Orbital Complexity in Intrinsic Magnetic Topological Insulators ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$ and ${\mathrm{MnBi}}_6{\mathrm{Te}}_{10}$

Using angle-resolved photoelectron spectroscopy (ARPES), we investigate the surface electronic structure of the magnetic van der Waals compounds ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$ and ${\mathrm{MnBi}}_6{\mathrm{Te}}_{10}$, the $n=1$ and 2 members of a modular $({\mathrm{Bi}}_2{\mathrm{Te}}_3{)}_n({\mathrm{MnBi}}_2{\mathrm{Te}}_4)$ series, which have attracted recent interest as intrinsic magnetic topological insulators. Combining circular dichroic, spin-resolved and photon-energy-dependent ARPES measurements with calculations based on density functional theory, we unveil complex momentum-dependent orbital and spin textures in the surface electronic structure and disentangle topological from trivial surface bands. We find that the Dirac-cone dispersion of the topologial surface state is strongly perturbed by hybridization with valence-band states for ${\mathrm{Bi}}_2{\mathrm{Te}}_3$-terminated surfaces but remains preserved for ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$-terminated surfaces. Our results firmly establish the topologically nontrivial nature of these magnetic van der Waals materials and indicate that the possibility of realizing a quantized anomalous Hall conductivity depends on surface termination.

Figure 1

Surface electronic structure for different (0001) surface terminations of $({\mathrm{Bi}}_2{\mathrm{Te}}_3{)}_n({\mathrm{MnBi}}_2{\mathrm{Te}}_4)$ with $n=1$ and 2. (a),(b) ARPES datasets for ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$ along $\overline{\mathrm{\Gamma }}\overline{\mathrm{K}}$ for a ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ septuple layer and a ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ quintuple layer termination, respectively. (c) Schematic of the possible terminations of ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$ and ${\mathrm{MnBi}}_6{\mathrm{Te}}_{10}(0001)$ surfaces, labeled with the panel showing the corresponding ARPES data. (d)–(f) ARPES datasets along $\overline{\mathrm{\Gamma }}\overline{\mathrm{M}}$ for ${\mathrm{MnBi}}_6{\mathrm{Te}}_{10}$ with (d) SL termination, (e) QL-SL termination, and (f) QL-QL termination.

Figure 2

CD-ARPES experiments for the SL-terminated surface of ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$. (a) ARPES intensity $I_R$ measured with right circularly polarized light. Wave vectors $k_y$ are perpendicular to the plane of light incidence. (b) Corresponding CD dataset defined as the intensity difference $I_R-I_L$. (c) ARPES intensity measured with $s$-polarized light. The overlaid markers indicate the dispersion extracted from CD-ARPES data in (b) and the red or blue color refers to the sign of the CD. (d) Momentum distribution curves measured with right and left circularly polarized light shown in blue and red, respectively. The energy regions above and below the Dirac point (DP) are labeled by CB and VB, respectively. (e) Constant energy contours of the CD-ARPES signal.

Figure 3

(a)–(d) Photon-energy-dependent ARPES data along $\overline{\mathrm{\Gamma }}\overline{\mathrm{K}}$ for the QL-terminated surface of ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$ obtained with $p$-polarized light, except for (b) measured with $s$ polarization [$T=8\mathrm{K}$]. (e) Intensity difference between datasets measured at $h\nu =61$ and $h\nu =79\mathrm{eV}$. (f) ARPES intensities traced as a function of $h\nu$ at specific points in the band structure, indicated by boxes in (a). The colors of the boxes in (a) correspond to the respective data sets in (f). (g)–(j) Orbital-projected surface spectral densities for the QL-terminated surface of ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$. (j) Difference between the surface spectral densities projected on Bi $J=1/2$ orbitals in (g) and Te $J=3/2$, $|M_J|=1/2$ orbitals in (i).

Figure 4

(a) ARPES data along $\overline{\mathrm{\Gamma }}\overline{\mathrm{K}}$ for QL-terminated ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$. Dashed lines indicate the energies of the momentum distribution curves (MDC) in (c). (b) Calculated surface spectral density along $\overline{\mathrm{M}}\overline{\mathrm{\Gamma }}\overline{\mathrm{K}}$. The intensity represents the projection on Bi and Te $J=1/2$ orbitals and red or blue colors denote the spin polarization perpendicular to $k_{||}$. The TSS and a surface resonance (SR) are indicated. (c) MDC of the spin-resolved intensities $I_{\uparrow y}$ and $I_{\downarrow y}$ at energies (i)–(iii) indicated in (a). (d) Spin-resolved constant energy contour at energy (i). The spin quantization is along $y$. Dashed lines indicate the integration width used to obtain the MDC in (c). (e) Color matrix used for the simultaneous depiction of intensity and spin polarization $S_y$.