Floquet Control of Electron and Exciton Transport in Kekulé-Distorted Graphene

This work investigates the Floquet dynamics of electrons and excitons (particle-hole pairs) in a Dirac material referred to as Kekulé-distorted graphene. Specifically, we examine the role played by a high frequency driving electromagnetic field on the tunneling and blocking by a potential barrier on both the charged single particles as well as the neutral composite particles. We demonstrate that the small effective masses of the electron and hole for the energy spectrum of this Kekulé distorted graphene leads to practically almost perfect transmission across a symmetric potential barrier for any angle of incidence of impinging excitons. However, this unexpected Klein paradox for excitons does not hold for the single-particle electrons. The reduced total transmission of electron due to Kekulé distortion is more suppressed due to irradiation. Additionally, we calculate and investigate the exciton binding energy since the quantum tunneling of a bound electron-hole pair across a potential barrier is governed by its mass measured in the center of mass and binding energy of the composite pair. Thus, irradiation with circularly polarized light fundamentally modifies exciton formation, coherence and transport properties, thereby producing unusual topological behaviors. These behaviors are unlike conventional Dirac materials. Possible technical applications of the results arising from our investigation include valleytronics due to the folding of the valleys, thereby making intervalley coupling feasible. Other practical applications include optoelectronics due to Floquet tuning of energy spectrum and transport properties.

💡 Research Summary

This paper presents a comprehensive Floquet‑theory study of charge‑carrier and exciton transport in Kekulé‑Y distorted graphene (Kek‑Y graphene) under high‑frequency circularly polarized light. The authors first derive the low‑energy Hamiltonian for Kek‑Y graphene, which contains two inequivalent Dirac cones folded onto the same Γ point. The cones possess different Fermi velocities, vF(1 ± Δ0), where Δ0 is a strain‑induced coupling parameter (typically 0.1–0.2). The resulting eigen‑energies εY(s,τ|k,Δ0)=s ℏvF(1+τΔ0)k (s = ±1 for conduction/valence, τ = ±1 for the “fast” and “slow” cones) give rise to a zero Berry phase, distinguishing this system from pristine graphene.

Next, the system is driven by a high‑frequency electromagnetic wave described by a vector potential A(t). Using the Floquet‑Magnus expansion in the high‑frequency limit (ℏΩ ≫ ε), the authors obtain an effective static Hamiltonian H_eff that contains a light‑induced mass term C and a dynamical gap Δ_gap≈2ℏΩ ζ² β(1 ± Δ0²), where ζ = −e vF E0/ℏΩ² measures the light intensity, β encodes the polarization (β = 1 for circular), and θp is the polarization angle. The gap opens at the Dirac point and makes the band structure anisotropic in kx and ky.

The paper then analyses quantum tunnelling through a rectangular potential barrier (height V0, width w) and a δ‑function barrier. Matching wavefunctions at the interfaces yields transmission probabilities for electrons, T_e(θ), that depend on the incident angle θ, the strain parameter Δ0, and the light parameter ζ. For normal incidence (θ = 0) Klein tunnelling remains perfect, but for oblique angles the transmission is strongly suppressed as Δ0 or ζ increase. Conductance σ(μ) is calculated by integrating T_e over angles and energies, showing that increasing light intensity reduces σ, yet a non‑monotonic recovery appears at certain parameter regimes, indicating a Floquet‑engineered conductance modulation.

A central result concerns excitons, i.e., bound electron‑hole pairs formed in the gapped Kek‑Y system. The exciton’s centre‑of‑mass mass m_CM≈(m_e+m_h)/2 and binding energy E_b are functions of the effective masses of the individual carriers, which are themselves set by Δ0 and the Floquet‑induced gap. Light‑induced gap reduces the effective masses and weakens the binding, making the exciton lighter. The tunnelling probability for an exciton, T_X, is derived from the composite wavefunction and depends inversely on m_CM and E_b. Because m_CM becomes very small, T_X≈1 for essentially any incident angle—an “exciton Klein paradox”. Thus, while electrons experience reduced transmission under Floquet driving, excitons retain near‑perfect transmission across the barrier.

The authors also discuss valley‑tronic implications. The folding of the two Dirac cones enables intervalley coupling that is otherwise negligible in pristine graphene. The light‑controlled gap and the strain‑induced Δ0 allow tuning of the intervalley mixing, opening pathways for valley filters, switches, and logic elements. Moreover, the ability to modulate exciton formation and coherence with light suggests applications in excitonic optoelectronics and quantum information platforms.

In conclusion, the paper demonstrates that (i) Kekulé‑Y distortion creates two Dirac cones with distinct velocities and a zero Berry phase; (ii) high‑frequency circularly polarized light introduces a dynamical mass and a small gap, suppressing electron transmission but preserving normal‑incidence Klein tunnelling; (iii) excitons in this system exhibit almost angle‑independent perfect transmission, a striking contrast to single‑particle behavior; and (iv) Floquet engineering provides a versatile toolbox for controlling valley degrees of freedom, exciton binding, and transport, pointing to novel valleytronic and optoelectronic devices.