Bloch classification surface for three-band systems

Abstract

Topologically protected states can be found in physical systems, that show singularities in some energy contour diagram. These singularities can be characterized by winding numbers, defined on a classification surface, which maps physical state parameters. We have found a classification surface, which applies for three-band hamiltonian systems in the same way than standard Bloch surface does for two-band ones. This generalized Bloch surface is universal in the sense that it classifies a very large class of three-band systems, which we have exhaustively studied, finding specific classification surfaces, applying for each one.

20 pages, 19 figures

References in corpus (6)

• Non-Abelian Anyons and Topological Quantum Computation
• Direct observation of anyonic braiding statistics at the $\nu$=1/3 fractional quantum Hall state
• Fractional statistics in anyon collisions
• Topological Phases for Fermionic Cold Atoms on the Lieb Lattice
• Fractionalisation and dynamics of anyons at $\nu =n+1/3$ in fractional quantum Hall effect and their experimental signatures
• Topology of contact points in Lieb-kagomé model