准周期阿哈罗诺夫-玻姆链中精确迁移率边的工程实现
Engineering exact mobility edges in quasiperiodic Aharonov-Bohm chains
浏览论文内容
中文总结 AI 辅助
该研究在准周期阿哈罗诺夫-玻姆链中，通过耦合受合成磁通量的辅助子晶格，推导出精确迁移率边表达式，为可控迁移率边工程提供理论框架。
中文摘要 AI 辅助
我们研究准周期阿哈罗诺夫-玻姆链中的局域化现象与精确迁移率边，该系统中一维典型的对角和非对角Aubry-André-Harper模型横向耦合至一个受合成磁通量穿过的辅助子晶格。通过利用阿维拉单频率薛定谔算子全局理论解析计算李雅普诺夫指数，我们推导出迁移率边的精确表达式。在对角极限下，与辅助子晶格的耦合产生双曲迁移率边，表现出变号发散特性，且可通过磁通量连续调控。在非对角区域，准周期隧穿与通过辅助子晶格的间接隧穿之间的干涉产生精确的反常迁移率边，可区分临界态与扩展态。即使在隧穿调制不存在非公度分布零点的情况下，临界态与反常迁移率边仍会出现，这一特性与传统非对角模型不同。我们的研究为工程可控迁移率边建立了严格的理论框架，合成磁通量提供了可调控的实验旋钮，为在超导量子电路、光子波导等平台中实现该现象铺平了道路。
英文摘要
We investigate localization phenomena and exact mobility edges in a quasiperiodic Aharonov-Bohm chain, where the 1D canonical diagonal and off-diagonal Aubry-André-Harper models are laterally coupled to an auxiliary sublattice threaded by a synthetic magnetic flux. By analytically computing the Lyapunov exponent via Avila's global theory of one-frequency Schrödinger operators, we derive exact expressions for mobility edges. In the diagonal limit, the coupling to the auxiliary sublattice generates hyperbolic mobility edges that exhibit a sign-changing divergence and can be continuously tuned by the magnetic flux. In the off-diagonal regime, the interference between quasiperiodic hopping and indirect tunneling through the auxiliary sublattice gives rise to exact anomalous mobility edges that separate critical and extended states. Critical states and anomalous mobility edges emerge even in the absence of incommensurately distributed zeros in the hopping modulation, a behavior distinct from that of conventional off-diagonal models. Our results establish a rigorous theoretical framework for engineering controllable mobility edges, with the synthetic flux providing a tunable experimental knob that paves the way for realizations in platforms such as superconducting quantum circuits and photonic waveguides.
