非手性瞬时边缘态和非 reciprocity Haldane 模型中异常点的级联
Non-chiral ephemeral edge states and cascading of exceptional points in the non-reciprocal Haldane model
AI总结：
非 reciprocity Haldane 模型中，异常点级联和非手性瞬时边缘态的动态稳定化现象。
摘要：
我们研究了一个变种的 Haldane 蜂窝模型，其中次近邻之间存在非 reciprocity 跳跃。在环状结构上，系统在能谱中保护了时间反演对称性异常环（ER）。这些 ER 作为 Berry 曲率通量管，即 Berry 曲率仅在 ER 内非零。在具有锯齿状边界的圆柱体上（以及横向动量 k_x），边缘态在 k_x=π 时具有零群速度，因此是“非手性”的。边缘态在 BZ 中的异常点经历分支转变，并扩散到本征态中。随着非 reciprocity 的增加，本征态接近的态因非厄米特性而转换为异常点对。进一步增加非 reciprocity 时，异常点对呈现“俄罗斯套娃”式的嵌套繁衍，导致异常点级联。异常点的繁衍仅在非厄米特参数的特定值时发生，导致当非厄米特性作为函数绘制时，异常点对密度呈现阶梯状结构。此外，通过波包动力学，我们发现一个可调谐的区域，其中非手性边缘态可以动态稳定地存在很长时间。方程中的“自加速”项会将波包扩散到本征态中，使其成为“瞬时边缘态”。但发现对于小非厄米特性，足够宽的波包在足够晚的时间内保持边缘局域化。因此，我们揭示了非 reciprocity Haldane 模型异常相的有趣现象学，这可能对如无序 Kitaev 蜂窝模型等系统具有直接相关性，其中此类 ER 已被预测。
英文摘要：
We study a variant of the Haldane honeycomb model that has non-reciprocal hoppings between the next-nearest neighbours. The system on a torus hosts time-reversal symmetry protected exceptional rings(ER) in the spectrum. The ERs act as Berry-curvature flux tubes i.e the Berry curvature is non-zero only inside the ERs. The system on a cylinder having zig-zag boundaries (and transverse momentum $k_x$) hosts edge-states that have zero group velocity at $k_x=π$ and are therefore `non-chiral'. The edge states undergo a bifurcation transition at an exceptional point(EP)in the BZ and delocalise into the bulk. As the non-reciprocity is increased, the bulk states that are approaching each other are converted into pairs of EPs due to non-Hermiticity. As the non-reciprocity is further increased, there is a `Russian doll'-like nested proliferation of pairs of EPs, leading to an EP-cascade. The proliferation of EPs takes place only at specific values of the non-hermiticity parameter, leading to a step-like structure in the EP-pair density when plotted as a function of non-Hermiticity. Further, using wave packet dynamics, we find a tunable regime where the non-chiral edge states can be dynamically stabilised for large timescales. The `self-acceleration' term in the equations of motion tends to diffuse the wave packets into the bulk, thus making them `ephemeral edge states'. But we find that for small non-hermiticity, the edge localisation is stabilised until late times for sufficiently wider wave packets. Thus, we have brought forth an intriguing phenomenology of the exceptional phase of the non-reciprocal Haldane model, which may bear direct relevance for systems such as disordered Kitaev honeycomb model, wherein such ERs have been predicted.
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