Electronic structure and g factors of narrow-gap zinc-blendenanowires 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 |k_z|, long nanorods can be modeled by the nanowires, the energy levels of the nanorods approximately equal the values of the energy band E(k_z) of the nanowires with the same radius at a special k_z, where k_z 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 k_z≠0. Especially, the highest hole state of the InSb nanowires is not at the k_z=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 g_z and g_x factors as functions of the k_z, radius R and length L are calculated for the wires and rods, respectively. For the wires, the g_z of the electron ground state increases, and the g_z of the hole ground state decreases first, then increases with the k_z increasing. For the rods, the g_z and g_x of the electron ground state decrease as the R or the L increases. The g_x of the hole ground state decreases, the g_z of the hole ground state increases with the L increasing. The variation of the g_z of the wires with the k_z is in agreement with the variation of the g_z of the rods with the L.