Quantum Waveguide Properties of Bethe Lattices with a Ring

Based on waveguide theory we investigate electronic transport properties of Bethe lattices with a mesoscopic ring threaded by a magnetic flux. The generalized eigen-function method (GEM) is used to calculate the transmission and reflection coefficients up to the fifth generation of Bethe lattices. The relationships among the transmission coefficient T, magnetic flux Φ and wave vector kl are investigated in detail. The numerical results are shown by the three-dimensional plots and contour maps. Some resonant-transmission features and the symmetry of the transmission coefficient T to flux Φ are observed and discussed.