Minimal conductivity, topological Berry winding and duality in three-band semimetals

Abstract

The physics of massless relativistic quantum particles has recently arisen in the electronic properties of solids following the discovery of graphene. Around the accidental crossing of two energy bands, the electronic excitations are described by a Weyl equation initially derived for ultra-relativistic particles. Similar three and four band semimetals have recently been discovered in two and three dimensions. Among the remarkable features of graphene are the characterization of the band crossings by a topological Berry winding, leading to an anomalous quantum Hall effect, and a finite minimal conductivity at the band crossing while the electronic density vanishes. Here we show that these two properties are intimately related: this result paves the way to a direct measure of the topological nature of a semi-metal. By considering three band semimetals with a flat band in two dimensions, we find that only few of them support a topological Berry phase. The same semimetals are the only ones displaying a non vanishing minimal conductivity at the band crossing. The existence of both a minimal conductivity and a topological robustness originates from properties of the underlying lattice, which are encoded not by a symmetry of their Bloch Hamiltonian, but by a duality.

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Cited by in corpus (34)

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• Frequency-dependent polarizability, plasmons, and screening in the 2D pseudospin-1 dice lattice
• Dualities and non-Abelian mechanics
• Dynamics of a quasiparticle in the $\alpha$-T${}_3$ model: Role of pseudospin polarization and transverse magnetic field on \textbf{\textit{zitterbewegung}}
• Two-dimensional Chern semimetals on the Lieb lattice
• Conductivity of pure graphene: Theoretical approach using the polarization tensor
• Electronic states of pseudospin-1 fermions in dice lattice ribbons
• Generalized WKB theory for electron tunneling in gapped $\alpha -{\mathcal{T}}_3$ lattices
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• Non-equilibrium transport in the pseudospin-1 Dirac-Weyl system
• Geometry and Topology Tango in Ordered and Amorphous Chiral Matter
• Magnon-magnon interaction and magnon relaxation time in ferromagnetic Cr2Ge2Te6 monolayer
• Self-Assembly of Isostatic Self-Dual Colloidal Crystals
• An analytic evaluation of Kane fermion magneto-optics in two and three dimensions
• Electronic states of pseudospin-1 fermions in $\alpha -{\mathcal{T}}_3$ lattice ribbons in a magnetic field
• Optical conductivity of bilayer dice lattices
• Duality,Hidden Symmetry and Dynamic Isomerism in 2D Hinge Structures
• Andreev reflection of massive pseudospin-1 fermions
• Tunneling valley Hall effect induced by coherent geometric phase
• Electrical and thermal transport through $\alpha -T_3$ NIS junction
• Dynamical charge and pseudospin currents in graphene and possible Cooper pair formation
• Fano resonances for tilted linear and quadratic band touching dispersions in a harmonically driven potential well
• Geometric semimetals and their simulation in synthetic matter
• Developing a semiclassical Wentzel-Kramers-Brillouin theory for $\alpha -{\mathcal{T}}_3$ model
• Transport properties of the pseudospin-3/2 Dirac-Weyl fermions in the double-barrier-modulated two-dimensional system
• Temperature Dependence of the Response Functions of Graphene: Impact on Casimir and Casimi-Polder Forces in and out of Thermal Equilibrium
• Floquet Control of Electron and Exciton Transport in Kekulé-Distorted Graphene
• Quantized Berry winding from an emergent $\mathcal{P}\mathcal{T}$ symmetry