The Wigner-function approach is used to describe the Zener transition between the conduction and the valence band in a semiconductor. In the Weyl quantization framework a diagonalization procedure is applied to the multiband $k\cdot p$ Hamiltonian and a new set of Wigner multiband functions is defined. An approximate closed-form solution is obtained by an iterative procedure which exploits the different time scales on which the intraband and interband dynamical variables evolve. The single-band limit has been discussed and some quantum corrections to the single-band trajectory have been obtained.

• Received 21 February 2009

DOI:https://doi.org/10.1103/PhysRevB.80.024301