相关扰动下的平坦带
Flat Bands Under Correlated Perturbations
摘要：
平带网络的特点是色散带和平带共存。平带（FB）是基于相消干涉，由具有局域网络对称性的紧凑局域本征态（CLS）产生的。相关无序和准周期势在没有额外重整化的情况下使CLS杂交，但却有令人惊讶的结果：（i）态从FB能量$E_{FB}$中被驱逐，（ii）本征态的局域长度为$ξ\sim 1 / \ln (E- E_{FB})$，（iii）态密度在数学上发散（iv）迁移率边缘曲线在$E_{FB}$处显示代数奇异性。我们的分析结果是基于微扰展开的CLS，并支持在一个和两个晶格维的数值数据。
英文摘要：
Flat band networks are characterized by coexistence of dispersive and flat bands. Flat bands (FB) are generated by compact localized eigenstates (CLS) with local network symmetries, based on destructive interference. Correlated disorder and quasiperiodic potentials hybridize CLS without additional renormalization, yet with surprising consequencies: (i) states are expelled from the FB energy $E_{FB}$, (ii) the localization length of eigenstates vanishes as $ξ\sim 1 / \ln (E- E_{FB})$, (iii) the density of states diverges logarithmically (particle-hole symmetry) and algebraically (no particle-hole symmetry), (iv) mobility edge curves show algebraic singularities at $E_{FB}$. Our analytical results are based on perturbative expansions of the CLS, and supported by numerical data in one and two lattice dimensions.
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