Coherent Optical Control of Electron Dynamics in Patterned Graphene Nanoribbons

TL;DR

The work addresses coherent control of electron dynamics in patterned graphene nanoribbons by using a periodic gate superlattice to flatten the valence and conduction bands and by applying optimally shaped linearly polarized driving pulses. It develops a two-band effective Hamiltonian under Peierls coupling and derives a Rabi-type driving term with on-resonant condition $\hbar\omega_{dr}=\Delta$, enabling collective Rabi oscillations that yield population inversion ($\pi$ pulse) and coherent superpositions ($\pi/2$ pulse) with measurable photocurrents. Time-resolved ARPES signatures are predicted to validate the dynamics, showing clearer coherence and inversion at larger gate voltages $U$ that flatten the bands. The approach offers a versatile solid-state platform for coherent electronics and potential quantum information processing in graphene nanoribbons, with applicability to other ribbon geometries and edge patterns.

Abstract

The field of coherent electronics aims to advance electronic functionalities by utilizing quantum coherence. Here, we demonstrate a viable and versatile methodology for controlling electron dynamics optically in graphene nanoribbons. In particular, we propose to flatten the band structure of armchair graphene nanoribbons via control electrodes, arranged periodically along the extended direction of the nanoribbon. This addresses a key mechanism for dephasing in solids, which derives from the momentum dependence of the energy gap between the valence and the conduction band. We design an optimal driving field pulse to produce collective Rabi oscillations between these bands, in their flattened configuration. As an example for coherent control, we show that these optimized pulses can be used to invert the entire electronic band population by a $π$ pulse in a reversible fashion, and to create a superposition state via a $π/2$ pulse, which generates an alternating photocurrent. Our proposal consists of a platform and methodological approach to optically control the electron dynamics of graphene nanoribbons, paving the way toward novel coherent electronic and quantum information processing devices in solid-state materials.

Figures (8)

• Figure 1: Patterned armchair graphene nanoribbon device. The periodically arranged gates (gray) introduce a one-dimensional superlattice, with lattice constant $a = \frac{3}{2}(N-1)a_0$, where $a_0 \approx 1.42\ \text{\AA}$ is the atom-atom distance and $N=7$ is the number of atoms along the finite direction of the nanoribbon. A zoom in of the unit cell of this superlattice is shown in the dashed orange box. The longitudinal photocurrent $I_{ph}$ can be coherently controlled by applying a laser pulse (red) which is linearly polarized at an optimal angle $\vartheta$.
• Figure 2: Band structure for different gate voltages. Low-energy bands for $U = 0\ V$ (a) and $U = 100\ V$ (b). (c) The band flatness $f$ of the two lowest-energy bands (red), calculated by Eq. (\ref{['eqn 4']}), as a function of the gate voltage.
• Figure 3: Dependence of the components of the effective Hamiltonian on the vector potential for $k=0$. In panel (a) we show $\delta H_{0,1\text{l}}$ and in panel (b) we show $\delta H_{0,z}$. The purple diagonal line indicates the optimal polarization angle Eq. (\ref{['eqn 17']}). (c) Components of the effective Hamiltonian for the optimal polarization angle and $k=0$. For small vector potentials $H_{0,y}$ is linear, $H_{0,z}$ and $H_{0,1\text{l}}$ are constant and $H_{0,x}$ is zero. The gate voltage is $U=100\ V$.
• Figure 4: Dependence of the optimal polarization angle (a) and the optimal factor $A_0$ (b) on the gate voltage.
• Figure 5: z-component of the Bloch vectors, $\left<\sigma_z\right>_k$, as a function of $k$ after applying a $\pi$ pulse (a) and after applying a $\pi/2$ pulse (b). For the simulation we use a pulse length of $\tau = 20\ fs$ (FWHM) and the optimal polarization angles and factors $A_0$ determined by Eq. (\ref{['eqn 17']}) and Eq. (\ref{['eqn 20']}), respectively. The driving frequencies are tuned to the band gaps which are around $\Delta \approx 1.11\ eV$ depending on the gate voltage, see Appendix \ref{['appendix A']}.