Magnetoresistance of a 2D Electron Gas Caused by Electron Interactions in the Transition from the Diffusive to the Ballistic Regime

On a high-mobility 2D electron gas we have observed, in strong magnetic fields $({\omega }_c\tau >1)$, a parabolic negative magnetoresistance caused by electron-electron interactions in the regime of $k_{B}T\tau /\hslash \sim 1$, which is the transition from the diffusive to the ballistic regime. From the temperature dependence of this magnetoresistance the interaction correction to the conductivity $\delta {\sigma }_{xx}^{ee}(T)$ is obtained in the situation of a long-range fluctuation potential and strong magnetic field. The results are compared with predictions of the new theory of interaction-induced magnetoresistance.

Figure 1

(a) Longitudinal resistivity versus magnetic field for electron density $n=6.8\times {10}^{10}{\mathrm{c}\mathrm{m}}^{-2}$ at different temperatures: $T=0.2$, 0.8, 1.2 K. (b) The same data presented as a function of $B^2$. (c) Zoomed-in region of ${\rho }_{xx}(B)$ from (a) at $T=1.2$ K, showing a flat region at small fields. (d) ${\rho }_{xx}$ versus $B^2$ for another density, $n=9\times {10}^{10}{\mathrm{c}\mathrm{m}}^{-2}$, at $T=0.4$ and 1.2 K.

Figure 2

Solid lines: Negative magnetoresistance for two electron densities. Dashed lines: NMR expected from the classical effect [16].

Figure 3

Conductivity correction due to interactions, obtained experimentally at different electron densities $n=0.46,0.57,0.68,0.90,1.2,1.4,2.0\times {10}^{11}{\mathrm{c}\mathrm{m}}^{-2}$ (different symbols for different densities, circles correspond to the lowest density). Solid line: theoretical prediction for the correction due to exchange interaction, shifted by $-0.07e^2/h$. Dashed line: theory for the total correction which includes Hartree interactions with $F_0^{\sigma }=-0.15$. Dotted line: the result of the interaction theory for point-like scatterers (exchange term at zero magnetic field), Ref.2. Inset: the same results presented in the logarithmic scales, with an extra curve for $F_0^{\sigma }=-0.3$.

Figure 4

The dependence of the Fermi liquid parameter on $r_s$. Dashed box indicates an approximate range of $r_s$ and $F_0^{\sigma }$ for the structure in this work. Open squares: results from Ref. 3 for hole gas in $p$-GaAs heterostructures. Solid squares: results from Ref. 4 for electron gas in Si MOSFETs. Solid line: the theoretical curve for small $r_s$, Ref. 2.