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We study quantum interference effects on the transition strength for stronglylocalized electrons hopping on 2D square and 3D cubic lattices in the presenceof a magnetic field B. These effects arise from the interference between phasefactors associated with different electron paths connecting two distinct sites.For electrons confined on a square lattice, with and without disorder, weobtain closed-form expressions for the tunneling probability, which determinesthe conductivity, between two arbitrary sites by exactly summing thecorresponding phase factors of all forward-scattering paths connecting them. Ananalytic field-dependent expression, valid in any dimension, for themagnetoconductance (MC) is derived. A positive MC is clearly observed whenturning on the magnetic field. In 2D, when the strength of B reaches a certainvalue, which is inversely proportional to twice the hopping length, the MC isincreased by a factor of two compared to that at zero field. We alsoinvestigate transport on the much less-studied and experimentally important 3Dcubic lattice case, where it is shown how the interference patterns and thesmall-field behavior of the MC vary according to the orientation of B. Theeffect on the low-flux MC due to the randomness of the angles between thehopping direction and the orientation of B is also examined analytically.Comment: 24 pages, RevTeX, 8 figures include

physical review. b, condensed matter

Analytical results on quantum interference and magnetoconductance for strongly localized electrons in a magnetic field: Exact summation of forward-scattering paths