Topological Mott insulator in three-dimensional systems with quadratic band touching

Abstract

We argue that a three dimensional electronic system with the Fermi level at the quadratic band touching point such as HgTe could be unstable with respect to the spontaneous formation of the (topological) Mott insulator at arbitrary weak long range Coulomb interaction. The mechanism of the instability can be understood as the collision of Abrikosov's non-Fermi liquid fixed point with another, quantum critical, fixed point, which approaches it in the coupling space as the system's dimensionality $d\to d_{low}+$, with the "lower critical dimension" $2<d_{low}<4$. Arguments for the existence of the quantum critical point based on considerations in the large-$N$ limit in $d=3$, as well as close to $d=2$, are given. In the one-loop calculation we find that $d_{low}=3.26$, and thus above, but not far from three dimensions. This translates into a temperature/energy window $(T_c,T_{\ast })$ over which the NFL scaling should still be observable, before the Mott transition finally takes place at the critical temperature $T_c\sim T_{\ast }\exp (-zC/(d_{low}-d{)}^{1/2})$. We estimate $C=\pi /1.1$, dynamical critical exponent $z\approx 1.8$, and the temperature scale $k_B{T}_{\ast }\approx (4m/m_{el}{\epsilon }^2)13.6eV$, with $m$ as the band mass and $\epsilon$ as the dielectric constant.

4+ pages, two figures. The updated version has one new figure, streamlined and improved presentation with additional comments and explanations, and new and updated references. Matches closely the published version

References in corpus (10)

• Topological Insulators with Inversion Symmetry
• Topological Crystalline Insulators
• Interactions and phase transitions on graphene's honeycomb lattice
• Topological Insulators and Nematic Phases from Spontaneous Symmetry Breaking in 2D Fermi Systems with a Quadratic Band Crossing
• SU(2) Non-Abelian Holonomy and Dissipationless Spin Current in Semiconductors
• Theory of interacting electrons on the honeycomb lattice
• Electronic multicriticality in bilayer graphene
• On the Phase Structure of Many-Flavor QED${}_3$
• Chiral symmetry breaking in ${\mathrm{QED}}_3$ in presence of irrelevant interactions: a renormalization group study
• Time reversal, fermion doubling, and the masses of lattice Dirac fermions in three dimensions

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