Anisotropic Magnetoresistance in Multiband Systems: 2DEGs and Polar Metals at Oxide Interfaces.

Low density two-dimensional electron gases (2DEGs) with spin-orbit coupling are highly sensitive to an in-plane magnetic field, which impacts their Fermi surfaces and transport properties. Such 2DEGs, formed at transition metal oxide surfaces or interfaces, can also undergo surface phase transitions leading to polar metals which exhibit electronic nematicity. Motivated by experiments on such systems, we theoretically study magnetotransport in $t_{2g}$ orbital systems, using Hamiltonians which include atomic spin-orbit coupling (SOC) and broken inversion symmetry, for both square symmetry (001) and hexagonal symmetry (111) 2DEGs. Using a numerical solution to the full multiband matrix-Boltzmann equation, together with insights gleaned from the impurity scattering overlap matrix, we explore the anisotropic magnetoresistance (AMR) in the presence of impurities which favor small momentum scattering. We find that transport in the (001) 2DEG is dominated by a single pair of bands, weakly coupled by impurity scattering, one of which has a larger Fermi velocity while the other provides an efficient current-relaxation mechanism. This leads to strong angle-dependent current damping and a large AMR with many angular harmonics. In contrast, AMR in the (111) 2DEG typically features a single $\cos(2\vartheta)$ harmonic, with the angle-averaged magnetoresistance being highly tunable by a symmetry-allowed trigonal distortion. We also explore how the (111) 2DEG Fermi sufaces are impacted by electronic nematicity via a surface phase transition into a 2D polar metal for which we discuss a Landau theory, and show that this leads to distinct symmetry components and higher angular harmonics in the AMR. Our results are in qualitative agreement with experiments from various groups for 2DEGs at the SrTiO$_3$ surface or the LaAlO$_3$-SrTiO$_3$ interface.