非周期性交错磁场中双链梯形网络的局域、输运和边缘态
Localization, transport and edge states in a two-strand ladder network in an aperiodically staggered magnetic field
摘要：
研究了双臂紧束缚梯形体系在外加磁场作用下的光谱和输运性质.在连续的梯形细胞中捕获的不同的磁通量模拟了轴向扭曲，使我们能够在原则上探测各种各样的系统，从带状Hofstadter几何形状到螺旋DNA链。我们进行了深入的数值分析，使用直接对角化的晶格哈密顿量来研究模型的电子光谱和输运性质。我们发现，这样的几何形状创建一个自相似的多重分形图案的能源景观。利用局域态密度分析了其光谱特性，并采用格林函数方法计算了双端传输概率。与标准的多重分形分析和评价的逆参与比，我们表明，该系统主机的临界和扩展阶段的缓慢变化的非周期性序列的流量表示一个可能的流动性边缘。最后，我们报告签名的拓扑边缘模式，被发现是强大的对最近邻跳跃积分的相关扰动。我们的研究结果可能是重要的实验涉及梯形量子网络，实现冷原子在光阱设置。
英文摘要：
We investigate the spectral and transport properties of a two-arm tight-binding ladder perturbed by an external magnetic field following an Aubry-André-Harper profile. The varying magnetic flux trapped in consecutive ladder-cells simulates an axial twist that enables us, in principle, to probe a wide variety of systems ranging from a ribbon Hofstadter geometry to helical DNA chains. We perform an in-depth numerical analysis, using a direct diagonalization of the lattice Hamiltonian to study the electronic spectra and transport properties of the model. We show that such a geometry creates a self-similar multifractal pattern in the energy landscape. The spectral properties are analyzed using the local density of states and a Green's function formalism is employed to obtain the two-terminal transmission probability. With the standard multifractal analysis and the evaluation of inverse participation ratio we show that, the system hosts both critical and extended phase for a slowly varying aperiodic sequence of flux indicating a possible mobility edge. Finally, we report signatures of topological edge modes that are found to be robust against a correlated perturbation given to the nearest neighbor hopping integrals. Our results can be of importance in experiments involving ladder-like quantum networks, realized with cold atoms in an optical trap setup.
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