Intrinsic layer-polarized anomalous Hall effect in bilayer $\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$

Layer-polarized anomalous Hall effect (LPAHE) is an attractive phenomenon in condensed-matter physics from the standpoints of both fundamental interest and device applications. The current LPAHE research is based on the extrinsic paradigm of using external electric fields, in which the generation and control of LPAHE are not straightforward. Here, we propose a mechanism that realizes intrinsic LPAHE in bilayer lattices, through the mediation of sliding physics and Berry curvature. Moreover, this mechanism can render the LPAHE in a controllable and reversible fashion. We analyze the symmetry requirements for a system to host such intrinsic LPAHE. Its validity is further demonstrated in a real material of bilayer $\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$. By stacking with broken inversion symmetry, the layer-locked Berry curvature enables the intrinsic LPAHE in bilayer $\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$, and the switchable control of its LPAHE is achieved by sliding ferroelectricity. Our work opens a significant alternative direction for LPAHE and two-dimensional materials research.

Figure 1

Schematic diagrams of ${\mathrm{AA}}^{\prime }$, ${\mathrm{AB}}^{\prime }1$, ${\mathrm{AB}}^{\prime }2$, and ${\mathrm{AC}}^{\prime }$ configurations of a bilayer lattice and their band edges.

Figure 2

(a) Crystal structures of single-layer $\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$ from top view and side view. (b) Band structures of single-layer $\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$ with SOC. The Fermi level is set to 0 eV. (c) Crystal structures of bilayer $\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$ under ${\mathrm{AB}}^{\prime }1$, ${\mathrm{AA}}^{\prime }$, ${\mathrm{AB}}^{\prime }$, and ${\mathrm{AC}}^{\prime }$ configurations.

Figure 3

Plane-averaged electrostatic potentials of (a) ${\mathrm{AB}}^{\prime }1$ and (b) ${\mathrm{AB}}^{\prime }2$ configurations for bilayer $\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$ along the $c$ direction. Insets in (a), (b) present the corresponding charge density of ${\mathrm{AB}}^{\prime }1$ and ${\mathrm{AB}}^{\prime }2$, respectively. Red and green isosurfaces represent electron accumulation and depletion, respectively. (c) Energy profiles for FE switching of bilayer $\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$. (d) Variation of out-of-plane electric polarization of bilayer $\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$ under FE switching from ${\mathrm{AB}}^{\prime }1$ to ${\mathrm{AB}}^{\prime }2$.

Figure 4

(a) Band structures and (c) density of states for ${\mathrm{AB}}^{\prime }1$ configuration of bilayer $\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$ with SOC. (b) Band structures and (d) density of states for ${\mathrm{AB}}^{\prime }2$ configuration of bilayer $\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$ with SOC. The Fermi level is set to 0 eV.

Figure 5

Berry curvature of the bottom conduction band as a contour map in the whole Brillouin zone for (a) ${\mathrm{AB}}^{\prime }1$ and (b) ${\mathrm{AB}}^{\prime }2$ configurations of bilayer $\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$. (c) Berry curvatures along high-symmetry points for ${\mathrm{AB}}^{\prime }1$ and ${\mathrm{AB}}^{\prime }2$ configurations of bilayer $\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$. (d) Anomalous Hall conductance for ${\mathrm{AB}}^{\prime }1$ and ${\mathrm{AB}}^{\prime }2$ configurations of bilayer $\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$. (e) Schematic diagrams of intrinsic LPAHE in bilayer $\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$.