Rational Design Principles of the Quantum Anomalous Hall Effect in Superlatticelike Magnetic Topological Insulators

As a paradigmatic phenomenon in condensed matter physics, the quantum anomalous Hall effect (QAHE) in stoichiometric Chern insulators has drawn great interest for years. Using model Hamiltonian analysis and first-principles calculations, we establish a topological phase diagram and map different 2D configurations to it, which are taken from the recently grown magnetic topological insulators ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$ and ${\mathrm{MnBi}}_6{\mathrm{Te}}_{10}$ with superlatticelike stacking patterns. These configurations manifest various topological phases, including the quantum spin Hall effect with and without time-reversal symmetry and QAHE. We then provide design principles to trigger the QAHE by tuning experimentally accessible knobs, such as the slab thickness and magnetization. Our work reveals that superlatticelike magnetic topological insulators with tunable exchange interactions are an ideal platform to realize the long-sought QAHE in pristine compounds, paving a new path within the area of topological materials.

Figure 1

(a) Topological phase diagram in the 2D limit of a 3D TI under an exchange field in terms of the film thickness $L$ and magnetization $gM$. Various phases, including the NI (gray area), $T$-preserved QSHE (blue line), $T$-broken QSHE (yellow area), and QAHE (cyan area), are shown. The DFT-calculated 2D configurations composed of ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ ($A$) and ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ ($B$) building blocks are also mapped on the phase diagram (see also Table 1 and Fig. 2). (b),(c) Energy gap at the $\mathrm{\Gamma }$ point $E_g(\mathrm{\Gamma })$ as functions of (b) $L$ and (c) $gM$.

Figure 2

(a) Crystal structures of ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$ and ${\mathrm{MnBi}}_6{\mathrm{Te}}_{10}$ with their different fragments (marked by black dashed lines) that can be exfoliated as 2D structures. The red dashed boxes denote the $A$ (${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ septuple layer) and $B$ (${\mathrm{Bi}}_2{\mathrm{Te}}_3$ quintuple layer) building blocks. (b) Band structure of the $B$ layer. (c) Band structure of the $A$ layer with the projection of spin operator ${\sigma }_z$. Red and blue denote spin-up and spin-down channels, respectively.

Figure 3

(a)–(c) Band structure with projection onto different atomic orbitals (a), edge states (b), and quantized spin Hall conductance (c) of $BB$ (bilayer ${\mathrm{Bi}}_2{\mathrm{Te}}_3$) configuration. (d)–(f) Same as (a)–(c) but for the $AB$ configuration. (g),(h) Same as (a),(b) but for the $ABA$ configuration. (i) Quantized anomalous Hall conductance of the $ABA$ configuration.