Quantum electronic transport through three-dimensional microconstrictions with variable shapes

Abstract

The transport properties of three-dimensional quantum microconstrictions in field-free conditions and under the influence of magnetic fields of arbitrary strengths and directions are studied via a generalized B\"uttiker model [Phys. Rev. B 41, 7906 (1990)]. It is shown that conductance quantization is influenced by the geometry of the microconstriction (that is, its length and the shape of its transverse cross section). In a weak longitudinal magnetic field, when ${r}_{c}\ensuremath{\gg}d$, where ${r}_{c}$ is the cyclotron radius and $d$ the effective transverse size of the narrowing of the microconstriction, the conductance exhibits Aharonov-Bohm---type behavior. This behavior transforms in the strong-field limit, ${r}_{c}\ensuremath{\ll}d$, into Shubnikov-de Haas oscillations with a superimposed Aharonov-Bohm fine structure. The dependence of the Aharonov-Bohm---type features on the length of the microconstriction and on temperature are demonstrated. Transverse magnetic fields lead to depopulation of the magnetoelectric subbands, resulting in a steplike decrease of the conductance upon increasing the strength of the applied magnetic field.