= Band curvature
{title2=$\partial^2E/\partial k_i\partial k_j$}
<Band curvature> is the <Hessian matrix> of an <energy band> as a function of <wavevector>. Dividing it by $\hbar^2$ gives the inverse <band effective mass> tensor. At a one-dimensional band minimum the curvature is positive, whereas at a maximum it is negative. Near a weak two-wave <avoided crossing> with reciprocal <wavenumber> $G$ and coupling magnitude $U$, the two edge curvatures are $E_\pm''=\hbar^2/m\pm\hbar^4G^2/(4m^2U)$. This is a crystal response coefficient, not a change in the bare <electron mass>.
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