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

Lukas Janssen; Igor F. Herbut

doi:10.1103/PhysRevB.95.075101

paper

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

arXiv:1611.04594 · doi:10.1103/PhysRevB.95.075101

Abstract

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. 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 $N_{c}$ . We further substantiate and quantify this scenario by various approaches. Using $ε$ expansion near two spatial dimensions, we show that $N_{c} = 64/ (25 ε^{2}) + O (1/ ε)$ and demonstrate that the instability for $N < N_{c}$ 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 $ε$ 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 Pr $_{2}$ Ir $_{2}$ O $_{7}$ , is a strong topological insulator with a dynamically-generated gap -- a topological Mott insulator.

16 pages, 7 figures; v2: additional reference, published version

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

Abstract

References in corpus (9)

Cited by in corpus (27)

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

Abstract

References in corpus (9)

Cited by in corpus (27)

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