Topological Modes in One Dimensional Solids and Photonic Crystals
  It is shown theoretically that a one-dimensional crystal with time reversal symmetry is characterized by a Z_{2} topological invariant that predicts the existence or otherwise of edge states. This is confirmed experimentally through the construction and simulation of a photonic crystal analogue in the microwave regime. 
Timothy J. Atherton, Celia A. M. Butler, Melita C. Taylor, Ian R.   Hooper, Alastair P. Hibbins, and J. Roy Sambles, Harsh M...
cond-mat.mes-hall