2015/12/31 by Jörn W. F. Venderbos, J. W. F. Venderbos · 1 citation
Physics and Astronomy · #Advanced Condensed Matter Physics #Condensed matter physics #Physics #Physics of Superconductivity and Magnetism #Quantum mechanics #Semimetal #Topological Materials and Phenomena #Topological insulator #Weyl semimetal #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.93.115108
published as Phys. Rev. B 93, 115108 (2016) · 14 + 4 pages, 5 + 0 figures; published version
openalex publication_date 2016/03/03 · arxiv created 2016/03/05 · arxiv updated 2016/03/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study hexagonal spin-channel (``triplet'') density waves with commensurate M-point propagation vectors. We first show that the three Q=M components of the singlet charge density and charge-current density waves can be mapped to multicomponent Q=0 nonzero angular momentum order in three dimensions (3D) with cubic crystal symmetry. This one-to-one correspondence is exploited to define a symmetry classification for triplet M-point density waves using the standard classification of spin-orbit coupled electronic liquid crystal phases of a cubic crystal. Through this classification we naturally identify a set of noncoplanar spin density and spin-current density waves: the chiral spin density wave and its time-reversal invariant analog. These can be thought of as 3D\phantom\rule4pt0exL=2 and 4 spin-orbit coupled isotropic \ensuremathβ-phase orders. In contrast, uniaxial spin density waves are shown to correspond to \ensuremathα phases. The noncoplanar triple-M spin-current density wave realizes a novel 2D semimetal state with three flavors of four-component spin-momentum locked Dirac cones, protected by a crystal symmetry akin to nonsymmorphic symmetry, and sits at the boundary between a trivial and topological insulator. In addition, we point out that a special class of classical spin states, defined as classical spin states respecting all lattice symmetries up to global spin rotation, are naturally obtained from the symmetry classification of electronic triplet density waves. These symmetric classical spin states are the classical long-range ordered limits of chiral spin liquids.