Isolated multi-MeV $\gamma$-rays with attosecond duration, high collimation and beam angular momentum (BAM) may find many interesting applications in nuclear physics, astrophysics, etc. Here, we propose a scheme to generate such $\gamma$-rays via nonlinear Thomson scattering of a rotating relativistic electron sheet driven by a few-cycle twisted laser pulse interacting with a micro-droplet target. Our model clarifies the laser intensity threshold and carrier-envelope phase effect on the generation of the isolated electron sheet. Three-dimensional numerical simulations demonstrate the $\gamma$-ray emission with 320 attoseconds duration and peak brilliance of $9.3\times 10^{24}$ photons s${}^{-1}$ mrad${}^{-2}$ mm${}^{-2}$ per 0.1$\%$ bandwidth at 4.3 MeV. The $\gamma$-ray beam carries a large BAM of $2.8 \times 10^{16}\mathrm{\hslash}$, which arises from the efficient BAM transfer from the rotating electron sheet, subsequently leading to a unique angular distribution. This work should promote the experimental investigation of nonlinear Thomson scattering of rotating electron sheets in large laser facilities.

The Righi–Leduc heat flux generated by the self-generated magnetic field in the ablative Rayleigh–Taylor instability driven by a laser irradiating thin targets is studied through two-dimensional extended-magnetohydrodynamic simulations. The perturbation structure gets into a low magnetization state though the peak strength of the self-generated magnetic field could reach hundreds of teslas. The Righi–Leduc effect plays an essential impact both in the linear and nonlinear stages, and it deflects the total heat flux towards the spike base. Compared to the case without the self-generated magnetic field included, less heat flux is concentrated at the spike tip, finally mitigating the ablative stabilization and leading to an increase in the velocity of the spike tip. It is shown that the linear growth rate is increased by about 10% and the amplitude during the nonlinear stage is increased by even more than 10% due to the feedback of the magnetic field, respectively. Our results reveal the importance of Righi–Leduc heat flux to the growth of the instability and promote deep understanding of the instability evolution together with the self-generated magnetic field, especially during the acceleration stage in inertial confinement fusion.