Past exam of the condensed matter physics major option course of the University of Oxford / 2019 / 2 / d

The photon energy fixes the resonant cyclotron frequency by $\hslash \omega =575\mu \mathrm{eV}$. ConsequentlyRead the two absorption maxima as approximately $B_L=0.95$--$0.97\mathrm{T}$ and $B_H=2.10\mathrm{T}$. For $\mathbf{B}\parallel [001]$, the two valleys whose long axis is along $z$ have $m_{\mathrm{cr}}=m_1$, whereas the other four have $m_{\mathrm{cr}}=\sqrt{m_1{m}_2}$. HenceFor the representative reading $B_L=0.96\mathrm{T}$, the values are $m_1=0.193m_e$ and $m_2=0.925m_e$. The graph does not warrant additional precision. The larger longitudinal effective mass means flatter dispersion and a longer constant-energy ellipsoid along the valley axis.

For $\mathbf{B}\parallel [111]$, its squared projection onto the long axis of every valley is $1/3$. All six valleys therefore have the same cyclotron effective mass:At the fixed photon energy,Thus the two-peak spectrum is replaced by one peak near $1.4\mathrm{T}$. The source does not determine the linewidth or absolute oscillator strength for the new direction; the sketch below shows only a normalized illustrative line at the computed position.