As a superconducting thin film becomes disordered and subject to an increasing magnetic field, a point is reached when it undergoes a transition from a superconducting to an insulating state. Dubi et al. use numerical simulations to study this transition — or, as it turns out, two types of transition. The key effect of disorder is to create 'islands' of strong superconductivity, coupled by regions that are only weakly superconducting. In the case of weak disorder, an increasing magnetic field eventually destroys the superconducting state throughout the material, leading to an insulator. When disorder is strong, superconductivity persists in the islands, and the effect of a magnetic field is to suppress the coupling between them — again leading to an insulating state. These findings may be relevant to the high-temperature superconductors, where intrinsic disorder may play a role. As a superconducting thin film is made more disordered, or subject to an increasing magnetic field, a point is reached when the material undergoes a transition from a superconducting to an insulating state. Numerical simulations have been used to shed light on the nature of this transition, or, as it turns out, two types of transition. The interplay of superconductivity and disorder has intrigued scientists for several decades. Disorder is expected to enhance the electrical resistance of a system, whereas superconductivity is associated with a zero-resistance state. Although superconductivity has been predicted to persist even in the presence of disorder1, experiments performed on thin films have demonstrated a transition from a superconducting to an insulating state with increasing disorder or magnetic field2. The nature of this transition is still under debate, and the subject has become even more relevant with the realization that high-transition-temperature (high-Tc) superconductors are intrinsically disordered3,4,5. Here we present numerical simulations of the superconductor–insulator transition in two-dimensional disordered superconductors, starting from a microscopic description that includes thermal phase fluctuations. We demonstrate explicitly that disorder leads to the formation of islands where the superconducting order is high. For weak disorder, or high electron density, increasing the magnetic field results in the eventual vanishing of the amplitude of the superconducting order parameter, thereby forming an insulating state. On the other hand, at lower electron densities or higher disorder, increasing the magnetic field suppresses the correlations between the phases of the superconducting order parameter in different islands, giving rise to a different type of superconductor–insulator transition. One of the important predictions of this work is that in the regime of high disorder, there are still superconducting islands in the sample, even on the insulating side of the transition. This result, which is consistent with experiments6,7, explains the recently observed huge magneto-resistance peak in disordered thin films8,9,10 and may be relevant to the observation of ‘the pseudogap phenomenon’ in underdoped high-Tc superconductors11,12.

Nature of the superconductor-insulator transition in disordered superconductors.

The introduction of disorder into thin superconducting films induces a droplet-like electronic texture, with superconducting islands immersed in a normal matrix. By fine-tuning this disorder, the system can be transformed from superconductor to insulator. A paper in this issue presents experimental evidence for the involvement of a previously uncharacterized 'superinsulating' state of matter in this process, a 'mirror image' equivalent of a superconductor with infinite resistance. During the transition from superconductor to insulator, a distinct conductivity state is formed, a Cooper-pair insulator, with thermally activated conductivity. Experiments in titanium nitride films show that at a certain finite temperature, a Cooper-pair insulator becomes a superinsulator, a state resembling superconductivity in that it is destroyed by a sufficiently strong critical magnetic field, and breaks down at some critical voltage. This paper shows that at a certain finite temperature, a Cooper-pair insulator undergoes a transition to a superinsulating state with infinite resistance. Experimental evidence of this transition in titanium nitride films is presented and it is demonstrated 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 which is analogous to the critical current in superconductors. Synchronized oscillators are ubiquitous in nature1, and synchronization plays a key part in various classical and quantum phenomena. Several experiments2,3,4 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 state4 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 system5. Here we show that at a certain finite temperature, a Cooper-pair 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.

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Superinsulator and quantum synchronization

In superconductors the zero-resistance current-flow is protected from dissipation at finite temperatures (T) by virtue of the short-circuit condition maintained by the electrons that remain in the condensed state. The recently suggested finite-T insulator and the "superinsulating" phase are different because any residual mechanism of conduction will eventually become dominant as the finite-T insulator sets-in. If the residual conduction is small it may be possible to observe the transition to these intriguing states. We show that the conductivity of the high magnetic-field insulator terminating superconductivity in amorphous indium-oxide exhibits an abrupt drop, and seem to approach a zero conductance at T < 0.04 K. We discuss our results in the light of theories that lead to a finite-T insulator.

/pdf/evidence-for-a-finite-temperature-insulator-1hp6zc4rs0.pdf

Evidence for a Finite Temperature Insulator

In order to understand the emergence of superconductivity it is useful to study the reverse process and identify the various pathways that lead to its destruction. One way is to increase the amount of disorder, as this leads to an increase in Coulomb repulsion that overpowers the attractive interaction responsible for Cooper pair formation. A second pathway—applicable to uniformly disordered materials—is to utilize the competition between superconductivity and Anderson localization, as this leads to electronic granularity in which phase and amplitude fluctuations of the superconducting order parameter play a role. Finally, a third pathway is to construct an array of superconducting islands coupled by some form of proximity effect that leads from a superconducting state to a state with finite resistivity, which appears like a metallic groundstate. This Review Article summarizes recent progress in understanding of these different pathways, including experiments in low dimensional materials and application in superconducting quantum devices. The breakdown of superconductivity is described as a reduction in the amplitude of the order parameter or a breakdown in phase coherence of Cooper pairs. This Review Article highlights recent results that show both mechanisms may be at play simultaneously.

/pdf/quantum-breakdown-of-superconductivity-in-low-dimensional-1zonnc9erh.pdf

Quantum breakdown of superconductivity in low-dimensional materials

In superconductors the zero-resistance current-flow is protected from dissipation at finite temperatures (T) by virtue of the short-circuit condition maintained by the electrons that remain in the condensed state. The recently suggested finite-T insulator and the "superinsulating" phase are different because any residual mechanism of conduction will eventually become dominant as the finite-T insulator sets-in. If the residual conduction is small it may be possible to observe the transition to these intriguing states. We show that the conductivity of the high magnetic-field insulator terminating superconductivity in amorphous indium-oxide exhibits an abrupt drop, and seem to approach a zero conductance at T<0.04 K. We discuss our results in the light of theories that lead to a finite-T insulator.

/pdf/evidence-for-a-finite-temperature-insulator-1981k9ju7z.pdf

We have studied magnetoresistance in thin films of amorphous indium oxide with various degrees of oxidation, i. e., with various densities of states in the vicinity of the Fermi level. A large negative magnetoresistance is observed when the films are in the insulating state. The negative field derivative partial derivative R/partial derivative H of the resistance persists up to 20 T, the highest magnetic field in our experiment. The magnetoresistance is described in terms of a field-dependent gap at the Fermi level. Such a gap can arise due either to tunneling in a system of fluctuation-induced superconducting clusters or to the Cooper interaction between electrons localized in shallow minima of the random potential. In the latter case, if the depth of the minima is smaller than the Debye energy, the electrons are virtually delocalized by short-wavelength phonons.

J. G S Lok

Papers

Giant negative magnetoresistance of semi-insulating amorphous indium oxide films in strong magnetic fields