Theory of cyclotron resonance at a model interface in a transverse magnetic field

The case of a magnetic field parallel to a step junction characterizing an interface is analyzed theoretically. Comparison is made between this "transverse-field" geometry and the usual "longitudinal-field" geometry for which the applied magnetic field is perpendicular to the interface. For the transverse-field configuration, the energy eigenstates and eigenfunctions are obtained exactly. They depend on three quantum numbers: (i) $p_z$ the particle momentum parallel to the field, (ii) $p_y$ measuring the distance between the center of the charge-carrier oscillation and the interface, and (iii) $n$ the Landau-level label. Different regimes are examined as a function of the step potential height with special emphasis on the case where the center of oscillation is on the interface ($p_y=0\mathrm{}$). For this case, selection rules for magneto-optical absorption predict strong harmonics especially for high potential steps. Reference is made to rare experimental data. The energy levels and wave functions of an electron in a uniform magnetic field can also be obtained by means of a transfer-matrix technique for an arbitrary set of step potentials.