Lattice generalization of the Dirac equation to general spin and the role of the flat band

Dóra, Balázs; Kailasvuori, Janik; Moessner, Roderich

doi:10.1103/physrevb.84.195422

Cited by 162 publications

(175 citation statements)

References 52 publications

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“…The triplons form novel spin-1 Dirac cones with threefold band touching. Such a feature has been seen in various contexts [41][42][43][44][45] . Our study elucidates its implications for band structure topology; the spin-1 structure naturally gives Chern numbers ± 2 instead of the more common ± 1.…”

Section: Discussionmentioning

confidence: 95%

Hall effect of triplons in a dimerized quantum magnet

2015

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SrCu 2 (BO 3 ) 2 is the archetypal quantum magnet with a gapped dimer-singlet ground state and triplon excitations. It serves as an excellent realization of the Shastry-Sutherland model, up to small anisotropies arising from Dzyaloshinskii-Moriya interactions. Here we demonstrate that these anisotropies, in fact, give rise to topological character in the triplon band structure. The triplons form a new kind of Dirac cone with three bands touching at a single point, a spin-1 generalization of graphene. An applied magnetic field opens band gaps resulting in topological bands with Chern numbers ±2. SrCu 2 (BO 3 ) 2 thus provides a magnetic analogue of the integer quantum Hall effect and supports topologically protected edge modes. At a threshold value of the magnetic field set by the Dzyaloshinskii-Moriya interactions, the three triplon bands touch once again in a spin-1 Dirac cone, and lose their topological character. We predict a strong thermal Hall signature in the topological regime.

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Section: Discussionmentioning

confidence: 95%

Hall effect of triplons in a dimerized quantum magnet

2015

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“…Note that in spite of the distinct dc conductivities of the pseudospin-1/2 and 1 Dirac-Weyl fermions around zero doping, the zero-frequency limit of their optical conductivites are finite and comparable. 13 For higher pseudospin generalizations of the Dirac-Weyl equation 11,13 in Eq. (1), where S = (S x ,S y ) is the matrix representation of an arbitrary spin S (integer or half-integer), interband transitions between two adjacent, propagating bands give a finite contribution the dc conductivity at the Dirac point.…”

Section: DC Conductivitymentioning

confidence: 99%

“…13 In particular, SrTiO 3 /SrIrO 3 /SrTiO 3 trilayer heterostructures 15 were found to realize the dice lattice structure, though further ab initio studies are desirable to decide how faithfully it can be described by Eq. (1).…”

Section: Introductionmentioning

confidence: 99%

Diverging dc conductivity due to a flat band in a disordered system of pseudospin-1 Dirac-Weyl fermions

et al. 2013

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Several lattices, such as the dice or the Lieb lattice, possess Dirac cones and a flat band crossing the Dirac point, whose effective model is the pseudospin-1 Dirac-Weyl equation. We investigate the fate of the flat band in the presence of disorder by focusing on the density of states (DOS) and dc conductivity. While the central hub site does not reveal the presence of the flat band, the sublattice resolved DOS on the noncentral sites exhibits a narrow peak with height ∼1/ √ g with g the dimensionless disorder variance. Although the group velocity is zero on the flat band, the dc conductivity diverges as ln(1/g) with decreasing disorder due to interband transitions around the band touching point between the propagating and the flat band. Generalizations to higher pseudospin are given.

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“…Indeed, one can check that, while the E = 0 component is longitudinally polarized, the other two are transverse, just like the propagating components of a photon. Pseudospin-one Dirac points have been reported in some two [29][30][31] and three-dimensional 32 systems.…”

Section: A Tight-binding Examplementioning

confidence: 99%

Existence of bulk chiral fermions and crystal symmetry

2012

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We consider the existence of bulk chiral fermions around points of symmetry in the Brillouin zone of nonmagnetic 3D crystals with negligible spin-orbit interactions. We use group theory to show that this is possible, but only for a reduced number of space groups and points of symmetry that we tabulate. Moreover, we show that for a handful of space groups the existence of bulk chiral fermions is not only possible but unavoidable, irrespective of the concrete crystal structure. Thus our tables can be used to look for bulk chiral fermions in a specific class of systems, namely that of nonmagnetic 3D crystals with sufficiently weak spin-orbit coupling. We also discuss the effects of spin-orbit interactions and possible extensions of our approach to Weyl semimetals, crystals with magnetic order, and systems with Dirac points with pseudospin 1 and 3/2. A simple tight-binding model is used to illustrate some of the issues.

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Lattice generalization of the Dirac equation to general spin and the role of the flat band

Cited by 162 publications

References 52 publications

Hall effect of triplons in a dimerized quantum magnet

Hall effect of triplons in a dimerized quantum magnet

Diverging dc conductivity due to a flat band in a disordered system of pseudospin-1 Dirac-Weyl fermions

Existence of bulk chiral fermions and crystal symmetry

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