Kondo transport in an anisotropic two-dimensional electron gas with quadratic momentum-dependent spin splitting

We investigate the transport properties of an anisotropic two-dimensional electron gas with a quadratic spin texture, described by a low-energy effective $k\cdot p$ model, in the presence of $S=1\mathrm{/}2$ Kondo impurities. We develop a Green’s function framework that captures the interplay between the spin texture and the Kondo scattering for calculating transport properties in such systems. Using this framework, we evaluate the longitudinal resistivity corrections $\mathrm{\Delta }{\rho }^{xx}\mathrm{/}{\rho }_0^{xx}$ and $\mathrm{\Delta }{\rho }^{yy}\mathrm{/}{\rho }_0^{yy}$ to third order in the $s$-$d$ exchange coupling and analyze their temperature dependence. We further determine the Kondo temperature $T_K$ and show that it is strongly suppressed with increasing quadratic spin-splitting coupling $\alpha$. In particular, we identify a critical coupling ${\alpha }_{cr}$ marking the onset of a Kondo collapse, at which $T_K$ is reduced by approximately 37% relative to that of the conventional two-dimensional electron gas.