Laser-induced topological phases in monolayer amorphous carbon

Abstract

Driving non-topological materials out of equilibrium using time-periodic perturbations, such as circularly-polarized laser light, is a compelling way to engineer topological phases. At the same time, topology has traditionally only been considered for crystalline materials. Here we propose an experimentally feasible way of driving monolayer amorphous carbon topological.We show that circularly polarized laser light induces both regular and anomalous edge modes at quasienergies $0$ and $\pm π$, respectively. We also obtain a complete topological characterization using an energy- and space-resolved topological marker based on the spectral localizer. Additionally, by introducing atomic coordination defects in the amorphous carbon, we establish the importance of the local atomic coordination in topological amorphous materials. Our work establishes amorphous systems, including carbon, as a versatile and abundant playground to engineer topological phases.

Figures (7)

• Figure 1: Schematic representation of a circularly polarized laser beam with field $\boldsymbol{\mathrm{A}}(t)$ on a monolayer amorphous carbon to engineer topological phases.
• Figure 2: (a) Quasienergy spectrum $E_m$ as a function of eigenstate index $m$ for crystalline graphene. Color encodes the IPR of the given state. Insets I1 and I2 show zoomed-in spectra close to $E=0$ and $\pi$, respectively. (b,c) Spatially resolved LDOS associated with states at quasienergy gaps $0$ and $\pi$, respectively. (d-f) Repeats (a-c) but for monolayer amorphous carbon. Here $A=2.5$, $\Omega=2.0$. For LDOS computation, we use a quasienergy window of $[-0.3,0.3]$ in $0$-gap and $[\pm \Omega/2, \mp 0.1]$ in the $\pi$-gap. Number of atoms in (a-c) is $1526$ and in (d-f) is $1442$.
• Figure 3: Average Chern numbers (a) $\bar{C}_0$ and (b) $\bar{C}_\pi$ as a function of driving amplitude $A$ and frequency $\Omega$ for crystalline graphene. Number of atoms in (a-b) is $880$. (c-d), Repeats (a-b) for monolayer amorphous carbon. Green lines indicate regions with a finite variance of the Chern numbers. Orange star marks parameters used in Fig. \ref{['Fig:Polycrystalline']}. Averages of $C_{x,y,E}$ in each sample are calculated using a $7 \times 7$ square in the center of the system, and $30$ different amorphous configurations are sampled with a system consisting of $837$ atoms.
• Figure 4: (a) TDOS as a function of the fraction of fourfold-coordinated sites $n_4$ in driven monolayer amorphous carbon averaged over $50$ random configurations of merging bonds, with all other parameters same as Fig. \ref{['Fig:Polycrystalline']}. Green line indicates the $n_4$ used in (b,c). (b) LDOS and (c) Chern number $C_0$ for the $0$-gap as a function of the system's dimension. For LDOS computation, we use a quasienergy window of $[0.2,0.3]$ in $0$-gap.
• Figure S1: (a) [(c)] Spatially resolved normalized localizer gap $\sigma_{\rm N}$ and (b) [(d)] Chern number $C_{x,y,E=0}$ [$C_{x,y,E=\pi}$] computed at $E=0$ [$\pi$] for driven crystalline graphene. (e-h) Repeats (a-d), but for driven monolayer amorphous carbon. Parameters are the same as Fig. 2 in the main text.