等谱图案化晶格的连续模型
Continuum Model of Isospectrally Patterned Lattices
AI总结：
本研究针对等谱图案化晶格（IPL）的能带结构问题，推导其连续模型以解析得到本征谱、本征态及局域长度表达式，分析其破缺手征对称性后的态配对特性与结构特征。
摘要：
等谱图案化晶格（IPL）近期被证实具有丰富的能带结构，同时包含局域态区域和扩展态区域。其局域态表现出单中心局域行为，具有特征性的局域长度。我们推导了IPL的连续对应模型，该模型允许我们解析确定其本征值谱和本征态，进而得到局域长度的表达式，该表达式涉及晶格元胞间耦合与晶格上相位梯度的比值。该连续模型破缺了手征对称性，但仍表现出正负能量配对的伙伴态，基态除外。我们开展了相应的对称性分析，阐明了该连续模型相较于对应手征对称哈密顿量的结构特征。
英文摘要：
Isospectrally patterned lattices (IPL) have recently been shown to exhibit a rich band structure comprising both regimes of localized as well as extended states. The localized states show a single center localization behaviour with a characteristic localization length. We derive a continuum analogue of the IPL which allows us to determine analytically its eigenvalue spectrum and eigenstates thereby obtaining an expression for the localization length which involves the ratio of the coupling among the cells of the lattice and the phase gradient across the lattice. This continuum model breaks chiral symmetry but still shows a pairing of partner states with positive and negative energies except for the ground state. We perform a corresponding symmetry analysis which illuminates the continuum models structure as compared to a corresponding chirally symmetric Hamiltonian.
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