Electric-field splitting of a Landau level in a rectangle
= Electric-field splitting of a Landau level in a rectangle
In <Landau gauge> with periodic boundary conditions of length $L_y$, adjacent guiding centres differ by $\Delta k_y=2\pi/L_y$. A perpendicular electric field tilts the energy by $-(E/B)\hbar k_y$, so adjacent states formerly in one degenerate <Landau level> are separated by $2\pi\hbar|E/B|/L_y$.