[Paper Review] A new phenomenon in graphene: The pseudospinorial Zitterbewegung

L. Diago‐Cisneros, Eduardo Serna+2 more|arXiv (Cornell University)|Oct 17, 2020

Graphene research and applications27 references4 citations

TL;DR

This paper proposes a novel pseudospinorial Zitterbewegung effect (PZBE) in monolayer graphene, arising from Dirac fermion dynamics under Rashba spin-orbit coupling. Using a custom nano-spintronic device model, it numerically demonstrates tunable, anti-phase oscillations in sub-lattice probability densities with a femtosecond decay time, including evidence of perfect Klein tunneling and anti-Klein backscattering in a single simulation—highlighting the PZBE's controllability via momentum and pseudospin configuration.

ABSTRACT

We foretell a new pseudospin-dependent phenomenon in mono-layer graphene (MLG), which is numerically simulated \emph{via} an innovator nano-spintronic device. We proposed a novel theoretical procedure for describing the dynamics of Dirac fermions, departing from classic theoretical modelling. More importantly, we have found appealing evidences of wiggling anti-phase oscillations in the probability density time-distribution for each sub-lattice state, which we called pseudospinorial Zitterbewegung effect (PZBE). The PZBE undergoes modulated by a robust transient character, with decay time of femtoseconds. Interestingly, several features of the PZBE become tunable, even up to fully vanishing it at the vicinity of the Dirac points, as well as for a symmetric pseudospin configuration. We have observed evidences of perfect Klein tunneling and perfect anti-Klein backscattering in a single simulation, which is unprecedented for Q1D-MLG, as far as we know.

Motivation & Objective

• To investigate the dynamics of Dirac fermions in monolayer graphene under Rashba spin-orbit interaction (SOI-R), a key challenge in graphene spintronics.
• To explore whether the pseudospinorial Zitterbewegung effect (PZBE) emerges as a distinct phenomenon in graphene, given its theoretical roots in relativistic quantum mechanics.
• To determine if SOI-R induces detectable traces on the Zitterbewegung effect and under-barrier scattering in graphene.
• To develop a novel theoretical and numerical framework for simulating PZBE in a quasi-one-dimensional graphene quantum well.
• To demonstrate the tunability and controllability of PZBE features, including its complete suppression near Dirac points.

Proposed method

• A theoretical model based on the Buresch-Rashba Hamiltonian is employed to describe Dirac fermion dynamics in a quasi-one-dimensional monolayer graphene nanoribbon.
• The system is simulated using a custom nano-spintronic device setup, incorporating SiO₂ substrate and hexagonal boron nitride (hBN) to enable localized Rashba spin-orbit coupling.
• Time-dependent simulations track the probability density evolution of wave packets on each sub-lattice (A and B), revealing anti-phase oscillations characteristic of PZBE.
• The simulation includes a potential barrier with tunable height and width to probe scattering behavior, including Klein tunneling and backscattering.
• Finite-difference numerical methods are applied to solve the time-dependent Dirac equation, with careful handling of boundary effects to minimize artifacts.
• The initial wave packet is prepared in a pseudospin superposition state (e.g., ξ = [1, i]ᵀ) to excite sub-lattice oscillations and probe PZBE.

Experimental results

Research questions

• RQ1 Does a pseudospinorial Zitterbewegung effect (PZBE) emerge in monolayer graphene under Rashba spin-orbit coupling?
• RQ2 How does the PZBE frequency and decay time depend on momentum and pseudospin configuration near Dirac and Γ points?
• RQ3 Can the PZBE be fully suppressed or tuned by adjusting the initial pseudospin state or wave vector?
• RQ4 What is the role of Rashba spin-orbit interaction in enabling or modifying the PZBE and related scattering phenomena?
• RQ5 Is perfect Klein tunneling and perfect anti-Klein backscattering simultaneously observable in a single quasi-one-dimensional graphene simulation?

Key findings

• The PZBE exhibits a robust transient character with a decay time of approximately 10.5 femtoseconds across all simulated conditions.
• The frequency of PZBE oscillations increases as the wave vector approaches the Γ point, while the group velocity decreases toward zero.
• The PZBE can be fully suppressed near the Dirac points (K and K') and for symmetric pseudospin configurations, indicating high tunability.
• Simultaneous evidence of perfect Klein tunneling and perfect anti-Klein backscattering is observed in a single simulation, a phenomenon not previously reported in quasi-one-dimensional graphene.
• Anti-phase oscillations in the probability density on sub-lattices A and B are numerically confirmed as the defining signature of the PZBE.
• The simulation reveals that the PZBE is sensitive to both the initial pseudospinor state and the strength of Rashba spin-orbit coupling, enabling control over its amplitude and persistence.