Topological Electronic Structure and Its Temperature Evolution in Antiferromagnetic Topological Insulator MnBi2Te4

Topological Insulator MnBi2Te4 Y. J. Chen, L. X. Xu, J. H. Li, Y. W. Li, H. Y. Wang , C. F. Zhang, H. Li, Y. Wu, A. J. Liang, C. Chen, S. W. Jung , C. Cacho, Y. H. Mao, S. Liu, M. X. Wang, Y. F. Guo, Y. Xu, Z. K. Liu, L. X. Yang , and Y. L. Chen State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China School of Physical Science and Technology, ShanghaiTech University and CAS-Shanghai Science Research Center, Shanghai 201210, China Center for Excellence in Superconducting Electronics, State Key Laboratory of Functional Material for Informatics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, China University of Chinese Academy of Sciences, Beijing 100049, China Department of Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha 410073, China School of Materials Science and Engineering, Tsinghua University, Beijing 10084, China Department of Mechanical Engineering and Tsinghua-Foxconn Nanotechnology Research Center, Tsinghua University, Beijing 100084, China Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA Diamond Light Source, Harwell Campus, Didcot OX11 0DE, United Kingdom Frontier Science Center for Quantum Information, Beijing 100084, China RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan

Recently, it was realized that a layered compound, MnBi2Te4 could be a promising magnetic TI with intrinsic A-type anti-ferromagnetic (AFM) order [10][11][12] that can serve as an ideal platform for the realization of QAH effects and other interesting magnetic topological phases including axion insulator and ideal Weyl semimetal phases [11]. Indeed, experimental efforts soon followed and topological phenomena such as magnetic-field-induced QAH effect [13] and quantum phase transition from axion insulator to Chern insulator [14] were recently observed. In order to understand the rich properties and explore the full application potential of MnBi2Te4, both the surface and bulk electronics structures need to be experimentally verified.
Unfortunately, although there have been several attempts to resolve the band structures of this interesting compound, the results remain controversial and even conflicting [15][16][17][18][19][20]. First of all, the identification of the topological surface states (TSSs) remains elusive, leading to significant difference in identifying the band gap of the surface state (due to the formation of magnetic order), ranging from 50 meV [15] to a couple of hundreds of meVs [16][17][18][19]. More intriguingly, these assumed gaps of the topological surface state persist well above the Né el temperature (TN) of MnBi2Te4 (25K, see ref [17]) and could even be observed at room temperature [16,18]. The order of magnitude's difference between the room temperature (300K) and the TN of MnBi2Te4 (25K) make it less convincing that the observed gap originates from the magnetic order. Finally, the fact that the measured gap size varies with photon energy [15][16][17][18][19], further alludes its bulk origin. These puzzles thus demand a systematic investigation on the electronic structure of MnBi2Te4 that can clearly distinguish the surface and bulk states in order to reveal their connection to the AFM transitionwhich can lay the foundation to the understanding of the interplay between the electronic structure, magnetic ordering and the rich topological phenomena of this material.
In this work, combining the use of synchrotron and laser light sources, we carried out comprehensive and high resolution angle-resolved photoemission spectroscopy (ARPES) studies on MnBi2Te4, and clearly identified its topological electronic structures including the characteristic TSSs. The broad photon energy range provided by the synchrotron light source allowed us to map out the subtle three-dimensional (3D) electronic structures; while the high resolution laser light source made it possible to investigate the TSSs with great precision.
Furthermore, by carrying out temperature dependent measurements, we were able to observe the temperature evolution from both the bulk and surface state bands, which shows interesting difference between their interplay with the magnetic phase transition: while the bulk states show clear splitting commencing at TN; the gap of TSSs is negligible within our energy resolution [2 mV at temperature (7.5 K) well below TN], which could be due to the highly delocalized nature of TSSs mediated by surface magnetic domains of different magnetization orientations. The identification of the detailed electronic structures of MnBi2Te4 will not only help understand its exotic properties, but also pave the way for the design and realization of novel phenomena and applications.
