Theory of anomalous magnetotransport from mass anisotropy

In underdoped YBa$_2$Cu$_3$O$_{6+x}$, there is evidence of a small Fermi surface pocket subject to substantial mass enhancement in the doping regime $0.12<p<0.16$. This mass enhancement may vary substantially over the Fermi surface, due to "hot spot" or other relevant physics. We therefore examine the magnetotransport of an electron-like Fermi pocket with large effective mass anisotropy. Within the relaxation time approximation, we show that even for a pocket with a fixed shape, the magnitude and sign of the Hall effect may change as the mass anisotropy changes (except at very large, likely inaccessible magnetic fields). We discuss implications for recent Hall measurements in near optimally doped cuprates in high fields. In addition we identify a novel intermediate asymptotic regime of magnetic field, characterized by B-linear magnetoresistance. Similar phenomena should occur in a variety of other experimental systems with anisotropic mass enhancement