Non-van der Waals 2D materials and where to find them

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The stoichiometric composition and crystal structure dictates the classification of layered and natural materials into graphene, transition metal di (mono) chalcogenide, sulfosalt, oxide, neo-, phyllo- silicate, and phosphate families. Alternatively, those can be classified based on the feasibility of their exfoliation into separate atomic layers. An energy, which is required for the isolation (or separation) of a singular atomic layer from its bulk would be the quantitative measure of the corresponding feasibility. Within this approach, it is reasonable to distinguish naturally-, potentially- exfoliable and robust materials with threshold exfoliation energies1 of  10 meVÅ-2, 100 meVÅ-2, and 1000 meVÅ-2. Originating within potentially exfoliable ones, the materials lacking the out-of-plane van der Waals bonds in their crystal structure are of particular interest. Those form bonds of a different nature, e.g., covalent, but of comparable strengths and bear the name of non-van der Waals materials. 

Non-van der Waals InGaS3

InGaS3 exhibits a hexagonal arrangement of III-III-IV group elements in P65 space group with lattice parameters of a = b = 6.6 Å and c = 17.9 Å, and appears with yellow-to-lustrous grey shades as displayed in Figure 1 (a). It contains various structural bonds, whose strengths can be estimated by first-principle calculations based on the density functional theory. To obtain energies required for the isolation of individual atomic layers, one can estimate the differences among the ground-state energy of relaxed structure and all of its unrelaxed states. Afterwards, seek for planes with minimal binding energies to determine potentially breakable, or in our case, exfoliable directions. Excluding relaxation energies along the c-axis, we found the exfoliation energy of Eexf ≈ 53 meVÅ-2 for planes shown in Figure 1 (b). Our results suggest an emergence of authentically delicate out-of-plane covalent bonds within the unit cell, and, consequently, a generation of artificial layered structure. This value locates alongside the evaluated exfoliation energies of conventional van der Waals materials (see Figure 1 (c)). Notably, the exfoliation energies of known non-van der Waals materials are of larger dispersion.

Figure 1| Crystal structure and interplane binding energies of non-van der Waals InGaS3. (a) 5X optical micrograph of bulk crystal on a glass slide. Inset: Top and side views of P65 space group hexagonal crystal structure with lattice constants of a = b = 6.6 Å, c = 17.9 Å. (b) Schematic representation of artificially generated layered structure achieved by cutting off the delicate non-van der Waals bonds along minimal energy atomic plane. UC stands for the unit cell, 1L for the monolayer. (c) Exfoliation energies of conventional van der Waals (black pentagons) and known non-van der Waals (red pentagons) materials evaluated by density functional theory. The green hexagon presents the evaluated exfoliation energy along the minimal energy atomic plane.

2D layers of InGaS3 

Typically, atomic layers of non-van der Waals materials are produced by means of vigorous sonication-assisted2 and cation-intercalation3 exfoliation methods. Nevertheless, an introduction of slightly elevated temperature treatment to the standard4 scotch-tape exfoliation (see Figure 2(a)) allows obtaining two-dimensional layers of InGaS3. Figure 2 (b-d) demonstrate AFM scans of our pristine flakes with nearly atomically smooth surfaces (RMS roughness of 0.3 nm).

Figure 2| Mechanical exfoliation of non-van der Waals InGaS3. (a) Optical micrograph of typical mechanical exfoliation procedure on Si/SiO2 substrate. (b) AFM topographical scan for 3L (5.53 ± 0.32 nm) and 4L (7.3 ± 0.34 nm) thick InGaS3 flakes. Height profile is taken along white dashed line. (c) Same as (b), but for a magnified region marked by dashed rectangle in panel (b) showing atomic strips with thicknesses of 1L (1.74 ± 0.24 nm) and 2L (3.6 ± 0.28 nm). Height profile is taken along white dashed line.

Anisotropic optical properties of non-van der Waals InGaS3

The studies of anisotropic dielectric tensor reveal material’s wide bandgap (2.73 eV), high refractive index (> 2.5), negligible losses, and a birefringence of Δn ~ 0.1 in the visible and infrared spectral ranges (see Figure 3(a)). The non-van der Waals interaction reduces the latter to a relatively small value in contrast to the huge anisotropy of Δn ~ 1.5 observed in transition metal dichalcogenides5 with natural van der Waals bonds. It is also present in our first-principle density functional theory calculations (see inset of Figure 3 (b)). Furthermore, our technique, which combines spectroscopic ellipsometry with density functional calculations unambiguously confirms the hexagonal structure of InGaS3 since the dielectric response is a fingerprint of material's electronic bandstructure.

Figure 3| Imaging spectroscopic ellipsometry of non-van der Waals InGaS3. (a) Experimental and (b) first-principle refractive indices and extinction coefficients for ab-plane (straight line) and c-axis (dashed line) of commensurate values and trends validating the hexagonal structure of InGaS3. Insets: material’s birefringence. The optical responses from four flakes were simultaneously recorded and analysed to ensure the high precision and reproducibility of our results (h = 3.6 nm, 68.5 nm, 103.0 nm, and 277.4 nm).

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  1. N. Mounet, et al., Nature Nanotechnology 13, 246-252 (2018).
  2. B. A. Puthirath, et al., Nature Nanotechnology 13, 602-609 (2018).
  3. J. Peng, et al., Nature Chemistry 13, 1235-1240 (2021).
  4. K. S. Novoselov, et al., Science 353, 6298 (2016).
  5. G. A. Ermolaev, et al., Nature Communications 12, 854 (2021).

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