Akash V. Maharaj, Ronny Thomale, S. Raghu
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 phases that break time-reversal and spin rotation symmetries can occur. We show that hexagonal lattice systems with extended repulsive interactions can exhibit instabilities in the particle-hole channel to phases with $d_{x^2-y^2}+id_{xy}$ 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 also be broken, resulting in various $d_{x^2-y^2}+id_{xy}$ density wave orders. In the weak-coupling limit, when the Fermi surfaces lie close to a van Hove singularity, instabilities of both types are obtained in a controlled fashion.
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http://arxiv.org/abs/1303.2361
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