Symmetry analysis of translational symmetry broken density waves: application to hexagonal lattices in two dimensions

Abstract

In this work we introduce a symmetry classification for electronic density waves which break translational symmetry due to commensurate wave vector modulations. The symmetry classification builds on the concept of extended point groups: symmetry groups which contain, in addition to the lattice point group, translations that do not map the enlarged unit cell of the density wave to itself, and become "non-symmorphic"-like elements. Multi-dimensional representations of the extended point group are associated with degenerate wave vectors. Electronic properties such as (nodal) band degeneracies and topological character can be straightforwardly addressed, and often follow directly. To further flesh out the idea of symmetry, the classification is constructed so as to manifestly distinguish time-reversal invariant charge (i.e., site and bond) order, and time-reversal breaking flux order. For the purpose of the present work we particularize to spin-rotation invariant density waves. As a first example of the application of the classification we consider the density waves of a simple single- and two-orbital square lattice model. The main objective, however, is to apply the classification to two-dimensional ($2D$) hexagonal lattices, specifically the triangular and the honeycomb lattices. The multi-component density waves corresponding to the commensurate $M$-point ordering vectors are worked out in detail. To show that our results generally apply to $2D$ hexagonal lattices, we develop a general low-energy $SU(3)$ theory of (spinless) saddle point electrons.

16 + 6 pages; 10 + 1 figures; published version

References in corpus (29)

• The electronic properties of graphene
• Topological Crystalline Insulators
• Dirac Semimetals in Two Dimensions
• Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
• Strong Correlations and Magnetic Frustration in the High Tc Iron Pnictides
• The space group classification of topological band insulators
• Topological Mott Insulators
• Theory of Electron Nematic Order in LaOFeAs
• Unconventional Fermi surface instabilities in the Kagome Hubbard Model
• Correlated electronic structure of LaOFeAs
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• A minimal two-band model for the superconducting Fe-pnictides
• Electron fractionalization in two-dimensional graphenelike structures
• Ising and Spin orders in Iron-based Superconductors
• Topological Insulators and Nematic Phases from Spontaneous Symmetry Breaking in 2D Fermi Systems with a Quadratic Band Crossing
• Scalar spin chirality and quantum Hall effect on a triangular lattice
• Properties of an algebraic spin liquid on the kagome lattice
• Theory of resonant multiphonon Raman scattering in graphene
• Time-Reversal Symmetry Breaking and Spontaneous Anomalous Hall Effect in Fermi Fluids
• Vestigial chiral and charge orders from bidirectional spin-density waves: Application to the iron-based superconductors
• Exotic topological density waves in cold atomic Rydberg fermions
• Pomeranchuk instability in doped graphene
• Chiral spin density wave, spin-charge-Chern liquid and d+id superconductivity in 1/4-doped correlated electronic systems on the honeycomb lattice
• Spontaneous quantum Hall effect via thermally induced quadratic Fermi point
• Non-abelian gauge fields and quadratic band touchings in molecular graphene
• Multi-$Q$ hexagonal spin density waves and dynamically generated spin-orbit coupling: time-reversal invariant analog of the chiral spin density wave
• Non-Abelian SU(2) gauge fields through density-wave order and strain in graphene
• Spontaneous time-reversal symmetry breaking for spinless fermions on a triangular lattice
• Spontaneous Quantum Hall Effect in chiral d-density waves

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