Distinct Topological Surface States on the Two Terminations of ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$

The recently discovered intrinsic magnetic topological insulator ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ has been met with unusual success in hosting emergent phenomena such as the quantum anomalous Hall effect and the axion insulator states. However, the surface-bulk correspondence of the Mn-Bi-Te family, composed by the superlatticelike ${\mathrm{MnBi}}_2{\mathrm{Te}}_4/{({\mathrm{Bi}}_2{\mathrm{Te}}_3)}_n$ ($n=0,1,2,3\dots$) layered structure, remains intriguing but elusive. Here, by using scanning tunneling microscopy and angle-resolved photoemission spectroscopy techniques, we unambiguously assign the two distinct surface states of ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$ ($n=1$) to the quintuple-layer (QL) ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ termination and the septuple-layer (SL) ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ termination, respectively. A comparison of the experimental observations with theoretical calculations reveals diverging topological behaviors, especially the hybridization effect between the QL and SL, on the two terminations. We identify a gap on the QL termination, originating from the hybridization between the topological surface states of the QL and the bands of the SL beneath, and a gapless Dirac-cone band structure on the SL termination with time-reversal symmetry. The quasiparticle interference patterns further confirm the topological nature of the surface states for both terminations, continuing far above the Fermi energy. The QL termination carries a spin-helical Dirac state with hexagonal warping, while at the SL termination, a strongly canted helical state from the surface lies between a pair of Rashba-like splitting bands from its neighboring layer. Our work elucidates an unprecedented hybridization effect between the building blocks of the topological surface states and also reveals the termination-dependent time-reversal symmetry breaking in a magnetic topological insulator.

Popular Summary

Topological insulators (TIs) have an insulating interior but a metallic surface, at which the electrons are conducting like relativistic particles without dissipation. In magnetic TIs with specific magnetization, the surface state loses most of its metallic nature because of the breaking of some key symmetries. These behaviors of the surface states are thought to be related to the bulk interior through a correlation known as the surface-bulk correspondence—a unifying feature of TIs. However, in the recently discovered magnetic TI ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$, which has alternating magnetic and nonmagnetic layers like ${\mathrm{L}\mathrm{E}\mathrm{G}\mathrm{O}}^{\circledR }$ building blocks, this correspondence is more complicated: The surface behaviors are termination dependent. Here, we present scanning tunneling microscope and angle-resolved photoemission spectroscopy measurements that help shed light on this intriguing behavior.

In , the surface can be terminated by a quintuple layer of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ or a septuple layer of ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$. Relying on scans of both terminations as well as theoretical calculations, we attribute the unexpected metallic surface on the septuple layer to a surface magnetic order that is different from the bulk. On the other hand, the quintuple layer exhibits a nonmetallic behavior as a result of the mixing of atomic orbitals from the neighboring layer underneath.

Our results suggest that the diverging behaviors at the two terminations of strongly rely on the interplay between different TI building blocks, providing new insights into the surface-bulk correspondence of magnetic TIs.

Figure 1

STM topographic images of the ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$ surface. (a) Schematic diagram of two terminations—the QL termination of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ and the SL termination of ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$—with atomic defects. (b) A large area topographic image of ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$ surface showing two kinds of terrace steps. The lower part of (b) shows a line profile with step heights of 1.01 and 1.35 nm along the blue line, for the QL termination of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ and the SL termination of ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$, respectively. A considerable number of defects can be found in the enlarged views of the QL (c) and SL (f) terminations. (d),(e) and (g),(h) are the atomic resolution images of the same areas at different biases on the QL and SL terminations, respectively. The dark defects are found on both QL and SL terminations. For the SL, an additional type of defect is observed as a bright dot at both positive and negative biases. Tunneling parameters: (b) $V_{\mathrm{bias}}=1.2\mathrm{V}$, and $I_t=20\mathrm{pA}$; (c),(f) $V_{\mathrm{bias}}=1.0\mathrm{V}$ and $I_t=20\mathrm{pA}$; (d) $V_{\mathrm{bias}}=0.5\mathrm{V}$ and $I_t=1\mathrm{nA}$; (e) $V_{\mathrm{bias}}=-1\mathrm{V}$ and $I_t=1\mathrm{nA}$; (g) $V_{\mathrm{bias}}=0.5\mathrm{V}$ and $I_t=200\mathrm{pA}$; (h) $V_{\mathrm{bias}}=-1\mathrm{V}$ and $I_t=200\mathrm{pA}$.

