Band hybridization
= Band hybridization
= Band hybridisation
{synonym}
<Band hybridization> mixes two orbital-derived bands through an off-diagonal <Hamiltonian> matrix element. For a real coupling $\alpha$,
$$
H(k)=\begin{pmatrix}E_a(k)&\alpha\\\alpha&E_b(k)\end{pmatrix},\qquad
E_\pm(k)=\frac{E_a+E_b\pm\sqrt{(E_a-E_b)^2+4\alpha^2}}2.
$$
An allowed bare crossing becomes an <avoided crossing> with direct separation $2|\alpha|$. Orbital character transfers continuously between branches through the crossing. A direct separation alone does not guarantee a global <band gap>; the extrema at different wavevectors must also be compared.