Particle-hole condensates of higher angular momentum in hexagonal systems

Abstract

Hexagonal lattice systems (e.g. triangular, honeycomb, kagome) possess a multidimensional irreducible representation corresponding to $d_{x^2-y^2}$ and $d_{xy}$ symmetry. Consequently, various unconventional phases that combine these $d$-wave representations can occur, and in so doing may break time-reversal and spin rotation symmetries. We show that hexagonal lattice systems with extended repulsive interactions can exhibit instabilities in the particle-hole channel to phases with either $d_{x^2-y^2}+d_{xy}$ or $d+id$ symmetry. When lattice translational symmetry is preserved, the phase corresponds to nematic order in the spin-channel with broken time-reversal symmetry, known as the $\beta$ phase. On the other hand, lattice translation symmetry can be broken, resulting in various $d_{x^2-y^2}+d_{xy}$ density wave orders. In the weak-coupling limit, when the Fermi surface lies close to a van Hove singularity, instabilities of both types are obtained in a controlled fashion.

6 pages, 3 figures. Journal reference added

References in corpus (11)

• Unconventional Fermi surface instabilities in the Kagome Hubbard Model
• Superconductivity in the repulsive Hubbard model: an asymptotically exact weak-coupling solution
• Sublattice Interference in the Kagome Hubbard Model
• Density waves and Cooper pairing on the honeycomb lattice
• Fermi liquid instabilities in the spin channel
• Superconductivity and spin-density-waves in multi-band metals
• Dynamic generation of spin orbit coupling
• Anisotropic chiral d+id superconductivity in NaxCoO2 yH2O
• Interplay of superconductivity and spin density wave order in doped graphene
• Broken translational symmetry in an emergent paramagnetic phase of graphene
• Spontaneous time-reversal symmetry breaking for spinless fermions on a triangular lattice

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• Chiral $d$-wave Superconductivity in SrPtAs
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• Pair-Density-Wave Superconducting States and Electronic Liquid Crystal Phases
• Symmetry analysis of translational symmetry broken density waves: application to hexagonal lattices in two dimensions
• Unconventional superconductivity in the extended Hubbard model: Weak-coupling renormalization group
• Multi-$Q$ hexagonal spin density waves and dynamically generated spin-orbit coupling: time-reversal invariant analog of the chiral spin density wave
• Nonzero angular momentum density wave phases in SU($N$) fermions with singlet-bond and triplet-current interactions
• Functional renormalization of spinless triangular-lattice fermions: $N$-patch vs. truncated-unity scheme