Quantum critical magnetotransport at a continuous metal-insulator transition

In contrast to the seminal weak localization prediction of a noncritical Hall constant (${R}_{H}$) at the Anderson metal-insulator transition (MIT), ${R}_{H}$ in quite a few real disordered systems exhibits both a strong $T$ dependence and critical scaling near their MIT. Here we investigate these issues in detail within a nonperturbative ``strong localization'' regime using cluster-dynamical mean-field theory (CDMFT). We uncover (i) clear and unconventional quantum-critical scaling of the Gell-Mann law, or $\ensuremath{\gamma}$ function for magnetotransport, finding that $\ensuremath{\gamma}({g}_{xy})=\frac{d[\text{log}({g}_{xy})]}{d[\text{log}(T)]}\ensuremath{\simeq}\phantom{\rule{4pt}{0ex}}\mathrm{log}({g}_{xy})$ over a wide range spanning the continuous MIT, very similar to that seen for the longitudinal conductivity, and (ii) strongly $T$ dependent and clear quantum critical scaling in both transverse conductivity and ${R}_{H}$ at the MIT. We show that these surprising results are in comprehensive and very good accord with signatures of a novel Mott-like localization in NbN near the MIT, providing substantial support for our ``strong'' localization view.