Gapless Dirac surface states in the antiferromagnetic topological insulator MnBi2Te4

TL;DR

This study combines ARPES and DFT to reveal that MnBi2Te4 hosts gapless Dirac surface states that are robust across its antiferromagnetic transition, challenging previous assumptions of a gapped surface state in such materials.

Contribution

The paper provides the first experimental evidence of gapless Dirac surface states in an intrinsic antiferromagnetic topological insulator, MnBi2Te4, across its magnetic transition.

Findings

Gapless Dirac cone remains protected across the AFM transition.

A second Dirac cone exists near the Fermi level as predicted.

Bulk band splitting occurs below the Néel temperature.

Abstract

We use high-resolution, tunable angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT) calculations to study the electronic properties of single crystals of MnBi2Te4, a material that was predicted to be the first intrinsic antiferromagnetic (AFM) topological insulator. We observe both bulk and surface bands in the electronic spectra, in reasonable agreement with the DFT calculations results. In striking contrast to the earlier literatures showing a full gap opening between two surface band manifolds along (0001) direction, we observed a gapless Dirac cone remain protected in MnBi2Te4 across the AFM transition (TN = 24 K). Our data also reveal the existence of a second Dirac cone closer to the Fermi level, predicted by band structure calculations. Whereas the surface Dirac cones seem to be remarkably insensitive to the AFM ordering, we do observe splitting of the bulk band that develops below the TN . Having a moderately high ordering temperature, MnBi2Te4 provides a unique platform for studying the interplay between topology and magnetic ordering.

Full text

The discovery of different types of exotic topological states that can be experimentally realized in semimetals has ignited intensive studies Hasan and Kane (2010); Tokura et al. (2019); Hsieh et al. (2008); Gibney (2018); Chiu et al. (2016); Plucinski (2019); Schoop et al. (2018). Besides their unprecedented importance for fundamental science, they also offer intriguing possibilities for device design revolutionizing computation capabilities, as well as laser technology Bandres et al. (2018). Among them, magnetic topological semimetals and insulators are promising materials for spintronics, especially in the context of the new generation of logic or memory devices. Manipatruni et al. (2018); Šmejkal et al. (2018); Pesin and MacDonald (2012); Jamali et al. (2015); Mankalale et al. (2019) The key challenge is to find new materials that provide desired spin structure at the chemical potential and allow an easy way for spin manipulation.

Antiferromagnetic topological insulators (AFM-TI) constitute a new unique subclass of topological quantum materials with additional magnetic degrees of freedom Mong et al. (2010); Moore (2010). They have a bulk band gap, but at the same time their surface states can be protected by $S=\Theta T_{1/2}$ symmetry, defined as the product of the time-reversal symmetry (TRS) $\Theta$ and the nonsymmorphic translation $T_{1/2}$. The preservation of $S$ symmetry provides surface states a protection from backscattering by non-trivial $Z_{2}$ topology even if the TRS is broken. Such remarkable properties of these materials open new opportunities, for example, for investigating the magnetoelectric effect. Tokura et al. (2019) To observe such phenomenon, it is necessary to gap out the Dirac cone by breaking the $T_{1/2}$ symmetry in intrinsic AFM-TIs by choosing a specific surface orientation Essin et al. (2009); Mong et al. (2010). However, despite tremendous theoretical and experimental efforts to find new AFM-TIs in single crystalline form Li et al. (2019a); Chowdhury et al. (2019); Xu et al. (2019); Wang et al. (2019), obtaining good quality AFM-TI material is very challenging.

Very recently, one of the magnetic variants of well-studied Bi2Te3 family 3D TIs Chen et al. (2009); Jiang et al. (2012) - MnBi2Te4 - has been theoretically proposed to be the first intrinsically stoichiometric AFM-TI, where the novel $Z_{2}$ topological invariant was protected by the $S$ symmetry in the A-type AFM configuration Otrokov et al. (2018); Gong et al. (2019); Otrokov et al. (2019); Zeugner et al. (2019); Vidal et al. (2019); Yan et al. (2019a); Li et al. (2019b); Chen et al. (2019a); Li et al. (2019a); Chowdhury et al. (2019). Its unusual electronic structure opens a route to study different variants of topological phenomena including 2D and 3D magnetic interaction, quantum anomalous Hall effect (QAH), axion states, chiral Majorana modes and an elusive single pair of Weyl nodes near the Fermi level Zhang et al. (2019); Liu et al. (2019); Varnava and Vanderbilt (2018); Lee et al. (2018). Such peculiar properties of the electronic states can be realized in MnBi2Te4 by breaking the $S$ symmetry on the (0001) surface due to magnetic phase transition. Otrokov et al. (2018) Its magnetic moments along $c$ axis are produced by the manganese sub-lattice with $C3v$ symmetry. In turn, its nontrivial topological surface states are formed by band inversion between Bi-$p_{z}^{+}$ and Te-$p_{z}^{-}$ states with $C3v$ and $D3d$ group symmetry due to SOC, and in consequence drives the system to a Chern insulator phase. Otrokov et al. (2018); Li et al. (2019b) Because MnBi2Te4 is built of the stacking blocks of Te-Bi-Te-Mn-Te-Bi-Te septuple layers composed of single atomic sheets, breaking the $S$ symmetry can be achieved by cleavage sample surface along (0001) direction or by adjusting the magnetic degree of freedom and inducing a transition from AFM to FM state by magnetic field. The magnetic structure with A-type AFM order is required for the occurrence of the gap in the 2D surface Dirac cone Otrokov et al. (2018); Chowdhury et al. (2019) and has been recently determined by neutron diffraction in the bulk. Yan et al. (2019b)

