标题： 自加速拓扑边缘态 显示英文标题

标题： Self-Accelerating Topological Edge States

摘要： 在具有非平凡拓扑的材料边界处出现的边缘态由于其对无序和局部边界变形的显著鲁棒性，对于许多实际应用具有吸引力。只要其能谱中的禁止拓扑间隙保持开放，这些边缘态在遇到此类缺陷时不会导致能量散射到材料内部。 这种沿拓扑绝缘体边缘传播的态的速度通常由其布洛赫动量决定。 相比之下，这里我们利用在两个具有破坏反演对称性的蜂窝晶格之间的畴壁上形成的谷霍尔边缘态，证明通过施加艾里包络线可以构造出边缘态，一方面，即使它们的布洛赫动量固定，它们也能在绝缘体边界上表现出\textit{自加速}，另一方面，即使它们的形状中存在局部特征，它们也能在绝缘体边界上表现出\textit{不要衍射}。 我们构建了线性和非线性自加速边缘态，并表明非线性对其包络线有显著影响。 这种自加速边缘态表现出典型的非衍射光束的自愈特性。 如果使用指数函数适当加权自加速拓扑态的振荡尾部，自加速谷霍尔边缘态可以绕过尖锐拐角。 我们的发现为控制拓扑绝缘体中边缘激发的传播动力学打开了新的前景，并允许研究非线性包络拓扑态相互作用时可能发生的各种丰富现象。 显示英文摘要

摘要： Edge states emerging at the boundaries of materials with nontrivial topology are attractive for many practical applications due to their remarkable robustness to disorder and local boundary deformations, which cannot result in scattering of the energy of the edge states impinging on such defects into the bulk of material, as long as forbidden topological gap remains open in its spectrum. The velocity of the such states traveling along the edge of the topological insulator is typically determined by their Bloch momentum. In contrast, here, using valley Hall edge states forming at the domain wall between two honeycomb lattices with broken inversion symmetry, we show that by imposing Airy envelope on them one can construct edge states which, on the one hand, exhibit \textit{self-acceleration} along the boundary of the insulator despite their fixed Bloch momentum and, on the other hand, \textit{do not diffract} along the boundary despite the presence of localized features in their shapes. We construct both linear and nonlinear self-accelerating edge states, and show that nonlinearity considerably affects their envelopes. Such self-accelerating edge states exhibit self-healing properties typical for nondiffracting beams. Self-accelerating valley Hall edge states can circumvent sharp corners, provided the oscillating tail of the self-accelerating topological state is properly apodized by using an exponential function. Our findings open new prospects for control of propagation dynamics of edge excitations in topological insulators and allow to study rich phenomena that may occur upon interactions of nonlinear envelope topological states.