Influence of quantum Hall effect on wave refraction in ferrite-semiconductor superlattices

Peculiarities of wave refraction are investigated in periodic structures consisting of alternating layers of ferromagnetic insulator and GaAs–AlGaAs-type semiconductor bilayers. It is shown that in quantum Hall effect conditions, the refractive indices and consequently the refraction angles of the propagating waves are quantized.Two different geometries of the refracting plane are considered: (I) parallel and (II) perpendicular to the quantizing magnetic field. It is shown that in the first case, negative refraction through the lateral surface of the structure is possible. A frequency region is found where the refraction is negative for all angles of incidence and regardless of the sign of permittivity tensor components. Analytical expressions for both phase and group refractive indices are obtained.In the second case, one of the propagating waves (in the birefringent regime) is backward. Despite this, and unlike in the case of non-quantizing magnetic fields, negative refraction is impossible.