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arXiv · 1401.6770

Edge states in 2D lattices with hopping anisotropy and Chebyshev polynomials

M. Eliashvili·G. I. Japaridze·G. Tsitsishvili·G. Tukhashvili
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Abstract

Analytic technique based on Chebyshev polynomials is developed for studying two-dimensional lattice ribbons with hopping anisotropy. In particular, the tight-binding models on square and triangle lattice ribbons are investigated with anisotropic nearest neighbouring hoppings. For special values of hopping parameters the square lattice becomes topologically equivalent to a honeycomb one either with zigzag or armchair edges. In those cases as well as for triangle lattices we perform the exact analytic diagonalization of tight-binding Hamiltonians in terms of Chebyshev polynomials. Deep inside the edge state subband the wave functions exhibit exponential spatial damping which turns into power-law damping at edge-bulk transition point. It is shown that strong hopping anisotropy crashes down edge states, and the corresponding critical conditions are found.

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M. Eliashvili, G. I. Japaridze, G. Tsitsishvili, G. Tukhashvili. 2014-01-27. Edge states in 2D lattices with hopping anisotropy and Chebyshev polynomials. https://doi.org/10.7566/jpsj.83.044706

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