We study quantum interference effects on the transition strength for strongly localized electrons hopping on 2D square and 3D cubic lattices in the presence of a magnetic field B. These effects arise from the interference between phase factors associated with different electron paths connecting two distinct sites. For electrons confined on a square lattice, with and without disorder, we obtain closed-form expressions for the tunneling probability, which determines the conductivity, between two arbitrary sites by exactly summing the corresponding phase factors of all forward-scattering paths connecting them. An analytic field-dependent expression, valid in any dimension, for the magnetoconductance (MC) is derived. A positive MC is clearly observed when turning on the magnetic field. In 2D, when the strength of B reaches a certain value, which is inversely proportional to twice the hopping length, the MC is increased by a factor of two compared to that at zero field. We also investigate transport on the much less-studied and experimentally important 3D cubic lattice case, where it is shown how the interference patterns and the small-field behavior of the MC vary according to the orientation of B. The effect on the low-flux MC due to the randomness of the angles between the hopping direction and the orientation of B is also examined analytically. Comment: 24 pages, RevTeX, 8 figures included
Digital Commons Citation
Lin, Yeong-Lieh and Nori, Franco, "Analytical results on quantum interference and magnetoconductance for strongly localized electrons in a magnetic field: Exact summation of forward-scattering paths" (1996). Faculty & Staff Scholarship. 52.
Lin, Yeong-Lieh., &Nori, Franco. (1996). Analytical Results On Quantum Interference And Magnetoconductance For Strongly Localized Electrons In A Magnetic Field: Exact Summation Of Forward-Scattering Paths. Physical Review B - Condensed Matter and Materials Physics, 53(23), 15543-15562. http://doi.org/10.1103/PhysRevB.53.15543