Band Connectivity for Topological Quantum Chemistry: Band Structures As A Graph Theory Problem

Understand

The conventional theory of solids is well suited to describing band structures locally near isolated points in momentum space, but struggles to capture the full, global picture necessary for understanding topological phenomena.

• In part of a recent paper [B.
• Bradlyn et al., Nature 547, 298 (2017)], we have introduced the way to overcome this difficulty by formulating the problem of sewing together many disconnected local "k-dot-p" band structures across the Brillouin zone in terms of graph theory.
• In the current manuscript we give the details of our full theoretical construction.