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

Abstract

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 details such states in the thermodynamic limit. Analitycity considerations then suggest the construction of a family of Riemman surfaces associated to the band structure of the system. In this picture, the corresponding edge states naturally wind around non contractile loops, defining by the way a topological invariant associated to each gap of the system.

Accepted version for publication in New Journal of Physics

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• Fermi arc reconstruction at junctions between Weyl semimetals
• Topological swing in Bloch oscillations
• Non-diffracting states in one-dimensional Floquet photonic topological insulators
• A Unified Perspective of Complex Band Structure: Interpretations, Formulations, and Applications
• On the generalized Langevin equation for a Rouse bead in a nonequilibrium bath
• Strongly Disordered Floquet Topological Systems
• Hybrid scale-free skin effect in non-Hermitian systems: A transfer matrix approach
• Topological chiral modes in random scattering networks
• Effective vacua for Floquet topological phases: A numerical perspective on switch-function formalism
• Topological chiral interface states beyond insulators
• Internal wave crystals
• Exact solutions for topological surface states of three-dimensional lattice models