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

Abstract

Abstract We study the tight-binding model with two distinct hoppings (tL, tS ) 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 tL = tS are exact eigenstates even for the system with tL ≠ t S, where their amplitudes are smoothly changed. By contrast, the other states are no longer eigenstates of the system with tL ≠ t S. This may imply the existence of macroscopically degenerate states which are characteristic of the system with tL = t S, and that a discontinuity appears in the number of the confined states in the thermodynamic limit.