Materials that exhibit topological phases can be classified by their dimensionality, symmetries and topological invariants to form conductive-edge states with peculiar transport and spin properties. For example, the quantum Hall effect can arise in two-dimensional (2-D) electron systems subjected to a perpendicular magnetic field. When distinct characteristics of quantum Hall systems are compared with time-reversal symmetric (entropy conserved) topological insulators (TIs), they appear to rely on Coulomb interactions between electrons to induce a wealth of strongly correlated, topologically or symmetry-projected phases in a variety of experimental systems.

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