Two-direction nearest-neighbour tight-binding dispersion
= Two-direction nearest-neighbour tight-binding dispersion
For hopping amplitude $-\lambda$ from each lattice site to its neighbours at $\pm a_1$ and $\pm a_2$, a Bloch state has energy
$$
E(k)=E_0-2\lambda\bigl(\cos(k\cdot a_1)+\cos(k\cdot a_2)\bigr).
$$
The band ranges from $E_0-4|\lambda|$ to $E_0+4|\lambda|$ and therefore has width $8|\lambda|$.