Snakelike trajectories of electrons released from quantum dots driven by the spin Hall effect

Using time dependent simulations, we analyze the trajectories of electrons released from a quantum dot in a waveguide made of a spin-orbit-coupled material (InSb). An electron released from the quantum dot, when driven by an electric field follows a trajectory that is deflected by spin-orbit interaction and undergoes spin precession that results in a spin-dependent, snake-like trajectory. The trajectory strongly depends on the initial state of the electron, enabling detection of the electron quantum state in the dot when connected to the T-junction. Notably, we show that the snake-like trajectory persists even under a small external magnetic field with low, incomplete initial electron spin polarization. Our findings are supported by semiclassical calculations of the electron trajectory, which show good agreement with full quantum mechanical simulations