Interplay between exchange-split Dirac and Rashba-type surface states at the ${\mathrm{MnBi}}_2{\mathrm{Te}}_4/\mathrm{BiTeI}$ interface

Based on ab initio calculations, we study the electronic structure of the $\mathrm{BiTeI}/\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$ heterostructure interface composed of the antiferromagnetic topological insulator ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ and the polar semiconductor trilayer BiTeI. We found a significant difference in the electronic properties of the different contacts between the substrate and overlayer. While the case of a Te-Te interface forms a natural expansion of the substrate, when the Dirac cone state locates mostly in the polar overlayer region and undergoes a slight exchange splitting, the Te-I contact is the source of a four-band state contributed by the substrate Dirac cone and Rashba-type state of the polar trilayer. Owing to magnetic proximity, the pair of Kramers degeneracies for this state is lifted, which produces a Hall response in the transport regime. We believe our findings provide new opportunities to construct novel spintronic devices.

Figure 1

(a) Schematic geometrical structure of the BiTeI/MBT interface with different orientations of the BiTeI trilayer. In-plane spin-resolved surface band structure calculated with large separation of 12 Å between the (b) pristine ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ (0001) surface and (c) BiTeI trilayer. Spin-resolved electron spectrum for (d) Te-Te and (e) Te-I interfaces in the case of equilibrium structures. The value and direction of the in-plane spin projection are coded by the circle size and color, where the positive value corresponds to red and the negative to blue. The light green area represents bulk projected bands, and the black rectangular emphasizes the trivial surface states of ${\mathrm{MnBi}}_2{\mathrm{Te}}_4\left(0001\right)$. For (b), (d), and (e), the magnetic exchange and hybridization energy gap at the center of SBZ are denoted by green (blue) rectangles. In (e), the hybridization energy gap is denoted as I and two exchange gaps as II and III. In (c) and (d), the unoccupied Rashba states are denoted by the R symbol. The trivial surface states of the MBT are shown by the T symbol.

Figure 2

Surface spin-resolved electronic structure of a Te–Te interface [(a)–(d)] for different separations between the MBT surface and trilayer with respect to the equilibrium geometry, $\mathrm{\Delta }d=d-d_0$, and [(e)–(h)] for a different spin-orbit coupling strength of the Bi and Te $p$ states of BiTeI trilayer. The natural SOC contribution gives $\lambda /{\lambda }_0=1$. In the panels, the magnetic exchange gap at the SBZ center is indicated by the green areas. For each panel, the gap width is denoted from the right side of the green area. In (a), the subsurface Rashba state is denoted by the R symbol.

Figure 3

(a) In-plane spin-resolved surface electronic structure of Te-Te interface with a vertical separation $d=3.24\text{Å}.$ (b) Charge density distribution of the upper part of the Dirac surface state (purple curves) at the $\overline{\mathrm{\Gamma }}$ point as function of out-of-plane direction (integrated over the $xy$ plane) for different vertical spacing between the MBT surface and trilayer (top) and spin-orbit coupling strength, $\lambda /{\lambda }_0$ (bottom) (see also Fig. 2). The integral of charge density inside the vicinity of adjoined atomic layers are color-coded by the intensities of green.

Figure 4

Surface electronic structure of Te-I interface for different spacings between the BiTeI overlayer and MBT surface. (a) The spacing is $0.3\mathsf{\text{Å}}$ greater (left) and $0.1\text{Å}$ lesser (right) than the equilibrium one. The colors highlight the extent of spacial localization of the states inside the trilayer (blue) or within the two utmost septuple layers of MBT (red). (b) Electronic band structure [Eq. (1)] of the proposed model (left) with parameters given in Table 1 (solid black lines) and without taking into account the magnetic contribution, $\widehat{H_m}$ (${\mathrm{\Delta }}_R={\mathrm{\Delta }}_D=0$) (dashed red lines). (Right) Energy dependence of Hall conductivity ${\sigma }_{xy}\left(E\right)=V/{\left(2\pi \right)}^2\int d^2\mathbf{k}{\sigma }_{xy}(\mathbf{k},E)$. For all panels, the magnetic exchange and hybridization energy gap at the center of SBZ are denoted by green (blue) areas. Hybridization energy gap is denoted as I and two exchange gaps as II and III.