Zero-modes in the random hopping model

Details Zero-modes in the random hopping model Zero-modes in the random hopping model

2002-01-31

arxiv.org/abs/cond-mat/0201580v1

Phys. Rev. B 66, 014204 (2002)

Physics

Condensed Matter

Disordered Systems and Neural Networks

12 pages, 11 figures

Scientific paper

10.1103/PhysRevB.66.014204

If the number of lattice sites is odd, a quantum particle hopping on a bipartite lattice with random hopping between the two sublattices only is guaranteed to have an eigenstate at zero energy. We show that the localization length of this eigenstate depends strongly on the boundaries of the lattice, and can take values anywhere between the mean free path and infinity. The same dependence on boundary conditions is seen in the conductance of such a lattice if it is connected to electron reservoirs via narrow leads. For any nonzero energy, the dependence on boundary conditions is removed for sufficiently large system sizes.

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