Nonmonotonic magnetic field and density dependence of in-plane magnetoresistance in dilute two-dimensional holes in ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$

We studied low temperature $(T=50\mathrm{}$ mK) in-plane magnetoresistance of a dilute two-dimensional hole system in GaAs/AlGaAs heterostructure that exhibits an apparent metal-insulator transition. We found an anisotropic magnetoresistance, which changes dramatically at high in-plane fields ${(B}_{\Vert }\gtrsim 5$ T) as the hole density is varied. At high densities where the system behaves metallic at $B_{\Vert }=0,$ the transverse magnetoresistance is larger than the longitudinal magnetoresistance. With decreasing the hole density the difference becomes progressively smaller, and at densities near the “critical” density and lower, the longitudinal magnetoresistance becomes larger than the transverse magnetoresistance.