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

We study the properties of two electrons with Coulomb interactions in a tight-binding model La-based cuprate superconductors. This is characterized by long-ranged hopping obtained previously advanced quantum chemistry computations. show analytically and numerically that repulsion leads to formation compact pairs propagating through whole system. The mechanism pair related emergence an effective...