Flat bands and Dirac cones in breathing lattices

Abstract

In breathing pyrochlores and kagomes, couplings between neighbouring tetrahedra and triangles are free to differ. Breathing lattices thus offer the possibility to explore a different facet of the rich physics of these systems. Here we consider nearest-neighbour classical Heisenberg interactions, both ferromagnetic and antiferromagnetic, and study how the anisotropy of breathing lattices modifies the mode spectrum of pyrochlore and kagome systems. The nature and degeneracy of the flat bands are shown to be preserved for any value of the anisotropy. These flat bands can coexist with Dirac nodes at the $\Gamma$ point when the model becomes particle-hole symmetric. We also derive the nature of the ground state for the breathing kagome lattice, which bears a spontaneous chirality when neighbouring triangles are alternatively ferromagnetic and antiferromagnetic.

submitted as a proceeding for HFM 2016

References in corpus (12)

• Weyl magnons in breathing pyrochlore antiferromagnets
• Hall effect of triplons in a dimerized quantum magnet
• Octupolar ordering of classical kagome antiferromagnets in two and three dimensions
• Experimental Realization of a Quantum Breathing Pyrochlore Antiferromagnet
• Anisotropic exchange within decoupled tetrahedra in the quantum breathing pyrochlore Ba3Yb2Zn5O11
• Novel Phase Transitions in the Breathing Pyrochlore Lattice: 7Li-NMR on LiInCr4O8 and LiGaCr4O8
• Quantum Spin Liquid in a Breathing Kagome Lattice
• Magnetic Phase Diagram of the Breathing Pyrochlore Antiferromagnet LiGa1-xInxCr4O8
• Low-Energy Excitations and Ground State Selection in Quantum Breathing Pyrochlore Antiferromagnet Ba${}_3$Yb${}_2$Zn${}_5$O${}_{11}$
• Weyl semimetal from spontaneous inversion symmetry breaking in pyrochlore oxides
• Chiral spin states in the pyrochlore Heisenberg magnet: Fermionic mean-field theory and variational Monte Carlo calculations
• Spin-lattice-coupled order in Heisenberg antiferromagnets on the pyrochlore lattice

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• Perfect transmission of 3D massive Kane fermions in HgCdTe Veselago lenses
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• Spinon band flattening by its emergent gauge field in quantum kagome ice
• Spinor ice correlation in flat-band electronic states on kagome and pyrochlore lattices with spin-orbit coupling
• Theta electromagnetism in quantum spin ice: Microscopic analysis of improper symmetries
• Mapping the Phase Diagram of a Frustrated Magnet: Degeneracies, Flat Bands, and Canting Cycles on the Pyrochlore Lattice
• Analytic description of spin waves in dipolar/octupolar pyrochlore magnets