Here, we present high-resolution ARPES data and first-principles calculations to investigate the surface states and bulk properties of MnBi2Te4. Since MnBi2Te4 has a relatively high Neel temperature $T_{N}$ = 24 K, we collected our ARPES data at 60 K and 8 K, e.g. far above and below AFM ordering. Unlike early ARPES findings of a surface state band gap ranging from about 50 meV to 200 meVs centered at binding energy of 300 meV at the $\Gamma$ point, Zeugner et al. (2019); Vidal et al. (2019); Lee et al. (2018); Chen et al. (2019a) we did not find any evidence for an opening of a gap at the Dirac point of the topological surface states. Furthermore, we do not see any difference in the spectral region around the Dirac point between paramagnetic and antifrromagnetic states. Also, we identified another 2D Dirac point with a binding energy of 50 meV on the same (0001) surface, originating from a nontrivial $Z_{2}$ topology. All of our experimental findings are supported by the band calculations based on a DFT calculation including SOC and assuming AFMG magnetic moment alignment. Finally, we also reveal the effect of AFM ordering on the electronic band structure in MnBi2Te4. Our findings provide a great platform for discovering new unusual quantum phases emerging due to the interplay of different types of magnetism with the topological states in one single crystal.

Single crystals of MnBi2Te4 were grown out of a Bi-Te flux Yan et al. (2019b). Platelike samples used for ARPES measurements were cleaved in situ at 60 K under ultrahigh vacuum (UHV). The data were acquired using a tunable VUV laser ARPES system, that consists of a Omicron Scienta DA30 electron analyzer, a picosecond Ti:Sapphire oscillator and fourth harmonic generator Jiang et al. (2014). Data were collected with photon energies of 6.7 and 6.36 eV. Momentum and energy resolutions were set at $\sim$ 0.005 Å*-1* and 2 meV. The size of the photon beam on the sample was $\sim$30 $\mu$m.

Band structures with spin-orbit coupling (SOC) in density functional theory (DFT) Hohenberg and Kohn (1964); Kohn and Sham (1965) have been calculated using a PBE Perdew et al. (1996) exchange-correlation functional, a plane-wave basis set and projector augmented wave method Blöchl (1994) as implemented in VASP Kresse and Furthmüller (1996, 1996). To account for the half-filled strongly localized Mn 3$d$ orbitals, a Hubbard-like U Dudarev et al. (1998) value of 3.0 eV is used. For bulk band structure of A-type anti-ferromagnetic (AFMA) MnBi2Te4, the rhombohedral unit cell is doubled along c direction with a Monkhorst-Pack Monkhorst and Pack (1976) ($9\times 9\times 3$) $k$-point mesh including the $\Gamma$ point and a kinetic energy cutoff of 270 eV. The band structure of the G-type anti-ferromagnetic (AFMG) configuration is calculated by further doubling the rhombohedral unit cell in the other two directions. Experimental lattice parameters Lee et al. (2013) have been used with atoms fixed in their bulk positions. A tight-binding model based on maximally localized Wannier functions Marzari and Vanderbilt (1997); Souza et al. (2001); Marzari et al. (2012) was constructed to reproduce closely the bulk band structure including SOC in the range of ${E}_{F}\pm$1 eV with Mn $sd$, Bi $p$ and Te $p$ orbitals. Then the spectral functions and Fermi surface of a semi-infinite MnBi2Te4 (001) surface were calculated with the surface Green’s function methods Lee and Joannopoulos (1981a, b); Sancho et al. (1984, 1985) as implemented in WannierTools Wu et al. (2017).

