Phase diagram of electronic systems with quadratic Fermi nodes in 2 < d < 4: 2+epsilon expansion, 4-epsilon expansion, and functional renormalization group

Article

关键词: TOPOLOGICAL INSULATORS;    QUANTUM PHENOMENA;    SEMIMETAL;    SUPERCONDUCTORS;    GRAPHENE;    HGTE;   

DOI  :  10.1103/PhysRevB.95.075101

来源: SCIE

【 摘 要 】

Several materials in the regime of strong spin- orbit interaction such as HgTe, the pyrochlore iridate Pr2Ir2O7, 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. Recently, it has been proposed that such a three- dimensional gapless state is unstable to a Mott- insulating ground state at low temperatures when the number of band touching points N at the Fermi level is smaller than a certain critical number Nc. We further substantiate and quantify this scenario by various approaches. Using epsilon expansion near two spatial dimensions, we show that N-c = 64/(25 epsilon(2)) + O(1/ epsilon) and demonstrate that the instability for N < N-c c is towards a nematic ground state that can be understood as if the system were under ( dynamically generated) uniaxial strain. We also propose a truncation of the functional renormalization group equations in the dynamical bosonization scheme which we show to agree to one- loop order with the results from epsilon expansion both near two as well as near four dimensions, and which smoothly interpolates between these two perturbatively accessible limits for general 2 < d < 4. Directly in d = 3 we therewith find N-c = 1.86, and thus again above the physical N = 1. All these results are consistent with the prediction that the interacting ground state of pure, unstrained HgTe, and possibly also Pr2Ir2O7, is a strong topological insulator with a dynamically generated gap- a topological Mott insulator.

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