MoB $_{2}$中具有$\mathcal{PT}$保护的声子螺旋节线
Phononic Helical Nodal Lines with $\mathcal{PT}$ Protection in MoB$_{2}$
摘要：
虽然凝聚态系统同时拥有费米和玻色子准粒子，但可靠地预测和经验验证拓扑状态仅适用于费米电子结构，而拓扑玻色子激发只是偶尔探索。这是不幸的，因为玻色子系统（例如声子）提供了评估无自旋能带结构的机会，其中可以实现节线，而无需调用特殊的附加对称性来防止自旋轨道耦合。在这里，我们结合第一性原理计算和兆电子伏分辨率的非弹性X射线散射，证明宇称-时间反转（$\mathcal{PT}$）对称性保护的螺旋节线的声子谱的MoB $_{2}$的第一个实现。这种结构是声子系统所独有的，因为电子系统中存在的自旋-轨道耦合倾向于将简并度从高对称位置提升。我们的研究建立了一个协议，以准确地识别拓扑玻色子激发，开辟了一条新的路线，探索奇异的拓扑状态在晶体材料。
英文摘要：
While condensed matter systems host both Fermionic and Bosonic quasi-particles, reliably predicting and empirically verifying topological states is only mature for Fermionic electronic structures, leaving topological Bosonic excitations sporadically explored. This is unfortunate, as Bosonic systems such a phonons offer the opportunity to assess spinless band structures where nodal lines can be realized without invoking special additional symetries to protect against spin-orbit coupling. Here we combine first-principles calculations and meV-resolution inelastic x-ray scattering to demonstrate the first realization of parity-time reversal ($\mathcal{PT}$) symmetry protected helical nodal lines in the phonon spectrum of MoB$_{2}$. This structure is unique to phononic systems as the spin-orbit coupling present in electronic systems tends to lift the degeneracy away from high-symmetry locations. Our study establishes a protocol to accurately identify topological Bosonic excitations, opening a new route to explore exotic topological states in crystalline materials.
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