Reflection of electromagnetic waves from two-dimensional magnetoelectric conductors

It is established now that mirror symmetry of some two-dimensional conductors (semiconductor heterostructures, conducting surface state, and interfaces) is broken. The intrinsic spin-orbit coupling, which is inherent to such electron structures, provides the structures with magnetoelectric properties. Namely, it gives rise to a modification of the constitutive relations by adding to them cross-terms which relate the spin magnetization of the current carriers to the applied electric field and the electric current to the applied magnetic field. The effect of the cross-terms on the reflection of electromagnetic waves is studied. The standard method - by means of the reduction to boundary conditions - is inapplicable here because both the jumps of electric and magnetic field on the conducting layer are essential. Another method is pointed out and the Fresnel's formulae are obtained. It is found that the effect of the cross-terms is opposite in sign for two possible orientations of the conductor with respect to incident wave. The results obtained may be used to determine the value of the cross-terms by measuring the angle dependence of the reflection and transmission amplitudes.