Anomalous optical response of graphene on hexagonal boron nitride

Published in Materials
Anomalous optical response of graphene on hexagonal boron nitride
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Combination of hexagonal boron nitride (hBN) with graphene into van der Waals heterostructures1,2 attracted much attention recently. hBN is an insulator with a large bandgap that possesses honeycomb crystal structure commensurate to the one of graphene, but with a slight mismatch of the lattice constants. When assembled into such heterostructures in its high-quality single-crystal form, it provides a suppression of external disorder in graphene and an enhancement of electron mobilities. Therefore, it has been proven to be a supreme substrate, encapsulator and tunneling barrier in graphene-based electronic devices. Likewise, hBN happen to be an irreplaceable constituent in graphene-based optoelectronic devices, such as photodetectors, DUV electroluminescent devices, THz optoelectronic elements, and light bulbs. From the standpoint of optical properties, the influence of hBN substrate or encapsulation on intrinsic optical response of an almost transparent graphene in visible spectral range yet remains undetermined. Here, we present an experimental study of optical properties of graphene on hBN substrates by imaging spectroscopic ellipsometry demonstrating an emergence of anomalous optical constants from its monolayer and comparing our results with the ones on one of the standard substrates (SiO2/Si). 

Highly sensitive imaging spectroscopic ellipsometry of graphene on hBN substrates

We used imaging spectroscopic ellipsometry technique to characterize the optical response of our graphene monolayers on hBN using the schematics presented in Figure 1 (a). The sensitivity of our technique3 allows us to study exfoliated and dry-transferred flakes in miniature regions of interest (~10 μm2). To obtain the dielectric function of graphene from the acquired ellipsometric spectra, we used the Drude-Lorentz oscillators model, which considers the optical response of quasi-free electrons, and graphene’s van Hove singularity for π-to-π* interband transitions. The determined real Re[ε] and imaginary Im[ε] parts of the dielectric function of our graphene monolayers are shown in Figure 1 ((b) and (c)). To further enhance the sensitivity of our spectroscopic imaging technique, we assembled a specific configuration of layers giving a rise to a larger difference in optical responses from the substrate with and without graphene layer, and therefore, to a higher sensitivity of ellipsometric parameters to graphene’s optical constants. This was achieved in the vicinity of topological phase singularities (TPS)4, which arise owing to the intersection of graphene optical constant’s dispersion with the substrate zero-reflection surface. We transferred ~ 152 nm thick graphene/hBN heterostructure on top of 200 nm Au film to ensure an appropriate formation of a cavity (see Figure 1 (e)) producing TPS in the vicinity of our ellipsometer’s best sensitivity (around ~ 500 nm). As a result, it allowed us to make a unique fit of the optical absorption of our graphene monolayer and calculate the difference between evaluated and measured ellipsometry spectra with respect to graphene’s absorption in terms of mean squared error (MSE). Figure 1 (f) shows the resulting dependence. Surprisingly, it reaches a minimum at values larger than πα, where α is the fine structure constant5. This suggests that the typical values of graphene’s absorption can therefore be mended on hBN substrates. The corresponding dependences of ellipsometric parameters on wavelength in the vicinity of our TPS are demonstrated in Figure 1 (g).

Figure 1| Imaging spectroscopic ellipsometry of monolayer graphene on hBN substrate. (a) Schematic illustration of the measurement setup. Real (b) and imaginary (c) parts of the obtained dielectric function of monolayer graphene on hBN/glass substrate. (e) Schematic illustration along with 50X optical image of monolayer graphene on hBN/Au substrate for highly sensitive ellipsometry. Dashed lines are a guide to an eye emphasizing graphene flake boundaries. (f) Evaluated (solid line) and measured (grey pentagons) mean squared error (MSE) dependence on the absorbance of monolayer graphene. (g) Ellipsometric parameters Ψ and Δ at 50° angle of incidence near the topological phase singularity (~ 477 nm). Solid lines represent the measured parameters. Dashed lines correspond to the evaluated ones.

Optical constants of graphene on hBN substrates

Acquired dependencies of refractive indices, extinction coefficients, and intrinsic absorbance of our graphene samples on hBN substrates in comparison with literature data6,7,8 (graphene on SiO2/Si) are shown in Figure 2. Despite the non-identical fitting approaches, all works report on universal optical responses for graphene on SiO2/Si, including our measurements. On the other hand, graphene on hBN demonstrates substantially higher optical constants. Its refractive index and extinction coefficient are about 20 % and 40 % higher on hBN than on SiO2/Si. In the case of an excitonic peak at 270 nm, the obtained behaviour can be explained by significant difference in static dielectric permittivities of SiO2 (εSiO2 ~ 3.8) and hBN (εhBN ~ 7), which strongly affects the excitonic response. The situation in visible-to-nearinfrared range is more complicated since we observed substantial enhancement of absorption by about 60 %. We attribute this behaviour to electron-electron interactions arising due to high static dielectric response of hBN. 

Figure 2| Optical constants of monolayer graphene on hBN and SiO2/Si substrates. (a) Refractive indices, (b) extinction coefficients, and (c) intrinsic absorbance A vs wavelength.

From a broader perspective, our studies reveal that the universal optical absorption of pristine graphene can be reconstructed in the dielectric environment.

Check out our manuscript at https://www.nature.com/articles/s42005-023-01129-9for more information.

References

  1. Novoselov, K. S., et al. 2D materials and van der Waals heterostructures. Science 353, 6298 (2016)
  2. Yankowitz, M., et al. Van der Waals heterostructures combining graphene and hexagonal boron nitride. Nature Reviews Physics 1, 112-125 (2019).
  3. Ermolaev, G. A., et al. Giant optical anisotropy in transition metal dichalcogenides for next-generation photonics. Nature Communications 12, 854 (2021).
  4. Ermolaev, G. A., et al. Topological phase singularities in atomically thin high-refractive-index materials. Nature Communications 13, 2049 (2022).
  5. Katsnelson, M. I. & Kat︠snel′son, M. I. Graphene: Carbon in Two Dimensions. Cambridge University Press (2012)
  6. Kravets, V. G., et al. Spectroscopic ellipsometry of graphene and an exciton-shifted van Hove peak in absorption. Physical Review B: Condensed Matter 81, 155413 (2010).
  7. Matković, A., et al. Spectroscopic imaging ellipsometry and Fano resonance modeling of graphene. Journal of Applied Physics 112, 123523 (2012).
  8. Weber, J. W., et al. Optical constants of graphene measured by spectroscopic ellipsometry. Applied Physics Letters 97, 091904 (2010).

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