A two-dimensional electron–hole system in terms of the Chern–Simons theory: slowly varying field operators

Abstract

In the previous paper [1], the conduction and the valence electrons of the two-dimensional (2D) semiconductor layer subjected to the action of an external perpendicular magnetic field and interacting with 2D quantum point vortices have been described in terms of the Chern–Simons (C–S) theory. The C–S unitary transformation introducing the vector and scalar potentials generated by the quantum point vortices into the Hamiltonian and transforming the conduction and valence electrons into composite particles attaching them equal numbers of 2D quantum point vortices has been used. In the present paper, slowly varying envelope-type field operators are introduced. The initial Hamiltonian containing the periodic lattice potential and bare electron mass 0 m is transformed into the form with effective electron and hole masses, which determine the cyclotron frequencies of the Landau quantization in the presence of a C–S field.