Scanning tunneling spectroscopy at very low temperature on homogeneously disordered superconducting Titanium Nitride thin films reveals strong spatial inhomogeneities of the superconducting gap ∆ in the density of states. Upon increasing disorder, we observe suppression of the superconducting critical temperature Tc towards zero, enhancement of spatial fluctuations in ∆, and growth of the ∆/Tc ratio. These findings suggest that local superconductivity survives across the disorder-driven superconductor-insulator transition.PACS numbers: 74.50.+r, 74.78.Db, A pioneering idea that in the critical region of the superconductor-insulator transition (SIT) the disorderinduced inhomogeneous spatial structure of isolated superconducting droplets develops [1,2], grew into a new paradigm [3]. Extensive experimental research of critically disordered superconducting films revealed a wealth of unusual and striking phenomena, including nonmonotonic temperature and magnetic field dependence of the resistance [2,4,5,6], activated behavior of resistivity in the insulating state [1,5,6,7,8], nonmonotonic magnetic field dependence of the activation temperature, and the voltage threshold behavior [8,9,10]. These features find a theoretical explanation based on the concept of disorder-induced spatial inhomogeneity in the superconducting order parameter [10,11,12,13,14]. Numerical simulations confirmed that indeed in the high-disorder regime, the homogeneously disordered superconducting film breaks up into superconducting islands separated by an insulating sea [15,16]. At the same time the direct observation of superconducting islands near the SIT justifying the fundamental but yet hypothetical concept of the disorder-induced granularity on the firm experimental foundation was still lacking.In this Letter, we report on the combined low temperature Scanning Tunneling Spectroscopy (STS) and transport measurements performed on thin Titanium Nitride films on approach to the SIT. The local tunneling density of states (LDOS) measured at 50 mK reveals disorderinduced spatial fluctuations of the superconducting gap, ∆, with both, standard deviation σ to the average gap and the gap to the critical temperature ratios, σ/∆ and ∆/T c , respectively, increasing towards the transition.Our samples were thin TiN films synthesized by atomic layer chemical vapor deposition onto a Si/SiO 2 substrate. TiN1 was a 3.6 nm thick film deposited at 400• C while TiN2 and TiN3 were 5.0 nm thick films deposited at 350 • C. TiN3 was then slightly plasma etched in order to reduce its thickness. Electron transmission images revealed that the films comprise of the densely-packed crystallites with a typical size of 4 to 6 nm. The samples were patterned into the Hall bridges using conventional UV lithography and plasma etching. It is worth noticing that identically fabricated TiN films undergo the disorder-and magnetic field-driven SIT [4,8]. Transport measurements and STS were carried out during the same run in a STM attached to a dilution refrigerator. The STM Pt/Ir t...

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 VT . These findings indicate formation of a distinct collective state of the localized Cooper pairs in the critical region at both sides of the transition.An early suggestion that tuning disorder strength can cause a direct superconductor-insulator transition (SIT) in two-dimensional systems [1] triggered explosive activity in experimental studies of superconductor films [2]. Experimentally, the SIT can be induced by decreasing the film thickness [3] and/or, close to the critical thickness, also by the magnetic field [4]. These scenarios are commonly referred to as disorder-driven SIT (D-SIT) and magnetic-field driven SIT. Recent studies on the Binduced insulator revealed several striking features: a magnetic-field-dependent thermally activated behavior of the conductivity [5] and a threshold response to the dc voltage [6], indicating the possible formation of a distinct collective insulating state. Importantly, these findings refer to the films belonging to the superconducting side of the D-SIT. This rises the question of whether the above findings are specific only to the superconducting side of the D-SIT or a characteristic feature of the whole critical region including both the insulating and superconducting sides of the D-SIT.In this Letter we focus on the insulating side of the disorder-driven superconductor-insulator transition in TiN films. The transition itself turns out to be exceptionally sharp. At zero and low magnetic fields we find thermally activated behavior of the conductivity. A positive magnetoresistance and a distinct threshold behavior in the low-temperature I-V characteristics persist on the insulating side of the D-SIT. Our results clearly indicate that, in the vicinity of the D-SIT, the response to applied magnetic and/or electric fields, is the same irrespective of whether the underlying ground state is superconducting or insulating.The 5-nm thick TiN films were grown by atomic layer chemical vapor deposition onto a Si/SiO 2 substrate. The samples for transport measurements were patterned into Hall bridges using conventional UV lithography and subsequent plasma etching. To increase sheet resistances (R ) without introducing structural changes, the films were thinned by an additional soft plasma etching. Electron transmission micrographs and diffraction patterns revealed a polycrystalline structure in both initial and etched films, the interfaces separating densely-p...

