Disorder influences the quantum critical transport at a superconductor-to-insulator transition

Abstract

We isolated flux disorder effects on the transport at the critical point of the quantum magnetic field tuned Superconductor to Insulator transition (BSIT). The experiments employed films patterned into geometrically disordered hexagonal arrays. Spatial variations in the flux per unit cell, which grow in a perpendicular magnetic field, constitute flux disorder. The growth of flux disorder with magnetic field limited the number of BSITs exhibited by a single film due to flux matching effects. The critical metallic resistance at successive BSITs grew with flux disorder contrary to predictions of its universality. These results open the door for controlled studies of disorder effects on the universality class of an ubiquitous quantum phase transition.Transport phenomena near quantum critical points receive ongoing scrutiny. Much attention comes from efforts to understand strange metal behavior in high T c [1,2] and heavy fermion compounds [3,4]. Others who are developing string theory based techniques to calculate many body properties of condensed matter in the strong coupling limit have focussed on quantum critical transport as well [5][6][7]. An interesting case is the superfluid to insulator transition in charged two dimensional systems such as superconducting films. This Superconductor to Insulator transition (SIT) appears in numerous thin film systems [8,9] as a change from superconducting to insulating transport when a physical parameter such as thickness [10,11] magnetic field [12] or a gating field [13][14][15][16] is tuned. At the critical value of the tuning parameter, film resistances asymptote to a constant value in the zero frequency, low temperature limit. The limiting critical resistance assumes a value near the quantum of resistance for electron pairs R c ∼ h 4e 2 = R Q [8,9]. Despite the simplicity of this behavior, questions remain regarding its universality and the influence of disorder.Indeed, the critical resistance near a superconductor to insulator transition is at the heart of studies, both theoretical and experimental. Fisher [17] and collaborators [18] provided the original arguments supporting the universality of R c . They focussed on bosonic systems presuming that fermion degrees of freedom in the form of unpaired electrons play no role. They argued that R c is likely to be constant in ordered systems within a universality class [18] especially in magnetic field. Disorder appeared to lead to an increase in R c . Numerical simulations [19,20] that R c grows with the normal state resistance, which is a similar measure of disorder. In both cases R c assumes values that are about a factor of two higher than observed in the most ordered systems, micro-fabricated Josephson Junction Arrays (JJA) [26,27]. Such an elaborate picture reflects the variety of approaches and systems employed to study R c . It suggests that deriving a new method for controllably varying disorder and selecting a thin film system with a bosonic SIT is crucial to making further experimental progress.Opportunities to care...

Superconductor-insulator transition of Josephson-junction arrays on a honeycomb lattice in a magnetic field

“…The f = 1/2 case is of particular interest since geometrical frustration combined with thermal fluctuations leads to an unusual phase transition as a function of temperature 17,25,26,29 . It should be of interest to investigate the effects of geometrical disorder in the quantum transition of this system 15,22,43 .…”

“…This has already been observed in experiments on artificial Josephson-junction arrays with controlled amount of positional disorder 44 , near the thermal resistive transition and in absence of charging effects. Very recently 22 , it has also been demonstrated in superconducting films with a pattern of nanoholes with controlled amount of positional disorder near the superconductor-insulator transition.…”

“…In part, this is due to the lack of experimental data for artificial arrays in this geometry. Recently, however, there has been a growing interest in a related system, in the form of an ultra-thin superconducting film with a triangular lattice of nanoholes [18][19][20][21][22] . A simple model for this system consists of a Josephson-junction array on a honeycomb lattice, with the triangular lattice of nanoholes corresponding to the dual lattice, and it has already been used to investigated the thermal resistive transition in absence of charging effects 17 .…”

Magnetic flux disorder and superconductor-insulator transition in nanohole thin films

“…Monte Carlo simulation in the path-integral representation is used to determine the critical behavior and the universal resistivity at the transition as a function of disorder and average number of flux quanta per cell, fo. The resistivity increases with disorder for noninteger fo while it decreases for integer fo, and reaches a common constant value in a vortex-glass regime above a critical value of the flux disorder D There is growing interest in the superconductorinsulator (SI) transition in ultra-thin films with a lattice of nanoholes [1][2][3][4][5][6] . This system is an important testing ground for models of the universality class of the quantum phase transition since the patterned nanostructure provides a sensitive probe for distinguishing between phase and amplitude fluctuations of the superconducting order parameter.…”

“…The zero-temperature quantum phase transition in the array model, driven by the competition between the charging energy and Josephson-coupling energy at different frustration parameters, corresponds to the SI transition in the nanohole film in the external magnetic field. The resistivity at the transition is expected to be finite and universal 12,13,20,21 , depending only on the universality class of the transition, which generally changes in the presence of a magnetic field and disorder.Very recently, intriguing experimental results have been obtained near the SI transition in thin films with a disordered triangular lattice of nanoholes with controlled amount of positional disorder 5,6 . Such disorder leads to spatial variations in the magnetic flux per unit cell, which increases with the magnetic field, similar to the effects of geometrical disorder in microfabricated Josephson-junction arrays 22,23 .…”