Reciprocal effective mass tensor ($(M^{-1}{)}_{ij}={\hslash }^{-2}{\partial }_{k_i}{\partial }_{k_j}E$)

The curvature tensor of a nondegenerate energy band, determining the linear relation between force and acceleration in semiclassical band dynamics. From group velocity $v_i={\hslash }^{-1}{\partial }_{k_i}E$ and $\hslash {\dot{k}}_j=F_j$, one obtains ${\dot{v}}_i=(M^{-1}{)}_{ij}{F}_j$. Near a parabolic minimum, $E-E_0={\hslash }^2\delta {\mathbf{k}}^T{M}^{-1}\delta \mathbf{k}/2$. The principal values are reciprocal curvature effective masses; a cyclotron experiment measures a direction-dependent combination rather than every tensor entry separately.