The suppression of finite size effect within a few lattice sites

Boundary modes localized on the boundaries of a finite-size lattice experience a finite size effect (FSE) that could result in unwanted couplings, crosstalks and formation of gaps even in topological boundary modes. It is commonly believed that the FSE decays exponentially with the size of the system and thus requires many lattice sites before eventually becoming negligibly small. Here we consider a two-dimensional strip geometry that is periodic along one direction and truncated along the other direction, in which we identify a special type of FSE of some boundary modes that apparently vanishes at some particular wave vectors along the periodic direction. Meanwhile, the number of wave vectors where the FSE vanishes equals the number of lattice sites across the strip. We analytically prove this type of FSE in a simple model and prove this peculiar feature. We also provide a physical system consisting of a plasmonic sphere array where this FSE is present. Our work points to the possibility of almost arbitrarily tunning of the FSE, which facilitates unprecedented manipulation of the coupling strength between modes or channels such as the integration of multiple waveguides and photonic non-abelian braiding.