We combine measurements of the longitudinal (ρxx) and Hall (ρxy) 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, Hc, the full resistivity tensor is T independent with ρxx(Hc)=h/4e2 and ρxy(Hc)=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=Hc. The transition separates the (presumably) superconducting state at H<Hc from a “Hall-insulator” phase in which ρxx→∞ as T→0 whereas ρxy approaches a nonzero value smaller than its “classical value” H/nec; i.e., 0<ρxy<H/nec. A still higher characteristic magnetic field, Hc*>Hc, at which the Hall resistance is T independent and roughly equal to its classical value, ρxy≈H/nec, marks an additional crossover to a high-field regime (probably to a Fermi insulator) in which ρxy>H/nec and possibly diverges as T→0. We also highlight a profound analogy between the H-SIT and quantum-Hall liquid-to-insulator transitions (QHIT).
Precision quantum Hall resistance measurement on epitaxial graphene device in low magnetic field
