Supersymmetric quantum mechanics of continuous topological insulators

In this paper, we construct a class of quantum systems in a space continuum inspired by results from topological insulator physics. Instead of adding spin–orbit coupling terms suggested by time-reversal invariance as in conventional topological insulators, the terms [Formula: see text] are determined using supersymmetry as a starting point. This procedure not only restricts the number of possible continuous topological insulators models, but also provides a systematic way to find new continuous topological insulators models. Some explicit quantum mechanical examples are discussed and applications to dark matter physics are also outlined.