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A Symmetry- and Geometry-Based Framework for Nodal Fermions and Topological Phases in Condensed Matter Physics
(University of Pennsylvania)
112:028 (Nordita South) ()
112:028 (Nordita South)
From graphene to Weyl semimetals to exotic topological insulators, we are every day being told of new and wondrous condensed matter systems with unique dispersion and degeneracy features. Adjectives like topological, Dirac, hourglass, and Type-II (and now III and IV) increasingly appear with each new set of arXiv postings, frequently used interchangeably and inconsistently. Here, we develop definitions grounded in geometry, fermion doubling theorems, and quantum criticality to construct a consistent framework for classifying this growing zoo of crystalline band features, and for predicting new examples. We introduce topics in electronic crystalline group theory such as “space groups” and symmetry algebra and show how a combination of these concepts can be used to exhaustively characterize all bulk and surface topological features in crystals. Finally, we present examples in simulations of real materials demonstrating new topological phases discovered using this framework.