Disorder-Induced Inhomogeneities of the Superconducting State Close to the Superconductor-Insulator Transition

Abstract

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...

Duality symmetry and its breakdown in the vicinity of the superconductor–insulator transition

“…Following this relationship, the experiments on the B-SIT and the experiments tuning the carrier density form a dual set of experiments. Interestingly, this analogy implies that the disorder-driven SIT at B = 0 must have a different mechanism for the insulating state; a distinction that cannot be made from experiments: Transport and scanning tunnelling experiments [24][25][26] as well as microscopic model calculations 27,28 suggest that Cooper pairs persist also in the disorder-driven insulating state.…”

Stability of the superfluid state in a disordered one-dimensional ultracold fermionic gas

“…Therefore both the spectral density and the spin gap will increase as λ increases. Close to the metal-insulator transition, strong density-density fluctuations in the one-body problem [3,28] further enhance the gap. This enhancement is a coherent effect and therefore it is expected to diminish as the coherence length becomes of the order of the system size which occurs in the region of strong coupling.…”

“…This is an ideal setting to test theoretical predictions on novel phases of quantum matter and quantum phase transitions [3]. Motivated by these possibilities we study a disordered 1D Fermi gas with short-range attractive interactions by the DMRG technique.…”

Universal scaling of the critical temperature for thin films near the superconducting-to-insulating transition

“…This observation began the race to understanding the superconductor insulator phase transition, which is believed by many researchers to be of a quantum nature [5]. To date, although much data for thin film superconductivity have been accumulated [11,12,[15][16][17][18][19][20][21][22][23][24][25][26][27][28], and the local disorder has already been observed directly [33], the mechanisms governing the collective behavior close to the superconducting-to-insulating transition, or near the onset of superconductivity have remained elusive. That is, a model equivalent to the BCS, but that is valid for thin films, is still missing.…”