具有次近邻跳跃的非互易准周期晶格中的解析迁移率边缘
Analytical mobility edge in nonreciprocal quasiperiodic lattices with next-nearest-neighbor hopping
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中文总结 AI 辅助
研究一维非厄米Aubry-André模型中的局域化转变与能谱拓扑，通过扩展费米面点匹配方法导出迁移率边缘表达式，分析其在不同非互易性下的特性，还研究了能谱拓扑，结果提供了联系局域化、能谱拓扑和非互易性的解析框架，可在多平台测试。
中文摘要 AI 辅助
我们研究了Aubry-André模型的一维非厄米推广中的局域化转变和能谱拓扑，其中最近邻和次近邻跳跃幅度都是非互易的。通过将费米面点匹配方法扩展到非互易跳跃，我们导出了能量相关迁移率边缘的封闭形式表达式，其中两个非互易参数被吸收到指数重整化的有效跳跃幅度中。迁移率边缘在能量-势平面上形成一条抛物线：最近邻非互易性将局域化边界刚性地移向更强的势，而次近邻非互易性减小了边界的曲率，从而拓宽了扩展态和局域态共存的能量窗口。精确对角化证实了纯最近邻、纯次近邻和组合非互易性的解析边界，并在互易极限下恢复了已知的厄米迁移率边缘。我们进一步分析了周期边界条件下的能谱拓扑，表明在两个能带边缘附近的基能量处评估的能谱缠绕数直接包围了混合相：当迁移率边缘进入能谱且第一个局域态出现时，下能带边缘的缠绕数下降，而上能带边缘的缠绕数在最后一个扩展态局域化时下降，描绘了扩展态和局域态共存的整个势强度窗口。这些结果提供了一个紧凑的解析框架，将准周期晶格中能量相关的局域化、能谱拓扑和非互易性联系起来，并且它们可以在光子、原子和电路平台上直接测试。
英文摘要
We investigate localization transitions and spectral topology in a one-dimensional non-Hermitian generalization of the Aubry-André model in which both the nearest-neighbor and the next-nearest-neighbor hopping amplitudes are nonreciprocal. By extending the Fermi-surface point-matching method to nonreciprocal hopping, we derive a closed-form expression for the energy-dependent mobility edge in which the two nonreciprocity parameters are absorbed into exponentially renormalized effective hopping amplitudes. The mobility edge forms a single parabola in the energy--potential plane: nearest-neighbor nonreciprocity rigidly shifts the localization boundary toward stronger potentials, whereas next-nearest-neighbor nonreciprocity reduces the curvature of the boundary and thereby broadens the energy window in which extended and localized states coexist. Exact diagonalization confirms the analytical boundary for purely nearest-neighbor, purely next-nearest-neighbor, and combined nonreciprocity, and recovers the known Hermitian mobility edge in the reciprocal limit. We further analyze the spectral topology under periodic boundary conditions and show that the spectral winding numbers evaluated at base energies near the two band edges directly bracket the mixed phase: the winding number at the lower band edge drops when the mobility edge enters the spectrum and the first localized states appear, while the winding number at the upper band edge drops when the last extended states localize, delineating the full potential-strength window over which extended and localized states coexist. These results provide a compact analytical framework that connects energy-dependent localization, spectral topology, and nonreciprocity in quasiperiodic lattices, and they are directly testable in photonic, atomic, and electrical-circuit platforms.
