Hopping integral
= Hopping integral
{title2=$t_{ij}=\langle i|H|j\rangle$}
A <hopping integral> is an off-diagonal <Hamiltonian> matrix element between localized orbitals on different lattice sites. It has units of energy and controls the dispersion in a <tight-binding model>. Its sign and phase depend on the orbital phase convention; observable band energies do not. The sign of a real nearest-neighbour $t$ in $E(k)=E_0+2t\cos(ka)$ determines the location of the minimum in that convention.