Discovering two-dimensional magnetic topological insulators by machine learning

Topological materials with unconventional electronic properties have been investigated intensively for both fundamental and practical interests. Thousands of topological materials have been identified by symmetry-based analysis and ab initio calculations. However, the predicted magnetic topological insulators with genuine full band gaps are rare. Here we employ this database and supervisedly train neural networks to develop a heuristic chemical rule for electronic topology diagnosis. The learned rule is interpretable and diagnoses with a high accuracy whether a material is topological using only its chemical formula and Hubbard $U$ parameter. We next evaluate the model performance in several different regimes of materials. Finally, we integrate machine-learned rules with ab initio calculations to high-throughput screen for magnetic topological insulators in a 2D material database. We discover six new classes (15 materials) of Chern insulators, among which four classes (seven materials) have full band gaps and may motivate for experimental observation. We anticipate the machine-learned rule here can be used as a guiding principle for inverse design and discovery of new topological materials.

Figure 1

Heuristic chemical rule diagnosis and DFT discovery of topological materials. (a) The topogivity-based heuristic diagnosis of a given material is evaluated by weighting the material's elements' topogivities ${\tau }_E$ with $\mathcal{F}(f_E,U_E)$, where $\mathcal{F}(f_E,U_E)$ is determined by element's fraction $f_E$ in the chemical formula and Hubbard parameter $U_E$. The high-throughput search for topological materials is performed by rapid heuristic rule screening through the material database to get candidate topological materials, and then followed by DFT calculations [66]. (b) Schematic of the ML workflow and structure of CNN, where the heuristic chemical rule is learned with both nonmagnetic and magnetic materials as input.

Figure 2

Periodic table of ML topogivities ${\tau }_E$ and combinatorial weight $\mathcal{F}(f,U)$. ${\tau }_E$ are shown by color coding and in values. Elements that appear less than 15 times in the labeled dataset are shown in gray with dashed box.

Figure 3

The computed $g\left(M\right)$ vs $U$ for Chern insulators, which were predicted by first-principles calculations under certain Hubbard $U$ parameters. Materials with $g\left(M\right)<0$ at $U=0$ is shown only, for they are even more negative at finite $U$.

Figure 4

Electronic structure and topological properties of monolayer ${\mathrm{RuO}}_2$ and TbBr by $\mathrm{DFT}+U$ ($U=2$, 4 eV for Ru-$d$, Tb-$f$ orbital, respectively). (a)–(e) ${\mathrm{RuO}}_2$, (f)–(i) TbBr. The top and side views of atomic structure; the band structure with SOC; topological edge states calculated along $x$ axis; anomalous Hall conductance ${\sigma }_{xy}$ as a function of Fermi energy. (b) Brillouin zone. The shaded regions in (e) and (k) denote the topological gap.