Realization of a tunable surface Dirac gap in Sb-doped ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$

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.

Figure 1

Presence of the surface state gap in Sb-doped ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$. Data taken on a $x_{\mathrm{nominal}}=0.075$ sample at $T=10$ K. (a)–(c) Raw (top) and second derivative (bottom) ARPES $k\text{−}E$ maps on three representative photon energies, close to the bulk high-symmetry points (a) ${\mathrm{\Gamma }}_3$, (b) $Z_3$, and (c) ${\mathrm{\Gamma }}_4$, respectively. BV: bulk valence band; SV/SC: surface valence/conduction band (bottom/top part of the gapped surface state); BC1/BC2: the two bulk conduction bands seen at $T<T_N$. The persistence of the surface state gap and the evolution of BV is seen clearly. (d) Extraction of $k_z$ dispersion for the bands at $\overline{\mathrm{\Gamma }}$. Photon energy ranges from 6.5 to 23 eV, corresponding to $\sim 5.5\pi /c<k_z<\sim 10.6\pi /c$. Colored lines are guides to the eye.

Figure 2

Temperature independence of the bulk and surface state gap. (a)–(d) Temperature evolution of the bands of Sample S2 ($x_{\mathrm{nominal}}=0.05$). Data is taken with a 6.36-eV laser ARPES setup [i.e., at $k_z\sim 5\pi /c$ ($Z_2$)]. (a)–(c) Raw (left) and second derivative (right) ARPES $k\text{−}E$ maps taken at three representative temperatures, below and above the bulk AFM-PM transition temperature $T_N\sim 23.5$ K. (d) Summary on the temperature evolution of BC1, BC2, and the surface state (SS) gap. While BC1 and BC2 merges into a single bulk conduction (BC) band around $T_N$, the SS gap remains essentially unchanged. (e)–(h) Effective band structure (EBS) calculation results for the AFM and PM state electronic structure on a $x=1/18$ (0.056) system. (e)/(h) Overall band structure of the AFM/PM state. Inset: AFM Brillouin zone with high-symmetry points. Red ellipses highlight the merging of BC1 and BC2 at $Z$. (f)/(g) Focused band structure of the AFM/PM state along $L\text{−}Z\text{−}L$.

Figure 3

Carrier concentration dependence of the SS gap and the bulk gap. Data is taken with a 6.36-eV laser ARPES setup at $T=30$-35 K (above $T_N$). (a)–(e) Raw (top) and second derivative (bottom) ARPES $k\text{−}E$ maps for five samples with different carrier concentrations ordered by $E_c$. Red/blue lines: SS/bulk gap. (f) $E_c$ dependence of the bulk gap at $Z$ (blue, left), and the SS gap (black, right). Data taken with Samples A7 and A10 (Section S11 [45]) is also included. (g) Bulk gap at $\mathrm{\Gamma }$ (black) and $Z$ (blue) calculated via supercell approach. Possible errors due to different Sb configuration are within symbol size. Solid lines are polynomial fits. TI: topological insulator; NI: normal insulator; TPT: topological phase transition.