Energy spectrum of a gapless semiconductor in a longitudinal magnetic field under spatial confinement

Abstract

The exact solution at zero boundary condition of the problem of the carrier in a spatially confined gapless semiconductor in a magnetic field parallel to the surface is presented. It is shown that, because the energy spectrum of a gapless semiconductor is formed by a strong relativistic spin-orbit interaction, the space confinement leads to the effective attraction of the electron to the surface, which is different for different spin states. As a result, the energy of Landau levels in the case of one-side confinement of a semiconductor can even diminish when the oscillator centre is shifted towards the surface. The manifestation of the considered effect in tunnelling experiments is discussed. By solving the same problem in a gapless semiconductor film it is shown that the most striking effect, which has the same origin, is the confluence of the lowest electronic levels a1 and b1 and inversion of the sign of the g-factor for states with n>1 as the ratio of film width to the magnetic length is reduced. The possibility of the experimental testing of this phenomenon is discussed.