The magnetic field Influence on the absorption threshold of VO?

The vanadium dioxide VO? is a material described as being intelligent because it can transit [1,2] from a reversible way of the semiconductor state to the metal state at a temperature θt = 68 °C. When we are at a temperature θt ? 68 °C, this material is in the semiconductor state with a gap [3,4] approximately 0.7 ev. When θt ? 68 °C, the vanadium dioxide becomes metal [14], there is an abrupt change of its structure and its optical properties [14,15] and electronic. We are interested in this study in the VO? semiconductor state [15] and, especially, in widening its gap by the application of a magnetic field Bz. By taking into account the spin of the electron of the band of conduction after having neglected the term of Coulomb interaction, we solved the Schrödinger’s equation in an exact way. Obtaining the levels of Landau [5,6,7] enables us to conclude the variation of the gap of ?Eg = 1/2ħωc, where ωc is the frequency cyclotron ωc =eB/μ, with e: the electron charge; μ: the reduced mass of the quasi particle (electron-hole); ħ: the Planck's constant reduced, and B is the intensity of the applied magnetic field. We will simulate by Maple this variation according to B for fixed μ on the one hand, and ?Eg according to μ for fixed B on the other hand.