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We combine measurements of the longitudinal ($\rho_{xx}$) and Hall($\rho_{xy}$) resistivities of disordered two dimensional amorphousindium-oxide films to study the magnetic-field tuned superconductor toinsulator transition (H-SIT) in the $T \to 0$ limit. At the critical field,$H_c$, the full resistivity tensor is $T$ independent with $\rho_{xx}(H_c) =h/4e^2$ and $\rho_{xy}(H_c)=0$ within experimental uncertainty in all films(i.e. these appear to be "universal" values), this is strongly suggestive thatthere is a particle-vortex self-duality at $H=H_c$. The transition separatesthe (presumably) superconducting state at $H<H_c$ from a "Hall-insulator" phasein which $\rho_{xx}\to \infty$ as $T\to 0$ while $\rho_{xy}$ approaches anon-zero value smaller than its "classical value" $H/nec$, i.e.$0<\rho_{xy}<H/nec$. A still higher characteristic magnetic field, $H_c^*>H_c$, at which the Hall resistance is $T$ independent and roughly equal to itsclassical value, $\rho_{xy}\approx H/nec$, marks an additional crossover to ahighfield regime (probably to a Fermi-insulator) in which $\rho_{xy} > H/nec$and possibly diverges as $T\to 0$. We also highlight a profound analogy betweenthe H-SIT and quantum-Hall liquid to insulator transitions (QHIT).

Self Duality and a possible Hall-insulator phase near the superconductor-to-insulator transition in two-dimensional indium-oxide films