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Valence bond solid phases on deformed kagome lattices: Application toRb2Cu3SnF12
Yang, Bohm-Jung,Kim, Yong Baek American Physical Society 2009 Physical review. B, Condensed matter and materials Vol.79 No.22
<P>Motivated by a recent experiment on Rb2Cu3SnF12, where spin-1/2 Cu2+ moments reside on the layers of kagome-like lattices, we investigate quantum ground states of the antiferromagnetic Heisenberg model on a series of deformed kagome lattices. The deformation is characterized by a weaker exchange coupling alpha J on certain lattice links appropriate for Rb2Cu3SnF12 with alpha=1 corresponding to the ideal kagome lattice. In particular, we study possible valence bond solid phases using the perturbation theory around isolated dimer limits, dimer series expansion, and self-consistent bond operator mean-field theory. It is shown that the valence bond solid phase with a 36-site unit cell of the ideal kagome lattice is quite sensitive to a small lattice distortion as the kind discovered in Rb2Cu3SnF12. As a result, we find that a more likely quantum ground state in Rb2Cu3SnF12 is the valence bond solid phase with a 12-site unit cell, where six dimers form a pinwheel structure, leading to strong modification of the elementary triplet and singlet excitation spectra in the deformed kagome lattices.</P>
Topological semimetals protected by off-centered symmetries in nonsymmorphic crystals
Yang, Bohm-Jung,Bojesen, Troels Arnfred,Morimoto, Takahiro,Furusaki, Akira American Physical Society 2017 Physical Review B Vol.95 No.7
<P>Topological semimetals have energy bands near the Fermi energy sticking together at isolated points/lines/planes in the momentum space, which are often accompanied by stable surface states and intriguing bulk topological responses. Although it has been known that certain crystalline symmetries play an important role in protecting band degeneracy, a general recipe for stabilizing the degeneracy, especially in the presence of spin-orbit coupling, is still lacking. Herewe showthat a class of novel topological semimetals with point/line nodes can emerge in the presence of an off-centered rotation/mirror symmetry whose symmetry line/plane is displaced from the center of other symmorphic symmetries in nonsymmorphic crystals. Due to the partial translation perpendicular to the rotation axis/mirror plane, an off-centered rotation/mirror symmetry always forces two energy bands to stick together and form a doublet pair in the relevant invariant line/plane in momentum space. Such a doublet pair provides a basic building block for emerging topological semimetals with point/line nodes in systems with strong spin-orbit coupling.</P>
Park, Sungjoon,Yang, Bohm-Jung American Physical Society 2017 Physical Review B Vol.96 No.12
<P>We classify all possible gap-closing procedures which can be achieved in two-dimensional time-reversal invariant noncentrosymmetric systems. For exhaustive classification, we examine the space-group symmetries of all 49 layer groups lacking inversion, taking into account spin-orbit coupling. Although a direct transition between two insulators is generally predicted to occur when a band crossing happens at a general point in the Brillouin zone, we find that a variety of stable semimetal phases with point or line nodes can also arise due to the band crossing in the presence of additional crystalline symmetries. Through our theoretical study, we provide the complete list of nodal semimetals created by a band inversion in two-dimensional noncentrosymmetric systems with time-reversal invariance. The transition from an insulator to a nodal semimetal can be grouped into three classes depending on the crystalline symmetry. First, in systems with a twofold rotation about the axis ( normal to the system), a band inversion at a generic point generates a two-dimensional Weyl semimetal with point nodes. Second, when the band crossing happens on the line invariant under a twofold rotation ( mirror) symmetry with the rotation ( normal) axis lying in the two-dimensional plane, a Weyl semimetal with point nodes can also be obtained. Finally, when the system has a mirror symmetry about the plane embracing the whole system, a semimetal with nodal lines can be created. Applying our theoretical framework, we identify various two-dimensional materials as candidate systems in which stable nodal semimetal phases can be induced via doping, applying electric field, or strain engineering, etc.</P>