Phases of disordered indium oxide near a superconductor-to-insulator transition

We investigate the possibility of a zero-temperature magnetic field-tuned superconductor-to-insulator transition in disordered films of amorphous indium oxide. This is an example of a quantum phase transition where an external parameter such as the magnetic field induces a transition from one quantum ground state to another, fundamentally different one. We were particularly interested in the transition between the zero-temperature superconducting state of disordered thin films and an insulating state which retains the integrity of Cooper pairs and hence the bosonic character of the system. In this transition, at a critical field Hc, a low field vortex-glass phase in which Cooper-pairs are itinerant and vortices are localized changes to Bose-insulating phase in which Cooper-pairs are localized and vortices are delocalized.; The different phases are studied by measuring the resistivity and the Hall resistance as a function of temperature and magnetic field for a series of films of varying disorder. Isotherms of the resistivity cross at a temperature-independent field, Hc, then peak at a higher field and decay slowly toward the normal state at the highest fields. We suggest that at the resistivity peak the film crosses over from a boson-dominated insulating phase at lower fields to a fermion-dominated phase at higher fields, a result of an increased depairing rate which destroys the Bose-insulator. Despite the crossover, pairing susceptibility persists to the highest accessible fields, approximately 32 T, as the normal state does not appear to be fully recovered and a vestige of superconductivity remains. The peak in the resistivity appears to be activated and characterizes the strength of the insulating phase. Our study reveals a wide range of insulator strength which depends on disorder and correlates with the nature of the phase transition at Hc. While for weak disorder scaling of the data near He reveals a more classical behaviour dominated by an intervening metallic phase, the limit of strong disorder seems to point to the behaviour of a true Bose-dominated superconductor-insulator transition. Such behaviour is probably aided by the strong magnetoresistance peak that separates the Bose-system from the Fermi-dominated system. This interpretation is reinforced by measurements of the Hall resistance.