论文标题
旋转轨道耦合在一维准晶体中与幂律跳跃的影响
Effect of spin-orbit coupling in one-dimensional quasicrystals with power-law hopping
论文作者
论文摘要
在一维的准二维Aubry-André-André-Harper Hamiltonian中，所有的邻居跳跃，所有单粒子特征状态都经历了从ergodic到局部状态的相位过渡到临界疾病强度$ W_C/T = 2.0 $。该系统没有移动性边缘。但是，在有$ 1/r^a $的表格的情况下，超越危害障碍强度的$ a> 1 $，而$ 0 <a \ leq 1 $出现，多违规边缘将扩展和多施加状态分开。在这两个限制上，根据疾病的强度，最低$β^s l $状态被定位。我们发现，在旋转轨道耦合的情况下，无论参数$ a $的价值如何，危险障碍强度总是更大。此外，我们证明，对于$ a \ leq 1 $，在存在自旋轨道耦合的情况下，存在多个多型边缘，并且能量谱分解为Delocalized and filefactal状态的替代带。此外，多重边缘的位置通常由分数$（β^s \ pmβ^m）$给出。能源谱的定性行为仍然不受$ a> 1 $的影响。但是，与先前报道的结果相反，我们发现在此限制中，与其他情况相似，有或没有自旋轨道耦合的情况下，多个移动性边缘可以存在。
In the one-dimensional quasiperiodic Aubry-André-Harper Hamiltonian with nearest-neighbor hopping, all single-particle eigenstates undergo a phase transition from ergodic to localized states at a critical disorder strength $W_c/t = 2.0$. There is no mobility edge in this system. However, in the presence of power-law hopping having the form $1/r^a$, beyond a critical disorder strength mobility edge appears for $a > 1$, while, for $0< a\leq 1$, a multifractal edge separates the extended and the multifractal states. In both these limits, depending on the strength of the disorder, lowest $β^s L$ states are delocalized. We have found that, in the presence of the spin-orbit coupling, the critical disorder strength is always larger irrespective of the value of the parameter $a$. Furthermore, we demonstrate that for $a\leq 1$, in the presence of spin-orbit coupling, there exists multiple multifractal edges, and the energy spectrum splits up into alternative bands of delocalized and multifractal states. Moreover, the location of the multifractal edges are generally given by the fraction $(β^s \pm β^m)$. The qualitative behavior of the energy spectrum remains unaffected for $a > 1$. However, in contrast to the previously reported results, we find that in this limit, similar to the other case, multiple mobility edges can exist with or without the spin-orbit coupling.
