**"Self-duality and a Hall-insulator phase near the superconductor-to-insulator transition in indium-oxide films"**

Nicholas P. Breznay: Myles A. Steiner, Steven Allan Kivelson, and Aharon Kapitulnik; Proceedings of the National Academy of Sciences, 01/12/16.

**Abstract**:

We combine measurements of the longitudinal (ρxxρxx) and Hall (ρxyρxy) resistivities of disordered 2D amorphous indium-oxide films to study the magnetic-field tuned superconductor-to-insulator transition (H-SIT) in the T→0T→0 limit. At the critical field, HcHc, the full resistivity tensor is *T* independent with ρxx(Hc)=h/4e2ρxx(Hc)=h/4e2 and ρxy(Hc)=0ρxy(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=HcH=Hc. The transition separates the (presumably) superconducting state at H<HcH<Hc from a “Hall-insulator” phase in which ρxx→∞ρxx→∞ as T→0T→0 whereas ρxyρxy approaches a nonzero value smaller than its “classical value” H/necH/nec; i.e., 0<ρxy<H/nec0<ρxy<H/nec. A still higher characteristic magnetic field, H*c>HcHc*>Hc, at which the Hall resistance is *T* independent and roughly equal to its classical value, ρxy≈H/necρxy≈H/nec, marks an additional crossover to a high-field regime (probably to a Fermi insulator) in which ρxy>H/necρxy>H/nec and possibly diverges as T→0T→0. We also highlight a profound analogy between the H-SIT and quantum-Hall liquid-to-insulator transitions (QHIT).