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 $2\pi\hbar|E/B|/L_y$.