chiral magnon edge mode in a magnonic crystal

A bosonic system with a periodically crystalline potential has a Chern integer associated with its magnetic Bloch wavefunction. As in its fermionic counterpart like integer quantum Hall states, the Chern number thus introduced is defined for each bosonic energy band which is energetically separated from the others. When two bosonic systems having different Chern integers are connected, or when a bosonic system with non-zero Chern integer is terminated with the vaccum, chiral bosonic edge modes appear in their boundaries. We argue that a simple magnonic crystal can realize such magnonic chiral edge modes. Based on this example, we show how to design spin-wave guides in a magnonic crystal and how to channelize, spit and manipulate them.