Past exam of the quantum condensed matter course of the University of Cambridge / 2015 / Paper 1 / 1 / a

In the isotropic parabolic-band approximation implied by the single supplied curvature, the hole mass from a valence-band maximum isThe hole has charge $+e$, so its cyclotron angular frequency isIf “frequency” means cycles per second, $f_c={\omega }_c/(2\pi )=5.59\times 10^{10}\mathrm{Hz}$. The curvature unit is $\mathrm{J}{\mathrm{m}}^2$, so ${\hslash }^2/E^{\prime \prime }$ has mass units. The external constants used are $\hslash =1.054571800\times 10^{-34}\mathrm{J}\mathrm{s}$, $e=1.6021766208\times 10^{-19}\mathrm{C}$ and $m_e=9.10938356\times 10^{-31}\mathrm{kg}$.^[ref] A genuinely anisotropic band would require the cyclotron mass for the orbit plane, not a single arbitrary directional curvature.