The 2d Kondo effect in p-type Quantum Wells in GaAs

Two groups [Huang et al. [1] and Hamilton et al. [2]] have observed minima in the resistivity $\rho$(T) at very low T well below $\rho$$_{max}$ at T$_{max}$ in metallic samples (p$>$p$_{c}$). Minima in [1] were found at 32 mK for p$\sim$ 2.1 p$_{c}$, 25 mK for p$\sim$ 1.76 p$_{c}$, while no minimum was observed down to 0.5 mK for p$\sim$ 1.24 p$_{c}$. Both groups have interpreted their results in terms of a crossover to insulating (nonmetallic) behavior for T $<$ T$_{m}$ where d$\rho$/dT $<$ 0. An alternative explanation arises from a 2d Kondo effect. Using the Hamann function [3] for the magnetic scattering contribution from localized magnetic moments and a term $\rho$(0)CT/T$_{F}$ from screening (interactions) one obtains an expression for T$_{m}$(p) which is very close to the Kondo temperature T$_{K}$(p) given by (E$_{F}$/k)x exp(-1/N(E$_{F}$absJ). The very strong p-dependence of T$_{m}$(p) and T$_{K}$(p) is dominated by N(E$_{F}$) which is shown to approach zero as p approaches p$_{c}$ because of the pseudogap in the DOS. Good agreement is obtained T$_{m}$(p) for both [1] and [2]. The data in [1] supports metallic behavior down to 0.5 mK. The implications for a true 2d MIT as a QPT are discussed. 1) J. Huang et al. Phys.Rev.Lett.98, 226801 (2007); 2) A. R. Hamilton et al. Phys.Rev.Lett.82, 1542 (1999); D. R. Hamann, Phys.Rev.158, 570 (1967).