Owerre S A
Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, Ontario N2L 2Y5, Canada. African Institute for Mathematical Sciences, 6 Melrose Road, Muizenberg, Cape Town 7945, South Africa.
J Phys Condens Matter. 2016 Sep 28;28(38):386001. doi: 10.1088/0953-8984/28/38/386001. Epub 2016 Jul 20.
It has been recently shown that in the Heisenberg (anti)ferromagnet on the honeycomb lattice, the magnons (spin wave quasipacticles) realize a massless two-dimensional (2D) Dirac-like Hamiltonian. It was shown that the Dirac magnon Hamiltonian preserves time-reversal symmetry defined with the sublattice pseudo spins and the Dirac points are robust against magnon-magnon interactions. The Dirac points also occur at nonzero energy. In this paper, we propose a simple realization of nontrivial topology (magnon edge states) in this system. We show that the Dirac points are gapped when the inversion symmetry of the lattice is broken by introducing a next-nearest neighbour Dzyaloshinskii-Moriya (DM) interaction. Thus, the system realizes magnon edge states similar to the Haldane model for quantum anomalous Hall effect in electronic systems. However, in contrast to electronic spin current where dissipation can be very large due to Ohmic heating, noninteracting topological magnons can propagate for a long time without dissipation as magnons are uncharged particles. We observe the same magnon edge states for the XY model on the honeycomb lattice. Remarkably, in this case the model maps to interacting hardcore bosons on the honeycomb lattice. Quantum magnetic systems with nontrivial magnon edge states are called topological magnon insulators. They have been studied theoretically on the kagome lattice and recently observed experimentally on the kagome magnet Cu(1-3, bdc) with three magnon bulk bands. Our results for the honeycomb lattice suggests an experimental procedure to search for honeycomb topological magnon insulators within a class of 2D quantum magnets and ultracold atoms trapped in honeycomb optical lattices. In 3D lattices, Dirac and Weyl points were recently studied theoretically, however, the criteria that give rise to them were not well-understood. We argue that the low-energy Hamiltonian near the Weyl points should break time-reversal symmetry of the pseudo spins. Thus, recovering the same criteria in electronic systems.
最近的研究表明，在蜂窝晶格上的海森堡（反）铁磁体中，磁振子（自旋波准粒子）实现了一种无质量的二维（2D）类狄拉克哈密顿量。研究表明，狄拉克磁振子哈密顿量保持由子晶格赝自旋定义的时间反演对称性，并且狄拉克点对于磁振子 - 磁振子相互作用是稳健的。狄拉克点也出现在非零能量处。在本文中，我们提出了在该系统中实现非平凡拓扑（磁振子边缘态）的一种简单方法。我们表明，当通过引入次近邻的Dzyaloshinskii - Moriya（DM）相互作用破坏晶格的反演对称性时，狄拉克点会出现能隙。因此，该系统实现了类似于电子系统中量子反常霍尔效应的哈代模型的磁振子边缘态。然而，与由于欧姆加热导致耗散可能非常大的电子自旋电流不同，非相互作用的拓扑磁振子作为不带电粒子可以长时间无耗散地传播。我们在蜂窝晶格上的XY模型中观察到了相同的磁振子边缘态。值得注意的是，在这种情况下，该模型映射到蜂窝晶格上相互作用的硬核玻色子。具有非平凡磁振子边缘态的量子磁系统被称为拓扑磁振子绝缘体。它们已经在 kagome晶格上进行了理论研究，并且最近在具有三个磁振子体带的kagome磁体Cu(1 - 3, bdc)上通过实验观察到。我们对蜂窝晶格的研究结果提出了一种实验方法，用于在一类二维量子磁体和被困在蜂窝光学晶格中的超冷原子中寻找蜂窝拓扑磁振子绝缘体。在三维晶格中，狄拉克点和外尔点最近进行了理论研究，然而，导致它们出现的标准尚未得到很好的理解。我们认为，外尔点附近的低能哈密顿量应该破坏赝自旋的时间反演对称性。因此，恢复了电子系统中的相同标准。
