Gauge theory of topological phases of matter (Vol. 44 No. 3)

Topologically protected states of matter are the focus of recent intensive research efforts. Such states may play an important role in future concrete implementations of devices for topological quantum computing. Prominent examples are incompressible 2D electron gases exhibiting the Quantum Hall effect or the spin Hall effect, 3D topological insulators and superconductors, etc. From a conceptual point of view it is important to note that the low-energy effective theories describing all these states can be derived, using only very general principles, from a unified theoretical framework which we have called “gauge theory of states of matter”.

A key idea underlying our framework is to promote fundamental or emergent global symmetries of idealized systems to local gauge symmetries of realistic systems, and to then study the response of such systems under variations of the corresponding gauge fields. For systems with a bulk energy gap, our theory predicts the general form of the response laws, transport equations, and the structure of gapless surface modes. It also elucidates how the structure of the ionic background, electromagnetic fields, velocity fields and curvature influence the properties of such systems.