Hybridization-induced gapped and gapless states on the surface of magnetic topological insulators

The layered $\mathrm{Mn}{\mathrm{Bi}}_{2n}{\mathrm{Te}}_{3n+1}$ family represents the first intrinsic antiferromagnetic (AFM) topological insulator (protected by a combination symmetry $S$) ever discovered, providing an ideal platform to explore novel areas of physics such as the quantum anomalous Hall effect at elevated temperature and axion electrodynamics. Some of the recent angle-resolved photoemission spectroscopy (ARPES) experiments on this family have revealed that all terminations exhibit (nearly) gapless topological surface states (TSSs) in the AFM state. The gapless behavior is inconsistent with the theoretical expectation, as the surfaces being studied are $S$-breaking and shall therefore open a gap. Here we explain this curious paradox using a surface-bulk band hybridization picture. Combining circular dichroism ARPES and first-principles calculations on $\mathrm{Mn}{\mathrm{Bi}}_6{\mathrm{Te}}_{10}$, we prove that gaplike features are induced through hybridization between TSSs and certain bulk bands with Rashba character. The observed (nearly) gapless features are consistently reproduced by tight-binding simulations where TSSs are coupled to a pair of Rashba-split bands (RSBs). The Dirac-cone-like spectral features actually originate from the RSBs. Our findings highlight the role of band hybridization, superior to magnetism in this case, in shaping the general surface band structure in this family of magnetic topological materials.

Figure 1

Lattice structure and characterization of $\mathrm{Mn}{\mathrm{Bi}}_6{\mathrm{Te}}_{10}$ single crystals. (a) Schematic lattice structure. (b) Single-crystal XRD result and peak index result. The inset shows a typical single crystal on a millimeter grid. (c) Zero-field in-plane longitudinal resistivity vs temperature. The inset shows the results up to $300\mathrm{K}$. (d) Magnetic susceptibility vs temperature for magnetic field ($300\mathrm{Oe}$) parallel to the $ab$ plane (red) and the $c$ axis (blue). The inset shows the Curie-Weiss fitting for temperatures ranging from 150 to 300 K. (e) Magnetization hysteresis at $2\mathrm{K}$. The inset highlights the coercive fields.

Figure 2

Termination-dependent electronic structure of $\mathrm{Mn}{\mathrm{Bi}}_6{\mathrm{Te}}_{10}$ single crystals. Parts (a)–(d) correspond to the results of S-, Q-, QQ-, and QQQ-terminations, respectively. For each section, the top-left panel shows the raw ARPES spectra, while the bottom-left panel shows the 2D curvature spectra [61]. The top-right panel shows the schematic structural configuration while the bottom-right panel presents the respective calculated band structure.

Figure 3

Evidence of TSS-RSBs hybridization at Q- and S-terminations of $\mathrm{Mn}{\mathrm{Bi}}_6{\mathrm{Te}}_{10}$. (a)–(e) ARPES and DFT results for Q-termination. (a)–(c) AFM DFT band structure with the fatted bands projected onto corresponding layers as indicated by the blue (b) and red (c) boxes in (a). (d) ARPES spectra in 2D curvature. Bands around the Dirac points are label as C1, V1, V2, and V3, respectively. The black arrow indicates the weak in-gap V1 band. (e) Left: ARPES spectra from the sum of right circular polarization (RCP) and left circular polarization (LCP) light (RCP+LCP); right: circular dichroism (CD) ARPES spectra from the polarization (RCP-LCP)/(RCP+LCP). Red and blue squares indicate the TSS Dirac cone dispersion. Red and blue filled circles indicate the RSBs dispersion. (f)–(j) Similar analysis for S-termination.

Figure 4

TB simulation on the TSS-RSBs hybridization. (a) Schematic of the TB model. (b)–(d) TB simulation for Q-termination band structure. (b) ARPES spectra in 2D curvature. (c) TB model simulated band structure and its evolution with increasing hybridization at the PM state. The color bar indicates the contribution from TSS and RSB for the hybridized bands, excluding the ordinary bulk conduction and valence band. (d) TB simulated bands at AFM order. (e)–(g) Similar results for S-termination.