Destruction of localized electron pairs above the magnetic-field-driven superconductor-insulator transition in amorphous In-O films

Abstract

We have investigated the field-induced superconductivity-destroying quantum transition in amorphous indium oxide films at low temperatures down to 30 mK. It has been found that, on the high-field side of the transition, the magnetoresistance reaches a maximum and the phase can be insulating as well as metallic. With further increasing magnetic field the film resistance drops and approaches in the high-field limit the resistance value at transition point so that at high fields the metallic phase occurs for both cases. We give a qualitative account of this behavior in terms of field-induced destruction of localized electron pairs.The theoretical description of the zero-field and fieldinduced quantum superconductor-insulator transitions (SIT) in a 2D superconductor is based on a concept of electron pairs which are delocalized on the superconducting side and localized on the insulating side of transition [1][2][3]. According to Refs. [1][2][3], the temperature dependence of the film resistance near the field-induced SIT is controlled by deviation δ = B − B c from the critical field B c and the most specific among perceptible features of SIT is fan-like set of resistance-vs-temperature curves R δ (T ). Such a set is expected to collapse onto a single curve as a function of scaling variable δ/T 1/y , where y is the critical index, see review [4]. Many of the SIT studies were performed on amorphous In 2 O x (x < 3) films whose conductivity is caused by oxygen deficiency compared to fully stoichiometric insulating compound In 2 O 3 : by changing the oxygen content one can cover the range from a superconductor to an insulator and thus realize the zero-field SIT. On the insulating side of this SIT, observation was reported of the activation behavior of the resistance R ∝ exp(T 0 /T ) p with p = 1 (Arrhenius law) and activation energy T 0 tending to zero as the phase boundary is approached [5]. It was found later that switching a magnetic field results in decreasing the resistance and weakening its temperature dependence from the Arrhenius law to the Mott law with exponent p = 1/4 [6]. This was explained in Ref.[6] by magnetic-fieldcaused suppression of the binding energy ∆ of localized electron pairs which manifests as a gap at the Fermi level.Field-induced SIT is realized on the superconducting side of zero-field SIT. It is indicated by fan-like structure of experimental curves R δ (T ) such that, in accordance with the scaling analysis, the expected collapse is indeed the case [7]. Above the field-induced SIT, the existence of two insulating phases was postulated based on results of Hall measurements [8]; however, temperature dependences of the resistance of these phases were not studied. Reversal of a zero-bias peak in the differential resistance at the critical field B c was observed and attributed to the granular structure of films [9].

Cooper-pair insulator phase in superconducting amorphous Bi films induced by nanometer-scale thickness variations

“…[7][8][9] Theoretical descriptions of this CPI phase often presume that disorder or magnetic field creates islands of Cooper pairs embedded in a non-superconducting background. [10][11][12][13] Although the description of the CPI as an inhomogeneous phase of matter is consistent with observations, the experimental support is limited. The most direct support provided so far is Scanning Tunneling Microscopy (STM) measurements which show evidence of spatial superconducting gap variations of ≲ 20% in superconducting films of InO x and TiN.…”

Absence of a zero-temperature vortex solid phase in strongly disordered superconducting Bi films

“…3 (with notable exceptions [21]). To fix problems with scaling like those in Fig 3a, Gantmakher suggested that the critical field corresponds to where the 2nd derivative of the resistance with respect to temperature is zero rather than the first derivative [30]. Until theory justifies this modification it seems more reasonable to assume that no critical field exists.…”

Superconductivity on the localization threshold and magnetic-field-tuned superconductor-insulator transition in TiN films

“…At finite temperatures, a quantum phase transition is influenced by the thermal fluctuations, and according to the theory, (i) the film resistance R near the magnetic-field-induced SIT at low temperature T in the vicinity of the critical field B c is a function of one scaling variable δ = (B − B c )/T 1/νz , with the critical exponents ν and z being constants of order of unity, and (ii) at the transition point, the film resistance is of the order h/(2e) 2 ≈ 6.5 kΩ (the quantum resistance for Cooper pairs). Although much work has been done, and in many systems the scaling relations hold [3,4,5,6,7,8], the magnetic-field-induced SIT in disordered films remains a controversial subject, especially concerning the insulating phase and the bosonic conduction at B > B c . There is experimental evidence [7] that, despite the magnetoresistance being nonmonotonic, and in the magnetic fields above the critical one, the derivative of resistance dR/dT is negative, the phase can be insulating as well as metallic.…”