Strongly Localized Electrons in a Magnetic Field: Exact Results on Quantum Interference and Magnetoconductance

Details Strongly Localized Electrons in a Magnetic Field: Exact Results on Quantum Interference and Magnetoconductance Strongly Localized Electrons in a Magnetic Field: Exact Results on Quantum Interference and Magnetoconductance

1996-11-25

arxiv.org/abs/cond-mat/9611198v1

Phys. Rev. Lett. 76 (1996) 4580-4583

Physics

Condensed Matter

Strongly Correlated Electrons

4 pages, RevTeX

Scientific paper

10.1103/PhysRevLett.76.4580

We study quantum interference effects on the transition strength for strongly localized electrons hopping on 2D square and 3D cubic lattices in a magnetic field B. In 2D, we obtain closed-form expressions for the tunneling probability between two arbitrary sites by exactly summing the corresponding phase factors of all directed paths connecting them. An analytic expression for the magnetoconductance, as an explicit function of the magnetic flux, is derived. In the experimentally important 3D case, we show how the interference patterns and the small-B behavior of the magnetoconductance vary according to the orientation of B.

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