Topological edge states in two-gap unitary systems: a transfer matrix approach

We construct and investigate a family of two-band unitary systems living on a cylinder geometry and presenting localized edge states. Using the transfer matrix formalism, we solve and investigate in detail such states in the thermodynamic limit. Analytic considerations then suggest the construction of a family of Riemann surfaces associated to the band structure of the system. In this picture, the corresponding edge states naturally wind around non-contractile loops, defining a topological invariant associated to each gap of the system.