There are many free fermion systems that possess topological edge/boundary states. Examples include quantum Hall insulators and topological insulators. No matter chiral or non-chiral, 2D or 3D, ...
As students on solid state physics, we are all taught to use the periodic boundary condition, taking 1D as an example: $\psi(x)=\psi(x+L)$ where $L$ is the length of the 1D crystal. My question is: ...