Zero-temperature Hall coefficient of an insulator

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

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/4e(2) 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).

Spin-Hall insulator

Recent theories predict dissipationless spin current induced by an electric field in doped semiconductors. Nevertheless, the charge current is still dissipative in these systems. In this work, we theoretically predict the dissipationless spin-Hall effect, without any accompanying charge current, in some classes of band insulators, including zero-gap semiconductors such as HgTe and narrow-gap semiconductors such as PbTe. This effect is similar to the quantum-Hall effect in that all the states below the gap contribute and there occurs no dissipation. However, the spin-Hall conductance is not quantized even in two dimensions. This is the first example of a nontrivial topological structure in a band insulator without any magnetic field.