Magnetophonon effect in a nonparabolic band:n-type InSb

Abstract

Measurements of the transverse Ohmic magnetophonon effect have been performed at 77 K in a set of samples of $n$-InSb having carrier concentrations in the range from $n=5\mathrm{}\times {10}^{13}$ ${\mathrm{cm}}^{-3\mathrm{}}$ to $n=7\mathrm{}\times {10}^{16}$ ${\mathrm{cm}}^{-3\mathrm{}}$. With increasing doping, the minima in the second derivative of the resistance with respect to the magnetic field are shifted to higher magnetic fields. Even in the purest samples the values of the resonant magnetic fields for harmonic numbers up to $N=12\mathrm{}$ can only be explained if the contributions of spin-conserving transitions involving both $L=0\mathrm{}$ spin levels and spin-split Landau levels with $L>\mathrm{}0\mathrm{}$ are taken into account. These transitions occur at magnetic fields which are higher than the fields for the $L=0\mathrm{}$ lower-spin-level transition because of the nonparabolicity of the InSb conduction band. A superposition of Lorentzian lines with an empiricall determined half-width $\Delta \mathrm{}\left(N\right)\mathrm{}$ proportional to the harmonic number $N$ and weighted with the value of the Fermi distribution function at the energy of the lower level is shown to give a good fit to the data yielding a bard-edge effective mass of ${m^{*}}_0=0.0138\mathrm{} m_0$. In more highly doped samples, the shift of the extrema to higher magnetic fields is partially caused by the larger value of the damping parameter $\gamma$ because of the lower mobility. After applying an appropriate correction to the extremal positions of the high-concentration samples, a shift remains which qualitatively can be explained by the increasing contribution of higher-order transitions because of the higher population of these levels. Finally, the shifts in extremal position as a consequence of an increased electron temperature, e.g., induced by application of electric fields or photoexcitation, are discussed within the framework of this model.