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.

Topological magnets are a new family of quantum materials providing great potential to realize emergent phenomena, such as the quantum anomalous Hall effect and the axion-insulator state. Here, we present our discovery that the stoichiometric ferromagnet ${\mathrm{MnBi}}_8{\mathrm{Te}}_{13}$ with natural heterostructure ${\mathrm{MnBi}}_2{\mathrm{Te}}_4/({\mathrm{Bi}}_2{\mathrm{Te}}_3{)}_3$ is an unprecedented “half-magnetic topological insulator,” with the magnetization existing at the ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ surface but not at the opposite surface terminated by triple ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ layers. Our angle-resolved photoemission spectroscopy measurements unveil a massive Dirac gap at the ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ surface and a gapless Dirac cone on the other side. Remarkably, the Dirac gap (about 28 meV) at the ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ surface decreases monotonically with increasing temperature and closes right at the Curie temperature, thereby representing the first smoking-gun spectroscopic evidence of a magnetization-induced topological surface gap among all known magnetic topological materials. We further demonstrate theoretically that the half-magnetic topological insulator is desirable to realize the surface anomalous Hall effect, which serves as direct proof of the general concept of axion electrodynamics in condensed matter systems.

Signatures of both the quantum anomalous Hall effect and axion electrodynamics have been recently observed to exist in thin films of ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$, a stoichiometric antiferromagnetic topological insulator. Direct evidence of the bulk topological magnetoelectric response in an axion insulator requires an energy gap at its topological surface state (TSS). However, independent spectroscopic experiments revealed that such a surface gap is much smaller than previously thought. Here we utilize angle resolved photoemission spectroscopy and density functional theory calculations to demonstrate that a sizable TSS gap unexpectedly exists in Sb-doped ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ where the bulk system remains topologically nontrivial. This gap is found to be insensitive to the bulk antiferromagnetic-paramagnetic transition, while it enlarges along with increasing Sb concentration, enabling simultaneous tunability of the Fermi level and the TSS gap size (up to $>100$ meV). Our work shows that Sb dopants in ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ can not only control the Fermi level but also induce a tunable surface gap, providing a potential platform to observe the key features of the high-temperature axion-insulator phase.

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.

The intertwining of charge order, superconductivity, and band topology has promoted the $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A=\mathrm{K}$, Rb, Cs) family of materials to the center of attention in condensed matter physics. Underlying those mysterious macroscopic properties such as giant anomalous Hall conductivity (AHC) and chiral charge density wave is their nontrivial band topology. While there have been numerous experimental and theoretical works investigating the nontrivial band structure and especially the van Hove singularities, the exact topological phase of this family remains to be clarified. In this work, we identify ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ as a Dirac nodal line semimetal based on the observation of multiple Dirac nodal lines and loops close to the Fermi level. Combining photoemission spectroscopy and density functional theory, we identify two groups of Dirac nodal lines along the $k_z$ direction and one group of Dirac nodal loops in the $A-H-L$ plane. These nodal loops are located at the Fermi level within the instrumental resolution limit. Importantly, our first-principles analyses indicate that these nodal loops may be a crucial source of the mysterious giant AHC observed. Our results not only provide a clear picture to categorize the band structure topology of this family of materials, but also suggest the dominant role of topological nodal loops in shaping their transport behavior.

Layered honeycomb lattice antiferromagnetic $\alpha \text{−}\mathrm{Ru}{\mathrm{Cl}}_3$ has been studied intensively recently as a Kitaev spin liquid candidate. Here we present strong evidence that this material host realistic Weyl fermions derived from Cl $2p$ electrons. Our theoretical analysis suggests the existence of quadratic Weyl fermions without spin-orbit coupling and linear Weyl fermion with spin-orbit coupling. Angle-resolved photoemission spectroscopy with systematic photon energy-dependent measurements demonstrates that this Weyl cone possesses linear dispersion at bulk Brillouin zone center along all the three reciprocal directions and hyperbolic dispersion off center. Our work reveals the rich topological physics lying in the band structure of Kitaev QSL candidates and will stimulate further investigation not only limited to $\alpha \text{−}\mathrm{Ru}{\mathrm{Cl}}_3$ but also honeycomb iridate family of materials.