Edge states in 2D lattices with hopping anisotropy and Chebyshev polynomials
| Autor: | Eliashvili, M., Japaridze, G. I., Tsitsishvili, G., Tukhashvili, G. |
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| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | J. Phys. Soc. Jpn., 83 (2014) 044706 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.7566/JPSJ.83.044706 |
| Popis: | 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. Comment: 10 pages, misprints in formulae (65) corrected |
| Databáze: | arXiv |
| Externí odkaz: |
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