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Several materials in the regime of strong spin-orbit interaction such as HgTe, the pyrochlore iridate Pr$_2$Ir$_2$O$_7$, and the half-Heusler compound LaPtBi, as well as various systems related to these three prototype materials, are believed to host a quadratic band touching point at the Fermi level.
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A similar observation was made for the relativistic Gross-Neveu universality classes relevant for the various possible transitions on graphene’s honeycomb lattice; see L. Janssen and I. F. Herbut, Antiferromagnetic critical point on graphene’s honeycomb lattice: A functional renormalization group approach, Phys. Rev. B 89
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2014
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2016
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2016
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