Past exam of the condensed matter physics major option course of the University of Oxford / 2015 / 5 / d / Solution

In a low-carrier-density semiconductor use a thin, cold sample in a transmission spectrometer. Direct microwave or far-infrared radiation through it, commonly with propagation parallel to $\mathbf{B}$ and electric field transverse to it. Sweep $B$ at fixed frequency and detect transmitted power. The active circular polarization shows an absorption peak, or transmission dip, near $B_{\mathrm{res}}=m^{\ast }\omega /e$. Resolving it requires a long enough scattering time, ${\omega }_c\tau \gtrsim 1$.

A metal's large plasma frequency usually prevents that radiation from sampling its bulk directly. In surface cyclotron resonance in a metal, put $\mathbf{B}$ approximately parallel to a clean metal surface and excite an rf electric field in the skin depth, transverse to $\mathbf{B}$. Electron orbits extend into the bulk and repeatedly return to that layer. Coherent energy absorption occurs when the rf phase repeats on a return, including harmonics $\omega =n{\omega }_c$. Measure cavity loss, reflected power, or surface impedance rather than attempting ordinary bulk transmission. The characteristic regime has cyclotron radius larger than the skin depth and sufficiently specular, long-lived orbits.

For the spherical parabolic band the metal harmonic fields areThey are evenly spaced in $1/B$, with amplitudes and widths determined by surface geometry and scattering. A semiconductor generally gives the simple bulk fundamental, whereas the metal can show this harmonic series in a surface-loss signal. For an anisotropic real Fermi surface the measured mass is the appropriate cyclotron effective mass rather than necessarily every component of a transport effective-mass tensor. These classical resonance harmonics are distinct from the Landau-level quantum oscillations in c.