Multisublevel magnetoquantum conductance in single and coupled double quantum wires

We study the ballistic and diffusive magnetoquantum transport using a typical quantum point contact geometry for single and tunnel-coupled double wires that are wide (≲1 μm) in one perpendicular direction with densely populated sublevels and extremely confined in the other perpendicular (i.e., growth) direction. A general analytic solution to the Boltzmann equation is presented for multisublevel elastic scattering at low temperatures. The solution is employed to study interesting magnetic-field dependent behavior of the conductance such as a large enhancement and quantum oscillations of the conductance for various structures and field orientations. These phenomena originate from the following field-induced properties: magnetic confinement, displacement of the initial- and final-state wave functions for scattering, variation of the Fermi velocities, mass enhancement, depopulation of the sublevels and anticrossing (in double quantum wires). The magnetoconductance is strikingly different in long diffusive (or rough, dirty) wires from the quantized conductance in short ballistic (or clean) wires. Numerical results obtained for the rectangular confinement potentials in the growth direction are satisfactorily interpreted in terms of the analytic solutions based on harmonic confinement potentials. Some of the predicted features of the field-dependent diffusive and quantized conductances are consistent with recent data from ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ double quantum wires.