Interacting Electrons in a Two-Dimensional Disordered Environment: Effect of a Zeeman Magnetic Field

The effect of a Zeeman magnetic field coupled to the spin of the electrons on the conducting properties of the disordered Hubbard model is studied. Using the determinant quantum Monte Carlo method, the temperature- and magnetic-field-dependent conductivity is calculated, as well as the degree of spin polarization. We find that the Zeeman magnetic field suppresses the metallic behavior present for certain values of interaction and disorder strength and is able to induce a metal-insulator transition at a critical field strength. It is argued that the qualitative features of magnetoconductance in this microscopic model containing both repulsive interactions and disorder are in agreement with experimental findings in two-dimensional electron and hole gases in semiconductor structures.

Figure 1

Conductivity ${\sigma }_{\mathrm{d}\mathrm{c}}$ (in units of $e^2/\hslash$) as a function of temperature $T$ for various strengths of Zeeman magnetic field $B_{\parallel }$. As $B_{\parallel }$ increases, a transition from metallic to insulating behavior is seen in ${\sigma }_{\mathrm{d}\mathrm{c}}$. Calculations are performed on $8\times 8$ lattices for $U/t=4$ at density $⟨n⟩=0.5$ with disorder strength ${\Delta }_t=2.0$ (see text); error bars result from averaging over typically 16 quenched disorder realizations. $B_{\parallel }$ and ${\Delta }_t$ are given in units of $t$.

Figure 2

Conductivity with value at very high $B$ field subtracted, $\delta {\sigma }_{\mathrm{d}\mathrm{c}}\equiv {\sigma }_{\mathrm{d}\mathrm{c}}(B_{\parallel },T)-{\sigma }_{\mathrm{d}\mathrm{c}}(B_{\parallel }=4,T)$, as a function of $B_{\parallel }$ for low temperature $T$. A sharp onset of conductivity is seen at a Zeeman field at which the slope of ${\sigma }_{\mathrm{d}\mathrm{c}}(T)$ changes sign in Fig. 1. Computational details and units are as in Fig. 1; for clarity, only error bars on $T=t/6$ data are shown; those on $T=t/8$ data are typically slightly larger (cf. Fig. 1).

Figure 3

Resistivity $\rho$ as a function of $B_{\parallel }$ for various low $T$. The crossing point provides another estimate for the critical field strength. Computational details and units are as in Figs. 1, 2; for clarity the error bars have been omitted, but can be estimated from Figs. 1, 2.

Figure 4

Degree of spin polarization $P=(n_{\downarrow }-n_{\uparrow })/(n_{\downarrow }+n_{\uparrow })$ (see text) as a function of $B_{\parallel }$ for fixed low $T=t/8$. The polarization shows little change through the metal-insulator transition and is only 0.31 at the estimated critical field strength.