Figure 2

Electronic structure of the two terminations of ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$. (a) Top: Averaged $dI/dV$ spectra of a series of STS spectra obtained at defect-free areas of the QL (green) and SL (black) terminations. Tunneling parameters: $V_{\mathrm{bias}}=0.5\mathrm{V}$ and $I_t=500\mathrm{pA}$. The arrows mark the hybridization gap opening on the QL termination (red and purple), the Dirac point (red), and the onset of the inner Rashba-like splitting band on the SL termination (brown), in good agreement with the ARPES measurement. Bottom: DFT-calculated surface-dependent DOS for both terminations. The surface projections include the top two surface layers, containing one SL and one QL. The calculated DOS plots are offset to $-285\mathrm{meV}$ to match the Dirac point of SL termination. The dashed line marks the Fermi level. (b) Spin-polarized ARPES map for both terminations of ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$, with a line cut at $E_B=0.08\mathrm{eV}$ showing the antiparallel helicity of the two bands. (c) and (d) are the ARPES intensity maps of the QL and SL terminations at the $\overline{\mathrm{\Gamma }}-\overline{M}$ direction, respectively. Arrows highlight important STS features in (a). (e) and (f) show the results from density functional theory calculations for the QL and SL terminations, respectively. The slab model assumes a nonmagnetic SL termination for (f), while for (e) an $A$-type AFM spin configuration is used with the assumption that the magnetic order of the second SL is protected by the topmost QL. The green dashed box in (e) marks the gapped Dirac cone of the surface states.

Figure 3

ARPES contours of constant energy, JDOS, and spin-selective JDOS calculated from ARPES data and FT STS maps at $-50\mathrm{meV}$ of the two terminations. (a) and (b) are the schematics of the spin texture derived from the $k·p$ Hamiltonian for the QL (a) and SL (b) terminations. Arrows and colors of the vectors represent the in-plane (purple) and out-of-plane (red, $+z$; blue, $-z$) components of spin at the contour maps of the Fermi energy, respectively. The black arrow indicates the $\overline{\mathrm{\Gamma }}-\overline{M}$ direction for all the maps. For QL termination, the hexagonal warping effect causes a canted spin at the $z$ direction. For SL termination, a pair of Rashba-like splitting bands contribute antiparallel helicity for the inner and outer rings in the CCE map. A strong warping effect is observed as a flower-shaped band in between the rings. (c),(d) CCE maps from ARPES measurements at 50 meV below Fermi level for QL (c) and SL (d) terminations. (e),(f) JDOS calculated from the intensity of the CCE map are shown for QL (e) and SL (f) terminations. For the calculation on the SL, idealized bands with an experimentally determined adjusted intensity ratio are used. The JDOS maps show unexpected scattering intensity at $\overline{\mathrm{\Gamma }}-\overline{K}$ directions. (g),(h) Taking into account the spin-selective joint density of states, the scattering maps are (g) for QL and (h) SL terminations. For both simulations, the scattering at $\overline{\mathrm{\Gamma }}-\overline{K}$ directions are greatly suppressed. (i) and (j) are the Fourier transformation on the $dI/dV$ maps (FT STS) at $V_{\mathrm{bias}}=-50\mathrm{mV}$, $I_t=500\mathrm{pA}$, image size $100\times 100{\mathrm{nm}}^2$, showing good agreement with the spin-selective JDOS maps. The scale bars are $0.1{\AA }^{-1}$ in CCE maps and $0.2{\AA }^{-1}$ in the rest maps. FT STS maps are rotationally symmetrized.

Figure 4

Dispersion of $\mathrm{\Gamma }-M$ scattering edges from ARPES and FT STS. (a),(b) Schematic of CCEs resulting in the edges of $q$ vectors observed in the FT STS maps along the $\overline{\mathrm{\Gamma }}-\overline{M}$ direction; arrows mark the spin orientation on these topological surface states: on the QL termination (a), the circular shape surface band is slightly warped for $E>-100\mathrm{meV}$, causing a canted spin along $z$, thus resulting in $q_{\mathrm{QL}}$ marked by the blue arrows; on the SL termination (b), for $E>-150\mathrm{meV}$, Rashba-like spin splitting contributes antiparallel helicity for the inner and outer rings in the CCE map (marked as blue and red arrows), where the outer ring hybridizes with a strongly warped surface band sandwiched in between. The middle warped band has the same helicity as the inner circular bands to fit the intensity along the $\overline{\mathrm{\Gamma }}-\overline{M}$ direction in the QPI map, leading to $q_{\mathrm{SL}}$ marked by the yellow arrow. (c) Dispersion of the $q$ vectors calculated from the ARPES data (solid lines) on the QL (blue) and SL (yellow) terminations and the $q$ vectors obtained from the FT STS data (orange stars for QL and purple circles for SL). The original FT STS and CCE maps are shown in Figs. S6–S9 [32], respectively.