Transverse Magnetosonic Waves and Viscoelastic Resonance in a Two-Dimensional Highly Viscous Electron Fluid

In high-mobility materials, conduction electrons can form a viscous fluid at low temperatures. We demonstrate that in a high-frequency flow of a two-dimensional electron fluid in a magnetic field the two types of excitations can coexist: those of the shear stress (previously unknown transverse magnetosound) and those associated with the charge density (conventional magnetoplasmons). The dispersion law and the damping coefficient of transverse magnetosound originate from the time dispersion of the viscosity of the fluid. Both the viscoelastic and the plasmonic components of the flow exhibit the recently proposed viscoelastic resonance that is related to the own dynamics of shear stress of charged fluids in a magnetic field. We argue that the generation of transverse magnetosound, manifesting itself by the viscoelastic resonance, is apparently responsible for the peak in photoresistance and peculiarities in photovoltage observed in ultrahigh-mobility GaAs quantum wells.

Figure 1

(a) Dispersion laws of magnetoplasmons ${\omega }_p(q)$ and transverse magnetosound ${\omega }_p(q)$. Dashed lines show the dispersion laws in zero magnetic field: ${\omega }_p^0(q)=sq$ and ${\omega }_s^0(q)=v_F^{\eta }q/2$ (here $s\gg v_F^{\eta }$; see Table 1). At $q\to 0$ the frequency ${\omega }_s(0)=2{\omega }_c$ corresponds to the own rotation of the shear stress tensor of the charged fluid in magnetic field. (b) Long sample in the external fields ${\mathbf{E}}_0(t)$ and $\mathbf{B}$ in the regime $\omega >2{\omega }_c\gg 1/{\tau }_{ee}$. In wide samples, $W\gg L_p,L_s$, the three regions are formed: the central region (orange) where the flow is controlled by the bulk momentum relaxation, the near-edge layers (dark-green) with the widths $L_s$ in which the flow is governed by viscosity, and the regions $L_s<|y-W/2|<L_p$ (red) where the magnetoplasmon contribution dominates.

Figure 2

Absorbtion power $\mathcal{W}$ as a function of ${\omega }_c$ at fixed $\omega$ for medium and narrow samples with the widths $W/l_{ee}=5.7$, 3.2, 1.8 (orange, blue, and red curves) at $\omega {\tau }_{ee}=50$ and $s/v_F^{\eta }=300$. Inset presents the imaginary part of the ac current $I_x({\omega }_c)$ for a medium sample ($W/l_{ee}=1.8$). The viscoelastic resonance at ${\omega }_c=\omega /2$ for all curves and the “magnetosonic resonances” at ${\omega }_c={\omega }_c^{s,m}$ for red curves are seen.