Theory of Linear Magnetoresistance in a Strange Metal

A central puzzle in strongly correlated electronic phases is strange metallic transport, marked by $T$-linear resistivity and $B$-linear magnetoresistance, in sharp contrast with quadratic scalings observed in conventional metals. Here, we demonstrate that proximity to quantum critical points, a recurring motif in the phase diagrams of strange metal candidates, can explain both transport anomalies. We construct and solve a minimal microscopic model by coupling electronic excitations at the Fermi surface to quantum critical bosons via a spatially disordered Yukawa interaction, as well as static pinned domains of density wave order. The resultant transport relaxation rate scales as $k_B T/\hbar$ at low magnetic fields, and as an effective Bohr magneton $\tildeμ_B B/\hbar$ at low temperatures. Further, the magnetoresistance in our model shows a scaling collapse upon rescaling the magnetic field and the resistance by temperature, in agreement with experimental observations.