发表机构
School of Materials Science and Engineering, Beihang University; National Key Laboratory of Artificial Intelligence for Material Science, Beihang University; Center for the Physics of Materials and Department of Physics, McGill University; Nanoacademic Technologies Inc.（北京航空航天大学材料科学与工程学院; 北京航空航天大学材料科学人工智能全国重点实验室; 麦吉尔大学物质物理中心及物理系; 纳米学术技术有限公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出时间反演选择定则，揭示层间扭转无序中反向散射的消失机制，导出电子和声子的普适厚度定律，并通过黑磷模型展示对称性过滤效应，使堆叠无序成为设计元素。
AI 中文摘要
随机层间旋转在层状物质中普遍存在，从乱层薄膜到旋转无序晶体，并强烈抑制跨层输运。这种无序由对称操作产生，在旋转轴上不存在，因此导电的厚度定律取决于反向散射在该处消失的速度。我们证明一个时间反演选择定则决定了这一点：层间键的每个扭转谐波要么是框架旋转（其反向散射相互抵消），要么是耦合变化（导致散射）。一个零集定理将该定则转化为电子和声子的普适厚度定律，由带边对称性决定；随机扭转增量会重新标度反向散射，但保持其阶数。在轴不受保护的地方，能带节点提供第二条途径：具有重尾无序的透明能量和一个$N^{-3}$定律。黑磷的第一性原理前向通道模型展示了这两条途径；其随机扭转薄膜充当对称性过滤器，相对于对齐堆叠，在64层时保留的电子电导是空穴电导的一百倍。因此，带边和声子支的对称性决定了什么能穿过无序堆叠，使堆叠无序成为一种设计元素。
英文摘要
Random layer rotations are ubiquitous in layered matter, from turbostratic films to rotationally disordered crystals, and strongly suppress transport across the layers. Generated by a symmetry operation, this disorder is absent on the rotation axis, so the thickness laws of conduction are set by how fast backscattering vanishes there. We show that a time-reversal selection rule decides this: each twist harmonic of the interlayer bond is either a frame rotation, whose backscattering cancels, or a coupling change, which scatters. A zero-set theorem turns the rule into universal thickness laws for electrons and phonons, fixed by band-edge symmetry; random twist increments rescale the backscattering but keep its order. Where the axis is unprotected, band nodes provide a second route: a transparent energy with heavy-tailed disorder and an $N^{-3}$ law. A first-principles forward-channel model of black phosphorus shows both routes; its random-twist films act as a symmetry filter that, relative to aligned stacks, retains a hundred times more of the electron than of the hole conductance at 64 layers. The symmetry of band edges and phonon branches thus decides what crosses a disordered stack, making stacking disorder a design element.
Comments8 pages, 3 figures, plus 61 pages of Supplemental Material with 19 figures
