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Experiments investigating magnetic-field-tuned superconductor–insulator transition (HSIT) mostly focus on two-dimensional material systems where the transition and its proximate ground-state phases, often exhibit features that are seemingly at odds with the expected behavior. Here we present a complementary study of a three-dimensional pressure-packed amorphous indium-oxide (InOx) powder where granularity controls the HSIT. Above a low threshold pressure of ∼0.2 GPa, vestiges of superconductivity are detected, although neither a true superconducting transition nor insulating behavior are observed. Instead, a saturation at very high resistivity at low pressure is followed by saturation at very low resistivity at higher pressure. We identify both as different manifestations of anomalous metallic phases dominated by superconducting fluctuations. By analogy with previous identification of the low resistance saturation as a ‘failed superconductor’, our data suggests that the very high resistance saturation is a manifestation of a ‘failed insulator’. Above a threshold pressure of ∼6 GPa, the sample becomes fully packed, and superconductivity is robust, withT_Ctunable with pressure. A quantum critical point atP_C∼ 25 GPa marks the complete suppression of superconductivity. For a finite pressure belowP_C, a magnetic field is shown to induce a HSIT from a true zero-resistance superconducting state to a weakly insulating behavior. Determining the critical field,H_C, we show that similar to the 2D behavior, the insulating-like state maintains a superconducting character, which is quenched at higher field, above which the magnetoresistance decreases to its fermionic normal state value.

 

Many experiments investigating magnetic-field tuned superconductor-insulator transition (H-SIT) often exhibit low-temperature resistance saturation, which is interpreted as an anomalous metallic phase emerging from a ‘failed superconductor’, thus challenging conventional theory. Here we study a random granular array of indium islands grown on a gateable layer of indium-oxide. By tuning the intergrain couplings, we reveal a wide range of magnetic fields where resistance saturation is observed, under conditions of careful electromagnetic filtering and within a wide range of linear response. Exposure to external broadband noise or microwave radiation is shown to strengthen the tendency of superconductivity, where at low field a global superconducting phase is restored. Increasing magnetic field unveils an ‘avoided H-SIT’ that exhibits granularity-induced logarithmic divergence of the resistance/conductance above/below that transition, pointing to possible vestiges of the original emergent duality observed in a true H-SIT. We conclude that anomalous metallic phase is intimately associated with inherent inhomogeneities, exhibiting robust behavior at attainable temperatures for strongly granular two-dimensional systems.

 

Resistivity saturation is found on both superconducting and insulating sides of an “avoided” magnetic-field-tuned superconductor-to-insulator transition (H-SIT) in a two-dimensional In/InO x composite, where the anomalous metallic behavior cuts off conductivity or resistivity divergence in the zero-temperature limit. The granular morphology of the material implies a system of Josephson junctions (JJs) with a broad distribution of Josephson coupling E J and charging energy E C , with an H-SIT determined by the competition between E J and E C . By virtue of self-duality across the true H-SIT, we invoke macroscopic quantum tunneling effects to explain the temperature-independent resistance where the “failed superconductor” side is a consequence of phase fluctuations and the “failed insulator” side results from charge fluctuations. While true self-duality is lost in the avoided transition, its vestiges are argued to persist, owing to the incipient duality of the percolative nature of the dissipative path in the underlying random JJ system. 

The magnetic-field–tuned superconductor-to-insulator transition was studied in a hybrid system of superconducting indium islands, deposited on an indium oxide (InOx) thin film, which exhibits global superconductivity at low magnetic fields. Vacuum annealing was used to tune the conductivity of the InOx film, thereby tuning the inergrain coupling and the nature of the transition. The hybrid system exhibits a “giant” magnetoresistance above the magnetic-field–tuned superconductor-to-insulator transition (H-SIT), with critical behavior similar to that of uniform InOx films but at much lower magnetic fields, that manifests the duality between Cooper pairs and vortices. A key feature of this hybrid system is the separation between the quantum criticality and the onset of nonequilibrium behavior.