Self-duality and a Hall-insulator phase near the superconductor-to-insulator transition in indium-oxide films
We combine measurements of the longitudinal ( ρ x x ) and Hall ( ρ x y ) resistivities of disordered 2D amorphous indium-oxide films to study the magnetic-field tuned superconductor-to-insulator transition (H-SIT) in the T → 0 limit. At the critical field, H c , the full resistivity tensor is T independent with ρ x x ( H c ) = h / 4 e 2 and ρ x y ( H c ) = 0 within experimental uncertainty in all films (i.e., these appear to be “universal” values); this is strongly suggestive that there is a particle–vortex self-duality at H = H c . The transition separates the (presumably) superconducting state at H < H c from a “Hall-insulator” phase in which ρ x x → ∞ as T → 0 whereas ρ x y approaches a nonzero value smaller than its “classical value” H / n e c ; i.e., 0 < ρ x y < H / n e c . A still higher characteristic magnetic field, H c * > H c , at which the Hall resistance is T independent and roughly equal to its classical value, ρ x y ≈ H / n e c , marks an additional crossover to a high-field regime (probably to a Fermi insulator) in which ρ x y > H / n e c and possibly diverges as T → 0 . We also highlight a profound analogy between the H-SIT and quantum-Hall liquid-to-insulator transitions (QHIT).