Figures 1(a) shows the crystal structure and A-type AFM (AFMA) magnetic orderings of MnBi2Te4. G-type AFM (AFMG) configuration can be generated by further doubling the rhombohedral unit cell in the other two directions. In the AFMA configuration, the $S$ symmetry is broken on the (0001) surface. However, in the AFMG configuration, breaking only the one along c axis on (0001) surface does not gap out DP, because the two others along a and b axis still remain. Thus, we would expect to observe gapless topological surface states on this surface. Fig. 1(c) shows the ARPES intensity plots of MnBi2Te4 measured using 6.7 eV photons at 60 K. Two shallow electron pockets and a blob of intensity can be seen at the $\Gamma$ point. Fig. 1(d) shows the band dispersion along the white dashed line in panel (c), where two large and one shallow electron pocket can be easily identified. Surprisingly, a gapless Dirac state is clearly present, in stark contrast to the previous predictions and ARPES results Otrokov et al. (2018); Gong et al. (2019); Otrokov et al. (2019); Zeugner et al. (2019); Vidal et al. (2019); Yan et al. (2019a); Li et al. (2019b); Chen et al. (2019a); Li et al. (2019a); Chowdhury et al. (2019). To elucidate the origin of this gapless Dirac state, we conducted DFT calculations on two types of magnetic moment configurations: A-type AFM and G-type AFM. In Figs. 1(e) and (f), we can see that the Fermi surface and band dispersion from DFT calculations partially agree with the ARPES results, whereas the significant gapless Dirac state is missing. On the other hand, with the AFMG configuration, the Fermi surface and band dispersion from DFT calculations reproduce the ARPES intensity pretty well. In order to achieve a better match between DFT and ARPES results, we have to shift the chemical potential of DFT calculations upwards by roughly 220 meV, which is probably due to the lattice defects Yan et al. (2019b).

In Fig. 2, we presented the DFT calculations and ARPES intensities of MnBi2Te4 in great detail. Fig. 2(c) shows the surface state contribution extracted from the DFT calculation results shown in panel (b). Other than the Dirac point marked by the red arrow, we can also identify another Dirac point marked by the blue arrow in panels (b) and (c). These surface Dirac states are protected by the effective TRS in the AFMG configuration, which has yet to be accounted for. To demonstrate that these two Dirac surface states indeed exist in the ARPES spectra, we plotted the second derivative of ARPES intensity with respect to momentum distribution curve (MDC) and energy distribution curve (EDC) in panels (e) and (f). We can clearly see that there are two distinct Dirac points at the binding energies of 50 and 280 meV as marked by the blue and red arrows, respectively. Similar features can be identified in the ARPES intensity measured using 6.36 eV photons at 60 K, as shown in panel (h). These results clearly demonstrate that there are two instead of just one gapless Dirac surface states on the (0001) surface in MnBi2Te4.

Next, let’s focus on the temperature evolution of the electronic structure in MnBi2Te4 as shown in Fig. 3. Panel (b) shows the second derivative of the ARPES intensity calculated with respect to EDC measured using 6.7 eV at 60 K (above the ${T}_{N}$ = 24 K). Other than the two gapless Dirac surface states identified in Fig. 2, we can also observe parabolic conduction and valence bands marked by the red arrows as shown in panel (b). Upon cooling the sample temperature down to 8 K [panels (c)-(d)], we can see that the single conduction band splits into two bands as marked by the two red arrows close to binding energy of 200 meV in panel (d). The same happened to the valence band sitting at ${E}_{B}$=400 meV measured using both 6.7 and 6.36 eV photons as shown in panels (d) and (h), respectively. Since MnBi2Te4 undergoes an AFM instead of FM transition, this splitting of the band is probably due to the bulk-surface interlayer ferromagnetic coupling. On the other hand, the two gapless Dirac surface states does not seem to be correlated with the bulk AFM transition, implicating that the surface may have a different configuration (i.e. AFMG) from the bulk (i.e. AFMA) Mou et al. (2016).

In conclusion, we presented high-resolution ARPES data and first-principles calculations to investigate the electronic properties of MnBi2Te4. In contrast to the observation of gapped surface state at the $\Gamma$ point from early ARPES measurements Zeugner et al. (2019); Vidal et al. (2019); Lee et al. (2018); Chen et al. (2019a), we observed two gapless topological surface states with Dirac points sitting at roughly 50 and 280 meV below Fermi level. Furthermore, the gapless Dirac state does not evolve along with the magnetic transition. On the contrary, the bulk states showed a significant band splitting below the transition, which is probably due to the interlayer ferromagnetic exchange correlation with the surface. Further studies of surface magnetism are required in order to validate this scenario.

Upon completion of this project we become aware that other groups Hao et al. (2019); Chen et al. (2019b); Li et al. (2019c) also independently studied MnBi2Te4 and showed an indication of a single gapless surface Dirac cone in this compound.

Research at Ames Laboratory and ORNL was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Science and Engineering. P. S and Y. W were supported by the Center for the Advancement of Topological Semimetals, an Energy Frontier Research Center funded by the U.S. DOE, Office of Basic Energy Sciences. Ames Laboratory is operated for the U.S. Department of Energy by Iowa State University under Contract No. DE-AC02-07CH11358. B. S. was supported by CEM, a NSF MRSEC, under Grant No. DMR-1420451.

Data for figures are available at https://doi.org/.