First-principle investigation of the electronic structure and optical properties of graphene/boron nitride lateral heterostructures

TL;DR

This work dissects graphene/BN armchair lateral heterostructures (AGBNs) to reveal how the graphene width $N$ governs both ground-state electronic structure and optical response. By combining DFT, G$_0$W$_0$, TD-DFT, and a tight-binding ladder model, the authors show that the gap organizes into three families $N=3m$, $N=3m+1$, $N=3m-1$, with GW corrections following family-specific linear trends, and that BN interface effects renormalize gaps relative to isolated ribbons. Near-gap states remain graphene-centric with limited BN hybridization, while the interface breaks transverse symmetry and activates additional optical transitions, yielding a richer absorption spectrum than that of the constituent ribbons. The results connect ground-state properties to spectra via interpretable models, offering a framework for predicting absorption features and guiding future studies on excitons and defects in Gr/hBN lateral heterostructures.

Abstract

We investigate the electronic and optical properties of lateral heterostructures made of alternated armchair ribbons of graphene and hexagonal boron nitride. It is known that the gapwidth of these heterostructures can be classified into three families depending on the width of the graphene part. Here, by employing ab initio methods (standard and time-dependent density functional theory and GW), we demonstrate that such classification still holds for other electronic states close to the gap. We show that they display trends substantially different from those known for the gapwidth and originate family-specific features in the screening properties and optical absorption spectra (peak energy and intensity). In addition, our use of a tight binding model originally introduced for isolated nanoribbons allows us to discuss some crucial heterostructure's properties in view of those of its isolated building blocks, including charge redistribution at the edges, gap hierarchy inversion, and specific optical selection rules. By bridging the electronic structure to optical absorption spectra in a comprehensive set of systems, this study sets the stage for more refined investigations on the absorption properties of graphene/boron nitride lateral heterostructures.

Figures (12)

• Figure 1: a: AGBN composed of graphene nanoribbons with $N$=5 (brown sticks) and hBN nanoribbons with $L$=9 (green-and-grey sticks). The mirror symmetry plane (m) is reported with a red solid line. Row indexes are also reported as $1 \le j \le$$N$ in the graphene ribbon, and $1 \le i \le$$L$ in the BN ribbon. b: AGBN with $N$=6 and $L$=9. A dashed red line indicates the glide symmetry plane ($\bar{b}$/2). Notable interatomic distances after relaxation are reported. In both panels, the simulation cell is reported as a solid black rectangle as well as the Cartesian reference indicating the perpendicular $x$ and the ribbon (parallel) $y$ axes.
• Figure 2: Voronoi deformation density analysis reporting the integrated charge of each atom (green for B, brown for C and grey for N). Excess and missing charges with respect to the nominal one are indicated below each atom.
• Figure 3: a: Evolution of the DFT gap of AGBN as a function of graphene size $N$ (black symbols) and G$_0$W$_0$ corrections (magenta diamonds). Dotted lines are guide for the eyes distinguishing the three families (circles for $N=3m-1$, triangles for $N=3m$ and squares for $N=3m+1$). The size of BN ribbons is either $L$=8 for $N$ even or $L$=9 for $N$ odd. b: DFT (solid black) and G$_0$W$_0$ (dashed magenta) band structure close to the gap in the reference heterostructure. Notable states at $\Gamma$ are highlighted with blue tics. c: G$_0$W$_0$ corrections to the gap versus DFT gapwidth. Dashed lines highlight a linear fit for each family. Angular coefficients $a_t$ are reported where $t\in\{0,+1,-1\}$ labels the family.
• Figure 4: Density of states of AGBN with different $N$ and $L=8$. All curves are aligned with TV at 0 eV.
• Figure 5: a: DFT band structure of the $N=5$ heterostructure projected onto the $\pi$ orbital components centered on C atoms (C$_\pi$ states). The circle size is proportional to the projected weight. Dashed lines indicate the band structure of the isolated Gr nanoribbon with $N$=5. b,c: The same as a for B$_\pi$ and N$_\pi$ states. Dashed lines are from the isolated BN ribbon with $L$=5. The shaded area corresponds to the DFT gapwidth of the isolated hBN monolayer. Green and red arrows highlight the expected and unexpected hybridization with C states at the interface. d: Electronic probability density |$\Psi$($\mathbf{r}$)|$^2$ at $\Gamma$ of the states TV and BC (top panels), TV$-$1 and BC+1 (middle panels), TV$-$3 and BC+3 (bottom panels) in the $N=5$ AGBN with its mirror symmetry plane marked as a red solid line. e, f, g, h: The same as panels a, b, c and d but in the $N=6$ heterostructure. In d, the glide symmetry plane is marked with a dashed red line.