Topology-Scaling Identification of Layered Solids and Stable Exfoliated 2D Materials

The Materials Project crystal structure database has been searched for materials possessing layered motifs in their crystal structures using a topology-scaling algorithm. The algorithm identifies and measures the sizes of bonded atomic clusters in a structure’s unit cell, and determines their scaling with cell size. The search yielded 826 stable layered materials that are considered as candidates for the formation of two-dimensional monolayers via exfoliation. Density-functional theory was used to calculate the exfoliation energy of each material and 680 monolayers emerge with exfoliation energies below those of already-existent two-dimensional materials. The crystal structures of these two-dimensional materials provide templates for future theoretical searches of stable two-dimensional materials. The optimized structures and other calculated data for all 826 monolayers are provided at our database (https://materialsweb.org).

Figure 1

Examples of structure types that challenge the search for layered materials by exhibiting (a) layers along an axis other than the $c$ axis, (b) corrugated layers, (c) thick layers, and (d) molecular (nonbonded) layers. Each of these examples is correctly classified with the present method.

Figure 2

Schematic of the topology-scaling algorithm. The black circle (bottom left in each frame) represents a cluster of bonded atoms in a given crystal structure’s unit cell. The colored circles represent the seven periodic images of the same cluster for a $2\times 2\times 2$ supercell of the original cell. The periodic images are either bonded to one another in (a) zero, (b) one, (c) two, or (d) three dimensions, defining the dimensionality of the structural motifs.

Figure 3

Distribution of (a) stoichiometries of the 826 layered compounds, and comparison of the compositional complexity among (b) the stable layered materials identified by this work and (c) all materials in the Materials Project database [15]. The top 5 stoichiometries ($ABC$, $A{B}_2$, $AB$, $A{B}_3$, and $AB{C}_2$) represent half of all compounds. In general, the relative abundance of a given stoichiometry scales inversely with the formula’s complexity. We observe that the percentage of binary compounds among layered materials is significantly higher than among all materials, suggesting that binary compounds (one cation and one anion) are particularly conducive to creating interlayer dispersion interactions.

Figure 4

Side views of the 15 unique structural templates identified for monolayers of $AB$ stoichiometry, labeled according to prototypical compounds possessing that crystal structure. The symmetries of structures (a) and (b) are related by a broken inversion symmetry, in the same way that the well-known 1T and 2H monolayer structures are related. Other structural pairs, such as (e),(f) and (h),(i) and (j),(k), are related to one another by simple buckling distortions.

Figure 5

Histogram of calculated exfoliation energies for all 826 layered materials compared to the range of calculated exfoliation energies for already synthesized 2D materials. Because of their relatively weak interlayer forces, most compounds found in our search exhibit low exfoliation energies ($<100\mathrm{meV}/\mathrm{atom}$), indicating the ease of exfoliation.

Figure 6

Side views of monolayers for the five elemental layered materials in the Materials Project database [15].

Figure 7

(a) Half-metallic band structure and (b) spin-polarized density of states for 2D ${\mathrm{FeCl}}_2$. The minority spin state is metallic (dashed red) and the majority state (solid blue) has a band gap of 4.4 eV.