered superconducting Titanium Nitride thin films reveals strong spatial inhomogeneities of the superconducting gap $\Delta$ in the density of states. Upon increasing disorder, we observe suppression of the superconducting critical temperature $T_c$ towards zero, enhancement of spatial fluctuations in $\Delta$, and growth of the $\Delta/T_c$ ratio. These findings suggest that local superconductivity survives across the disorder-driven superconductor-insulator transition., Comment: 4 pages, 3 figures. Minor changes. Accepted for publication in Phys. Rev. Lett

We investigate low-temperature transport properties of thin TiN superconducting films in the vicinity of the disorder-driven superconductor-insulator transition. In a zero magnetic field, we find an extremely sharp separation between superconducting and insulating phases, evidencing a direct superconductor-insulator transition without an intermediate metallic phase. At moderate temperatures, in the insulating films we reveal thermally activated conductivity with the magnetic field-dependent activation energy. At very low temperatures, we observe a zero-conductivity state, which is destroyed at some depinning threshold voltage V_T. These findings indicate formation of a distinct collective state of the localized Cooper pairs in the critical region at both sides of the transition., Comment: 4 pages, 4 figures, published version

We investigate ultrathin superconducting TiN films, which are very close to the localization threshold. Perpendicular magnetic field drives the films from the superconducting to an insulating state, with very high resistance. Further increase of the magnetic field leads to an exponential decay of the resistance towards a finite value. In the limit of low temperatures, the saturation value can be very accurately extrapolated to the universal quantum resistance h/e^2. Our analysis suggests that at high magnetic fields a new ground state, distinct from the normal metallic state occurring above the superconducting transition temperature, is formed. A comparison with other studies on different materials indicates that the quantum metallic phase following the magnetic-field-induced insulating phase is a generic property of systems close to the disorder-driven superconductor-insulator transition., Comment: 4 pages, 4 figures, published version

We have investigated low-temperature transport properties of two-dimensional arrays of superconductor--normal-metal--superconductor (SNS) junctions. It has been found that in two-dimensional arrays of SNS junctions (i) a change in the energy spectrum within an interval of the order of the Thouless energy is observed even when the thermal broadening far exceeds the Thouless energy for a single SNS junction; (ii) the manifestation of the subharmonic energy gap structure (SGS) with high harmonic numbers is possible even if the energy relaxation length is smaller than that required for the realization of a multiple Andreev reflection in a single SNS junction. These results point to the synchronization of a great number of SNS junctions. A mechanism of the SGS origin in two-dimensional arrays of SNS junctions, involving the processes of conventional and crossed Andreev reflection, is proposed., Comment: 5 pages, 5 figures

Temperature- and magnetic-field dependent measurements of the resistance of ultrathin superconducting TiN films are presented. The analysis of the temperature dependence of the zero field resistance indicates an underlying insulating behavior, when the contribution of Aslamasov-Larkin fluctuations is taken into account. This demonstrates the possibility of coexistence of the superconducting and insulating phases and of a direct transition from the one to the other. The scaling behavior of magnetic field data is in accordance with a superconductor-insulator transition (SIT) driven by quantum phase fluctuations in two-dimensional superconductor. The temperature dependence of the isomagnetic resistance data on the high-field side of the SIT has been analyzed and the presence of an insulating phase was confirmed. A transition from the insulating to a metallic phase is found at high magnetic fields, where the zero-temperature asymptotic value of the resistance being equal to h/e^2., Comment: 5 pages, 4 eps figures, RevTeX4, Published version

We report the experimental observation of a magnetic-field-tuned superconductor-insulator transition (SIT) in ultrathin TiN films. The low temperature transport properties of these films show scaling behavior consistent with a transition driven by quantum phase fluctuations in two-dimensional superconductor. The magnetoresistance reveals peak and a subsequent decrease in fields higher than the critical field. The temperature dependences of the isomagnetic resistance data on the high-field side of the SIT have been analyzed and the transition from insulating to metallic phase is found, with at high fields the zero-temperature asymptotic value of the resistance being equal to h/e^2., Comment: Submitted to LT23 Proceedings

Low temperature transport measurements on superconducting film - normal metal wire - superconducting film (SNS) junctions fabricated on the basis of 6 nm thick superconducting polycrystalline PtSi films are reported. The structures with the normal metal wires of two different lengths L=1.5 $\mu$m and L=6$\mu$m and the same widths W=0.3$\mu$m are studied. Zero bias resistance dip related to pair current proximity effect is observed for all junctions whereas the subharmonic energy gap structure originating from phase coherent multiple Andreev reflections have occurs only in the SNS junctions with short wires., Comment: ReVTex, 4 pages, 4 eps figures included