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IC PROPERTIES OF SOLID

Electrodynamic Response of Charge Carriers in Doubly Periodic Semiconductor n-Type Superlattices in a Permanent Homogeneous Magnetic Field A. A. Perov*, A. S. Rul’kov, E. A. Morozova, and E. S. Zolina Lobachevsky Nizhny Novgorod State University, Nizhny Novgorod, 603950 Russia * e-mail: [email protected] Received October 17, 2016

Abstract—The electromagnetic response of the two-dimensional electron gas of a surface superlattice placed in a perpendicular permanent homogeneous magnetic field is studied. The magneto–optic Kerr and Faraday effects are calculated. The conditions of transparency of model semiconductor structures in the terahertz frequency region are found and the field-induced spin density of the electronic states is calculated. The features of the frequency dependences of complex Kerr and Faraday angles are connected with the symmetry of the spinor states of the charge carriers in a superlattice. DOI: 10.1134/S1063776117040070

INTRODUCTION The quantum-mechanical motion of charge carriers in semiconductors placed in an external magnetic field has been studied for more than half a century [1– 7]. This problem attracted fundamental interest as soon as it became clear that the periodic electrostatic field of a crystal and the magnetic field act on an electron or a hole in a semiconductor in cardinally different ways. Thus, a crystal lattice field leads to the formation of energy bands [1], while a magnetic field quantizes the transverse motion of a charged particle. As a result, in the conduction and valence bands of a semiconductor in a magnetic field, mini bands with exponentially small widths are formed rather than Landau level ladders. The reason is the lift of the degeneracy of the states in a magnetic field over the orbit center due to the interaction of a charged particle with the electrostatic periodic field of a crystal. The lift of the degeneracy of the states of carriers in the magnetic field over the orbit center can be explained as follows (even for a one-dimensional potential model). As the position of the point of support of an oscillator changes within the period of the electrostatic potential, each of the Landau levels in the parabola shifts in energy, thereby forming mini bands in which the charge energy becomes dependent on the charge quasi-momentum. The experimental observation of the band structure of real crystals split in a magnetic field is complicated by the necessity of generating megagauss pulsed magnetic fields. At the same time, artificial low-dimensional semiconductor crystals, the so-called superlat-

tices, are promising objects for theoretical and experimental studies of the magnetic Bloch states of carriers [6–8]. Modern doubly periodic semiconductor superlattices are produced by the methods of high-resolution electron-beam lithography [7] and epitaxial growth [8]. The mean free path of charge carriers in such structures considerably exceeds their period of a few tens of nanometers. The electron Bloch states (Bloch–Peierls states) in an external ma