Electrically modulated Josephson junction of light-dressed topological insulators

In a Josephson junction mediated by a two-dimensional irradiated topological insulator, the current-phase relation can be electrically modulated, including the 0-$\ensuremath{\pi}$ phase transition and the anomalous phase shift of the current. Qualitatively combining analyses and numerical simulations, we find that the $0\text{\ensuremath{-}}\ensuremath{\pi}$ phase transition and anomalous phase shift can be controlled by a gate voltage and a transverse electric field, respectively. These possible electrical modulations result from the photoinduced anisotropic helical edge states. Due to the anisotropy and spin-momentum locking nature in the edge channels, an effective Zeeman field is caused by an electrical potential whose orientation automatically matches the spin alignment of the edge modes. The photoinduced anisotropy provides potential applications in Flouqet engineering helical supercurrent and electrically modulated topological superconducting devices.