On the Green's Function of the almost-Mathieu Operator

Details On the Green's Function of the almost-Mathieu Operator On the Green's Function of the almost-Mathieu Operator

2001-06-26

arxiv.org/abs/cond-mat/0106529v2

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

9 pages, 3 figures corrected some minor errors and typos

Scientific paper

10.1088/0305-4470/35/10/309

The square tight-binding model in a magnetic field leads to the almost-Mathieu operator which, for rational fields, reduces to a $q\times q$ matrix depending on the components $\mu$, $\nu$ of the wave vector in the magnetic Brillouinzone. We calculate the corresponding Green's function without explicit knowledge of eigenvalues and eigenfunctions and obtain analytical expressions for the diagonal and the first off-diagonal elements; the results which are consistent with the zero magnetic field case can be used to calculate several quantities of physical interest (e. g. the density of states over the entire spectrum, impurity levels in a magnetic field).

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