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Effective Mass

A parameter that describes how an electron responds to an external force within a band, accounting for interactions with the crystal lattice.

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The statement of the theorem

The effective mass tensor

m^*_{ij}

for an electron band

E(\mathbf{k})

is defined by the inverse of the curvature of the dispersion relation with respect to the wave vector

\mathbf{k}

:\n

\left( \frac{1}{m^*} \right)_{ij} = \frac{1}{\hbar^2} \frac{\partial^2 E(\mathbf{k})}{\partial k_i \partial k_j} \bigg|_{\mathbf{k}=\mathbf{k}_0}

Source: Wikipedia