Synchronized oscillators are ubiquitous in nature, and synchronization plays a key part in various classical and quantum phenomena. Several experiments have shown that in thin superconducting films, disorder enforces the droplet-like electronic texture--superconducting islands immersed into a normal matrix--and that tuning disorder drives the system from superconducting to insulating behaviour. In the vicinity of the transition, a distinct state forms: a Cooper-pair insulator, with thermally activated conductivity. It results from synchronization of the phase of the superconducting order parameter at the islands across the whole system. Here we show that at a certain finite temperature, a Cooper--air insulator undergoes a transition to a superinsulating state with infinite resistance. We present experimental evidence of this transition in titanium nitride films and show that the superinsulating state is dual to the superconducting state: it is destroyed by a sufficiently strong critical magnetic field, and breaks down at some critical voltage that is analogous to the critical current in superconductors.

A superconducting state is characterized by the gap in the electronic density of states, which vanishes at the superconducting transition temperature T c . It was discovered that in high-temperature superconductors, a noticeable depression in the density of states, the pseudogap, still remains even at temperatures above T c . Here, we show that a pseudogap exists in a conventional superconductor, ultrathin titanium nitride films, over a wide range of temperatures above T c . our study reveals that this pseudogap state is induced by superconducting fluctuations and favoured 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.

A superconductor in a magnetic field acquires a finite electrical resistance caused by vortex motion. A quest to immobilize vortices and recover zero resistance at high fields made intense studies of vortex pinning one of the mainstreams of superconducting research. Yet, the decades of efforts resulted in a realization that even promising nanostructures, utilizing vortex matching, cannot withstand high vortex density at large magnetic fields. Here, we report a giant reentrance of vortex pinning induced by increasing magnetic field in a W-based nanowire and a TiN-perforated film densely populated with vortices. We find an extended range of zero resistance with vortex motion arrested by self-induced collective traps. The latter emerge due to order parameter suppression by vortices confined in narrow constrictions by surface superconductivity. Our findings show that geometric restrictions can radically change magnetic properties of superconductors and reverse detrimental effects of magnetic field.

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/e2. 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.

For nearly a half century the dominant orthodoxy has been that the only effect of the Cooper pairing is the state with zero resistivity at finite temperatures, superconductivity. In this work we demonstrate that by the symmetry of the Heisenberg uncertainty principle relating the amplitude and phase of the superconducting order parameter, Cooper pairing can generate the dual state with zero conductivity in the finite temperature range, superinsulation. We show that this duality realizes in the planar Josephson junction arrays (JJA) via the duality between the Berezinskii-Kosterlitz-Thouless (BKT) transition in the vortex-antivortex plasma, resulting in phase-coherent superconductivity below the transition temperature, and the charge-BKT transition occurring in the insulating state of JJA and marking formation of the low-temperature charge-BKT state, superinsulation. We find that in disordered superconducting films that are on the brink of superconductor-insulator transition the Coulomb forces between the charges acquire two-dimensional character, i.e. the corresponding interaction energy depends logarithmically upon charge separation, bringing the same vortex-charge-BKT transition duality, and realization of superinsulation in disordered films as the low-temperature charge-BKT state. Finally, we discuss possible applications and utilizations of superconductivity-superinsulation duality.

We investigate transition to the superconducting state in the ultrathin (≤ 5 nm thick) 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, Tc, 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 TBKT /Tc follows the universal Beasley-Mooij-Orlando relation. Our results call for revisiting the past data on superconducting transition in thin disordered films.