Lévy flight for electrons in graphene in the presence of regions with enhanced spin-orbit coupling

Abstract

We propose an electronic Lévy glass built from graphene nanoribbons in the presence of regions with enhanced spin-orbit coupling. Although electrons in graphene nanoribbons present a low spin-orbit coupling strength, it can be increased by a proximity effect with an appropriate substrate. We consider graphene nanoribbons with different edge types, which contain circular regions with a tunable Rashba spin-orbit coupling, whose diameter follow a power-law distribution. We find that spin-orbital clusters induce a transition from superdiffusive to diffusive charge transport, similar to what we recently reported for nanoribbons with electrostatic clusters [Phys. Rev. B. 107, 155432 (2023)]. We also investigate spin polarization in the spin-orbital Lévy glasses, and show that a finite spin polarization can be found only in the superdiffusive regime. In contrast, the spin polarization vanishes in the diffusive regime, making the electronic Lévy glass a useful device whose electronic transmission and spin polarization can be controlled by its Fermi energy. Finally, we apply a multifractal analysis to charge transmission and spin polarization, and find that the transmission time series in the superdiffusive regime are multifractal, while they tend to be monofractal in the diffusive regime. In contrast, spin polarization time series are multifractal in both regimes, characterizing a marked difference between mesoscopic fluctuations of charge transport and spin polarization in the proposed electronic Lévy glass.

References in corpus (11)

• The electronic properties of graphene
• Lévy walks
• Van der Waals heterostructures for spintronics and opto-spintronics
• Experimental evidence of chiral symmetry breaking in Kekulé-ordered graphene
• Detecting the spin-polarization of edge states in graphene nanoribbons
• Dirac wave transmission in Lévy disordered systems
• A Lévy flight for electrons in graphene: superdiffusive-to-diffusive transport transition
• Spin-to-Charge Conversion in 2D Electron Gas and Single-layer Graphene Devices
• Effect of proximity-induced spin-orbit coupling in graphene mesoscopic billiards
• Tailoring giant quantum transport anisotropy in disordered nanoporous graphenes
• Spin Hall angle in single-layer graphene

Cited by in corpus (3)

• Topological characterization of modified Kane-Mele-Rashba models via local spin Chern marker
• Coexistent multifractal mesoscopic fluctuations in Integer Quantum Hall Transition and in Orbital Hall Transition
• Noise-Assisted Metastability: From Lévy Flights to Memristors, Quantum Escape, and Josephson-based Axion Searches