MnBi2Te4 crystallizes into a rhombohedral lattice with space group of R3 ̅ m [19,28]. It exhibits a layered structure by staking van der Waals septuple Te-Bi-Te-Mn-Te-Bi-Te layers, which has an extra Mn-Te layer sandwiched at the middle of the well-known quintuple-layer of Bi2Te3, as shown in Fig. 1a. The high quality of the single crystalline samples used in this work is demonstrated by the single crystal X-ray diffraction patterns (Fig. 1b) and angle scan (Fig 1c). The magnetic susceptibility and electric transport measurements (Fig. 1d)  The bulk band structure of MnBi2Te4 is illustrated in Fig. 2. The conduction and valance bands form an inverted bulk gap [10,11] whose magnitude varies with the photon energies used for the ARPES measurements (Fig. 2a, b), indicting its bulk nature. Depending on the methods used for gap extraction (see SI for details), the bulk gap size at different kz momentum varies from 180~220meV [fitted peak-peak gap in energy distribution curves (EDCs)] or 80~160meV (EDC leading edge gap), as summarized in Fig. 2b(iii). Interestingly, besides the bulk bands with very strong photoemission spectra intensity that agree well with the calculations (Fig. 2c(i)), one can notice that there is also weak spectra intensity within the bulk band gap (Fig. 2c(ii-iv)), showing an "X" shape dispersion centered at the  point, similar to the dispersion of the TSSs of other 3D TIs [29,30].
To further investigate the TSSs in the bulk band gap, we carried out laser based ARPES measurements with superb energy and momentum resolution, as illustrated in Fig. 3. The evolution of band structures with different binding energy (Fig. 3a, b) clearly shows the gapless TSSs with conical shape dispersion across the Dirac point located at E ~ -0.27 eV within the bulk band gap. The linear dispersion of these TSSs can be directly seen in Fig. 3c, with vanishing energy gap less than the energy resolution of the experiments (E~2 meV), which can be better seen in the zoom-in plot around the Dirac point (Fig. 3d).
Besides the TSSs, the high resolution in the measurement of laser based ARPES also allow us to investigate the bulk states with great details. From the spectra intensity map (Fig.3c), the 2 nd derivative plot (Fig. 3e) or the stacking momentum distribution curves (MDC) plot (Fig. 3f), one can clearly see three conduction bands. Interestingly, by comparing with theoretical calculation of bulk bands in Fig. 2c(i), we notice that an extra bulk band is observed, whose origin will be discussed later. We mark the observed conduction bands as CB2, CB1a, and CB1b respectively as shown in Fig. 3e, f (the reason of the naming will be discussed below).
To understand the interplay between the band structure and the magnetic properties of MnBi2Te4, we carried out a series of temperature dependent ARPES measurements across TN, which are summarized in Fig. 4. For the bulk conduction bands, upon the increase of temperature, the CB1a and CB1b bands move towards each other and eventually merge into one single band (CB1) above TN, as illustrated in Fig. 4a, b. When the temperature is sequentially cooled down to below TN, CB1 splits into CB1a and CB1b again, as can be clearly seen in Fig.   4a(vi) and Fig.4b(vi), the same behavior has been observed in the measurements on multiple samples (see SI for more details). The side-by-side comparison between the band structure above and below TN can be seen in Fig. 4c for clarity and the temperature evolution of the EDCs at the  point is summarized in Fig. 4d, with the fitted peak-to-peak splitting of the CB1a and CB1b on multiple temperatures plotted in Fig. 4e. The coincidence of the splitting temperature and the TN near 25 K indicates a correlation between the band splitting and the formation of the magnetic order. Although the observed bulk band splitting is beyond expectation of an AFM system, it is accessible considering the surface ferromagnetic ordering, which has been shown to induce considerable exchange splitting in AFM EuRh2Si2 [31]. On the other hand, according to first-principles calculations, CB1a and CB1b are mainly contributed by Te pz orbital. When the temperature increases above TN, the exchange induced splitting vanishes, which has complicated influence on interlayer coupling and band dispersion, leading to the merge of the CB1a and CB1b bands.
Interestingly, in contrast to the bulk bands, the TSSs show no observable temperature dependence (Fig. 4a, b), with diminishing gap in a large temperature range. In the AFM below TN, the material will transit into A-type AFM state, as revealed by previous studies [10,11]. Therefore, if the surface magnetism is ideally ordered along the out-of-plane z direction, a surface gap of ~40 meV would develop, as indicated by theoretical calculations [10]. The observed surface gap, however, is vanishingly small, suggesting that the surface magnetism may not be well ordered. The result could presumably be explained by following mechanisms.

First-principles calculations:
First-principles calculations were performed by density functional theory (DFT) using the Vienna ab initio Simulation Package . The plane-wave basis with an energy cutoff of 350 eV was adopted. The electron-ion interactions were modeled by the projector augmented wave potential and the exchange-correlation functional was approximated by the Perdew-Burke-Ernzerhof type generalized gradient approximation (GGA) [37]. The GGA+U method was applied to describe the localized 3d-orbitals of Mn atoms, for which U = 4.0 eV was selected according to our previous tests [10]. The structural relaxation for optimized lattice constants and atomic positions was performed with a force criterion of 0.01 eV/ Å and by using the DFT-D3 method to include van der Waals corrections. Spin-orbit coupling was included in selfconsistent calculations and the Monkhorst-Pack k-point mesh of 9×9×3 was adopted. Surface state calculations were performed with WannierTools package [38], based on the tight-binding Hamiltonians constructed from maximally localized Wannier functions (MLWF) [39] .