Electronic structure and g factors of narrow-gap zinc-blende nanowires and nanorods

The Hamiltonian in the framework of eight-band effective-mass approximation of the zinc-blende nanowires and nanorods in the presence of external homogeneous magnetic field is given in the cylindrical coordinate. The electronic structure, optical properties, magnetic energy levels, and g factors of the nanowires and nanorods are calculated. It is found that the electron states consist of many hole-state components, due to the coupling of the conduction band and valence band. For the normal bands which are monotone functions of |kz|, long nanorods can be modeled by the nanowires, the energy levels of the nanorods approximately equal the values of the energy band E(kz) of the nanowires with the same radius at a special kz, where kz is the wave vector in the wire direction. Due to the coupling of the states, some of the hole energy bands of the nanowires have their highest points at kz≠0. Especially, the highest hole state of the InSb nanowires is not at the kz=0 point. It is an indirect band gap. For these abnormal bands, nanorods can not be modeled by the nanowires. The energy levels of the nanorods show an interesting plait-like pattern. The linear polarization factor is zero, when the aspect ratio L/2R is smaller than 1, and increases as the length increases. The gz and gx factors as functions of the kz, radius R and length L are calculated for the wires and rods, respectively. For the wires, the gz of the electron ground state increases, and the gz of the hole ground state decreases first, then increases with the kz increasing. For the rods, the gz and gx of the electron ground state decrease as the R or the L increases. The gx of the hole ground state decreases, the gz of the hole ground state increases with the L increasing. The variation of the gz of the wires with the kz is in agreement with the variation of the gz of the rods with the L