具有自旋-轨道相互作用的一维准晶的自对偶性
Self-duality of One-dimensional Quasicrystals with Spin-Orbit Interaction
摘要：
一维准晶中无相互作用的无自旋电子在准周期势的临界强度下发生金属-绝缘体跃迁（MIT），这一过程由最近邻跳跃的Aubry-André-Harper（AAH）哈密顿量描述.这种转变与AAH哈密顿量的自对偶性有关。有趣的是，在临界点，这也被称为自对偶点，所有的单粒子波函数是多重分形或非遍历的性质，而它们是遍历和离域（本地化）低于（高于）临界点。本文研究了存在Rashba型自旋-轨道（SO）耦合的一维准周期AAH哈密顿量，其中引入了额外的自旋守恒复跳跃和自旋翻转跳跃.我们发现，虽然AAH哈密顿量的自对偶性质保持不变，但自对偶点受到显著影响。此外，复合物和自旋翻转跳跃的效果在性质上是相同的。我们推广了Kohn的准粒子定域张量计算的思想，并非常精确地探测到了临界点。这些计算之后，详细的多重分形分析，随着逆参与比和冯诺伊曼熵的计算，这清楚地表明，准粒子本征态确实是多重分形和非遍历的临界点。最后，在准周期势和SO耦合强度的参数空间中绘制了相图。
英文摘要：
Non-interacting spinless electrons in one-dimensional quasicrystals, described by the Aubry-André-Harper (AAH) Hamiltonian with nearest neighbour hopping, undergoes metal to insulator transition (MIT) at a critical strength of the quasi-periodic potential. This transition is related to the self-duality of the AAH Hamiltonian. Interestingly, at the critical point, which is also known as the self-dual point, all the single particle wave functions are multifractal or non-ergodic in nature, while they are ergodic and delocalized (localized) below (above) the critical point. In this work, we have studied the one dimensional quasi-periodic AAH Hamiltonian in the presence of spin-orbit (SO) coupling of Rashba type, which introduces an additional spin conserving complex hopping and a spin-flip hopping. We have found that, although the self-dual nature of AAH Hamiltonian remains unaltered, the self-dual point gets affected significantly. Moreover, the effect of the complex and spin-flip hoppings are identical in nature. We have extended the idea of Kohn's localization tensor calculations for quasi-particles and detected the critical point very accurately. These calculations are followed by detailed multifractal analysis along with the computation of inverse participation ratio and von Neumann entropy, which clearly demonstrate that the quasi-particle eigenstates are indeed multifractal and non-ergodic at the critical point. Finally, we mapped out the phase diagram in the parameter space of quasi-periodic potential and SO coupling strength.
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