Negative Magnetoresistance in Viscous Flow of Two-Dimensional Electrons

At low temperatures, in very clean two-dimensional (2D) samples, the electron mean free path for collisions with static defects and phonons becomes greater than the sample width. Under this condition, the electron transport occurs by formation of a viscous flow of an electron fluid. We study the viscous flow of 2D electrons in a magnetic field perpendicular to the 2D layer. We calculate the viscosity coefficients as the functions of magnetic field and temperature. The off-diagonal viscosity coefficient determines the dispersion of the 2D hydrodynamic waves. The decrease of the diagonal viscosity in magnetic field leads to negative magnetoresistance which is temperature and size dependent. Our analysis demonstrates that this viscous mechanism is responsible for the giant negative magnetoresistance recently observed in the ultrahigh-mobility GaAs quantum wells. We conclude that 2D electrons in those structures in moderate magnetic fields should be treated as a viscous fluid.

Figure 1

The mean free paths $l(T)$ and $l_2(T)$ for relaxation of the electron momentum and the second moment of the electron distribution function. Calculations are performed for the sample studied in Ref. [21].

Figure 2

The physical origin of the decrease of electron viscosity in the magnetic field (schematics). Two adjacent layers of the electron fluid move with different velocities $V_x(y_1)$ and $V_x(y_2)$. The viscous friction is due to the interlayer penetration of electrons. Without magnetic field (a) the penetration length (defining the viscosity) is of the order of $l_2$. In the strong magnetic field $\mathbf{B}=B{\mathbf{e}}_z$ (b) this length is limited by the cyclotron radius $R_c\ll l_2$.

Figure 3

Temperature-dependent magnetoresistance of high-mobility 2D electrons in the GaAs quantum well experimentally studied in Ref. [21]. Panel (a) is taken from Ref. [21]. The curves in panel (b) are drawn according to Eqs. (5) and (12) with the numerical parameters presented in the main text.