Effect of spin-orbit coupling in one-dimensional quasicrystals with power-law hopping

TL;DR

This paper investigates how spin-orbit coupling influences localization, multifractality, and mobility edges in one-dimensional quasiperiodic systems with power-law hopping, revealing increased critical disorder strength and complex spectral structures.

Contribution

It introduces the effects of spin-orbit coupling on localization and multifractal properties in power-law hopping quasiperiodic systems, highlighting the emergence of multiple multifractal and mobility edges.

Findings

Spin-orbit coupling increases the critical disorder strength for localization.

Multiple multifractal edges appear for $a \,\leq\, 1$ with spin-orbit coupling.

Multiple mobility edges can exist for $a > 1$, with or without spin-orbit coupling.

Abstract

In the one-dimensional quasiperiodic Aubry-Andr\'{e}-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 $\beta^s L$ 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 $(\beta^s \pm \beta^m)$. 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.