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 γ function for magnetotransport, finding that γ (g_{x y}) =d/[log(g_{x y}) ] d [log(T )] ≃log (g_{x y}) 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.