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arXiv · 2210.15108

Confined states in the tight-binding model on the hexagonal golden-mean tiling

Toranosuke Matsubara·Akihisa Koga·Sam Coates
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Abstract

We study the tight-binding model with two distinct hoppings $(t_L, t_S)$ on the two-dimensional hexagonal golden-mean tiling and examine the confined states with $E=0$, where $E$ is the eigenenergy. Some confined states found in the case $t_L=t_S$ are exact eigenstates even for the system with $t_L \neq t_S$, where their amplitudes are smoothly changed. By contrast, the other states are no longer eigenstates of the system with $t_L \neq t_S$. This may imply the existence of macroscopically degenerate states which are characteristic of the system with $t_L=t_S$, and that a discontinuity appears in the number of the confined states in the thermodynamic limit.

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Toranosuke Matsubara, Akihisa Koga, Sam Coates. 2022-10-27. Confined states in the tight-binding model on the hexagonal golden-mean tiling. https://doi.org/10.1088/1742-6596%2F2461%2F1%2F012003

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