Self-duality of One-dimensional Quasicrystals with Spin-Orbit Interaction

Abstract

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.

arXiv comment12 pages, 10 figures

References in corpus (33)

• Spintronics: Fundamentals and applications
• A spin-orbit coupled Bose-Einstein condensate
• Anderson localization of a non-interacting Bose-Einstein condensate
• Topological States and Adiabatic Pumping in Quasicrystals
• Spin-Orbit Coupled Degenerate Fermi Gases
• Spin-Injection Spectroscopy of a Spin-Orbit Coupled Fermi Gas
• The Quantum-Mechanical Position Operator in Extended Systems
• Electron Localization in the Insulating State
• Direct observation of a localization transition in quasi-periodic photonic lattices
• Ballistic spin-polarized transport and Rashba spin precession in semiconductor nanowires
• Polarization and localization in insulators: generating function approach
• The Insulating State of Matter: A Geometrical Theory
• Anderson localization on the Bethe lattice: non-ergodicity of extended states
• Fluctuations of the inverse participation ratio at the Anderson transition
• One-dimensional quasicrystals with power-law hopping
• Mutifractal Analysis of Broadly Distributed Observables at Criticality
• Emergence of criticality through a cascade of delocalization transitions in quasiperiodic chains
• The Anderson Transition in Two-Dimensional Systems with Spin-Orbit Coupling
• Topological equivalence of crystal and quasicrystal band structures
• Exotic Multifractal Conductance Fluctuations in Graphene
• Anderson Localization of cold atomic gases with effective spin-orbit interaction in a quasiperiodic optical lattice
• Critical quantum chaos and the one dimensional Harper model
• Localization by bichromatic potentials versus Anderson localization
• Multifractal and Network Analysis of Phase Transition
• Network Model for a 2D Disordered Electron System with Spin-Orbit Scattering
• $f(\alpha )$ Multifractal spectrum at strong and weak disorder
• Localization problem of the quasiperiodic system with the spin orbit interaction
• Transport, multifractality, and the breakdown of single-parameter scaling at the localization transition in quasiperiodic systems
• Study of counterintuitive transport properties in the Aubry-André-Harper model via entanglement entropy and persistent current
• Spin-polarized currents through interacting quantum wires with nonmagnetic leads
• Kohn's localisation in disordered fermionic systems with and without interactions
• Anderson localization of Cooper pairs and Majorana fermions in an ultracold atomic Fermi gas with synthetic spin-orbit coupling
• Spinful Aubry-Andre model in a magnetic field: Delocalization facilitated by a weak spin-orbit coupling

Cited by in corpus (4)

• Localization, $\mathcal{P}\mathcal{T}$-Symmetry Breaking and Topological Transitions in non-Hermitian Quasicrystals
• Supercurrent-enabled Andreev reflection in a chiral quantum Hall edge state
• Localization of ultracold atoms in incommensurate spin-orbit-coupling and Zeeman lattices
• Effect of spin-orbit coupling in one-dimensional quasicrystals with power-law hopping