Flat bands and long range Coulomb interactions: conducting or insulating?

Abstract

Dispersionless (flat) electronic bands are investigated regarding their conductance properties. Due to "caging" of carriers these bands are usually insulating at partial filling, at least on the non-interacting level. Considering the specific example of a ${\mathcal{T}}_3$--lattice we study long-range Coulomb interactions. A non-trivial dependence of the conductivity on flat band filling is obtained, exhibiting an infinite number of zeros. Near these zeros, the conductivity rises linearly with carrier density. At densities half way in between adjacent conductivity-zeros, strongly enhanced conductivity is predicted, accompanying a solid-solid phase transition.

5 pages, 2 figures

References in corpus (8)

• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• The $p_{x,y}$-orbital counterpart of graphene: cold atoms in the honeycomb optical lattice
• Fractional Chern Insulators in Topological Flat bands with Higher Chern Number
• Interaction corrections to the polarization function of graphene
• Exact many-electron ground states on the diamond Hubbard chain
• Wigner crystal and bubble phases in graphene in the quantum Hall regime

Cited by in corpus (9)

• Optical response of two-dimensional Dirac materials with a flat band
• Non-equilibrium transport in the pseudospin-1 Dirac-Weyl system
• Andreev reflection of massive pseudospin-1 fermions
• Compact localised states in magnonic Lieb lattices
• Quantum transport of a spin-1 chiral fermion
• Electrical conductivity and screening effect of spin-1 chiral fermions scattered by charged impurities
• Symmetry-enforced double Weyl points, multiband quantum geometry, and singular flat bands of doping-induced states at the Fermi level
• Transport properties of the pseudospin-3/2 Dirac-Weyl fermions in the double-barrier-modulated two-dimensional system
• Quantum Transport in Spin-1 Chiral Fermion: Self-Consistent Born Approximation