 Hybridization gap

A hybridization gap is a separation in electronic band structure caused by mixing orbital-derived states. For $E_a=A{k}^2$, $E_b=E_0>0$, $A>0$ and constant coupling $\alpha >0$, the lower eigenvalue is everywhere below $E_0$ and tends to it as $k\to \infty$. The upper eigenvalue has minimum $(E_0+\sqrt{E_0^2+4{\alpha }^2})/2$. The unbounded model therefore has an indirect gap of width $(\sqrt{E_0^2+4{\alpha }^2}-E_0)/2$, approximately ${\alpha }^2/E_0$ at weak coupling. This differs from the direct separation $2\alpha$ at the bare crossing. A finite Brillouin zone bounds the lower band farther below $E_0$.