Blocking particle dynamics in diamond chain with spatially increasing flux

Spatial non-uniformity in tight-binding models serves as a source of rich phenomena. In this paper, we study a diamond-chain tight-binding model with a spatially-modulated magnetic flux at each plaquette. In the numerical studies with various combinations of the minimum and maximum flux values, we find the characteristic dynamics of a particle, namely, a particle slows down when approaching the plaquette with $\pi$-flux. This originates from the fact that the sharply localized eigenstates exist around the $\pi$-flux plaquette. These localized modes can be understood from a squared model of the original one. This characteristic blocked dynamics will be observed in photonic waveguides or cold atoms.