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

TL;DR

This work develops a Floquet framework for Kek-Y graphene to study electron and exciton transport across barriers under high-frequency driving. It derives a low-energy Hamiltonian with folded Dirac cones and constructs a Floquet effective Hamiltonian under elliptically/circularly polarized irradiation, revealing dynamical gaps and valley-dependent transport. The study shows that excitons, due to their extremely light center-of-mass mass, tunnel with near-unit probability across barriers, while irradiation can sustainably suppress electron transmission and induce anisotropic, valley-mixing transport; normal-incidence Klein tunneling persists for moderate drives. Collectively, these results demonstrate Floquet engineering as a powerful tool to control transport, with implications for valleytronics and optoelectronic applications in 2D Dirac materials.

Abstract

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.

Figures (11)

• Figure 1: (Color online) Kekulé distorted honeycomb lattice (left) and pictorial representation of two Dirac cones (right) of Kek-Y distorted graphene .
• Figure 2: (Color online) Energy dispersions $\varepsilon_Y(s,\tau\,\vert\,k, \Delta_0)$ for Kek-Y graphene represented by two inequivalent Dirac cones with different Fermi velocities $\upsilon_{F,1}$ and $\upsilon_{F,2}$ corresponding to $\upsilon_F (1 \pm \Delta_0)$ .
• Figure 3: (Color online) Energy dispersions $\varepsilon_Y(s,\tau\,\vert\,k, \Delta_0)$ for Kek-Y graphene under normal incident circularly polarized irradiation (i.e., $\theta_p =0$, $\beta = 1$) represented by two inequivalent Dirac cones with different Fermi velocities $\upsilon_{F,1}$ and $\upsilon_{F,2}$. Plots in (a) are along $k_x$ and plots in (b) are along $k_y$. The energy bands are anisotropic along two perpendicular momentum directions . In each plot, the dispersion close to the Dirac points are focused, which shows the opening of band gaps and vertical separation of the valleys. These results are for light irradiation with frequency of 100 THz, $\Delta_0 =0.2$ and $\tilde{\zeta} = 0.1$.
• Figure 4: (Color online) Schematics of electron transmission through potential barrier in Kek-Y graphene. The inner red and outer green cone represent the fast and slow cone or $\tau_+$ and $\tau_-$ valley respectively. The Dirac electron $e^+_i$ from $\tau_+$ valley in incident region is incident to the barrier at $x=0$ from left with incident angle $\theta_{k^+}$. This electron crosses the barrier of width $d$ and height $V_0$ and transmit to the transmission region as a $\tau_+$ valley electron $e^+_t$ with angle of transmission $\theta_{k^+}$ and probability $\cal T_{++}$ or as a $\tau_-$ valley electron $e^-_t$ with angle of transmission $\theta_{k^-}$ and probability $\cal T_{+-}$ such that the total probability of transmission $\cal T = \cal T_{++} + \cal T_{+-}$. $e^+_r, e^-_r$ are reflected electrons through the barrier with angle of reflection $\pi-\theta_{k^+}$ and $\pi-\theta_{k^-}$ as a $\tau_+$ valley and $\tau_-$ valley electrons respectively. $e^+_a$ and $e^-_a$ are the forward moving electron at $x=0$ in scattering region through $\tau_+$ valley and $\tau_-$ valley making angles $\theta_{q^+}$ and $\theta_{q^-}$ respectively. Similarly, $e^+_b$ and $e^-_b$ are the backward moving electron at $x=d$ in scattering region through $\tau_+$ valley and $\tau_-$ valley making angles $\pi-\theta_{q^+}$ and $\pi- \theta_{q^-}$ respectively.
• Figure 5: (Color online) Valley resolved angular transmission of monolayer Kek$-$Y graphene through a potential barrier of uniform height. Polar plots (a), (b), (c) and (d) in the upper panel are for barrier width $d$ equal $300a, 600a, 1200a$ and $2400a$, respectively, with Kekulé parameter $\Delta_0 = 0.2$. Plots (e), (f), (g) and (h) in the lower panel are for undistorted graphene with $\Delta_0 = 0$ with corresponding barrier width, in the absence of irradiation. Here, $a = 2.46 \AA$ is the lattice constant of graphene. The energy of the incident particle is $\varepsilon_Y = 0.028$eV and the potential height is $V_0 = 3 \varepsilon_Y$. The notation ${\cal T}_{++}$ represents the intravalley transmission from the $\tau_+$ valley to $\tau_+$ valley while ${\cal T}_{+-}$ represents the intervalley transmission from the $\tau_+$ valley to the $\tau_{-}$ valley. The total transmission is ${\cal T} ={\cal T}_{++}+{\cal T}_{+-}$. For undistorted graphene in the lower panel, the transmission is through only one valley. Klein tunneling at normal incidence is preserved in both distorted and undistorted graphene.