Surface state evolution induced by magnetic order in axion insulator candidate ${\mathrm{EuIn}}_2{\mathrm{As}}_2$

Gapping of Dirac surface states through time reversal symmetry breaking may realize the axion insulator state in condensed matter. Despite tremendous efforts, only a few material systems fall into this category of intrinsic magnetic topological insulators. Recent theoretical calculations proposed the antiferromagnetic (AFM) ${\mathrm{EuIn}}_2{\mathrm{As}}_2$ to be a topologically nontrivial magnetic insulator with gapped surface states. Here we use scanning tunneling microscopy and spectroscopy complemented with density-functional theory calculations and modeling to probe the surface electronic states in ${\mathrm{EuIn}}_2{\mathrm{As}}_2$. We find a spin-orbit induced bulk gap of $\sim 120\mathrm{meV}$ located only a few meV above the Fermi energy, within which topological surface states reside. Temperature-dependent measurements provide evidence of the partial gapping ($\sim 40\mathrm{meV}$) of the surface states at low temperatures below the AFM order, which decreases with increasing temperature but remains finite above $T_{\mathrm{N}}$.

Figure 1

Topographic image of cleaved ${\mathrm{EuIn}}_2{\mathrm{As}}_2$ single crystal showing (a) the stripe and atomic surfaces (−200 mV, −30 pA), (b) the disordered stripe surface (−200 mV, −30 pA), and (c) large-scale atomic surface with the disordered stripe surface (−200 mV, −300 pA). The lower insets correspond to the topographic height across the lines in (a–c). Zoom-in of the surface structure of the (d) the stripe surface (−200 mV, −100 pA) and (e) the disordered stripe surface (−200 mV, −100 pA). (f) The atomic surface with different surface coverage (left: −200 mV, −30 pA; right: 200 mV, −150 pA). (g) Crystal structure of ${\mathrm{EuIn}}_2{\mathrm{As}}_2$ and a corresponding schematic of the layered structure showing the different observed cleaves with distances between different levels indicated ($\mathrm{red}=\mathrm{Eu}, \mathrm{blue}=\mathrm{As}, \mathrm{green}=\mathrm{In}$). (h) Schematics of the two observed reconstructions. The schematic on the left represents the atomic surface, while the one on the right represents the stripe surface. (i) Topographic line cuts across the atomic, stripe, and disordered stripe surfaces. The different colors correspond to the three different directions.

Figure 2

(a) Topography (−200 meV,−300 pA) showing the large-scale atomic structure exhibiting two layers. (b) Close-in topography (−200 meV, −50 pA) of the double atomic layer, with good visibility of the structure within the lower layer (blue surface). (c) Two line cuts. Blue line is the line cut along the black line shown in (b), going along the atomic structure seen within the lower atomic layer (with the amplitude multiplied by 3.5). The calculated lattice constant is 6.45Å, which agrees strongly with the 1.$5a$ reconstruction of the most commonly seen upper layer atomic surface. The red line is a line cut along the upper atomic surface, showing the same periodicity. (d) Line cut showing the step between the lower and upper atomic layers, with a step height of around 2 Å. (e–g) Fourier transforms of the stripe, disordered stripe, and atomic surfaces. Red circles correspond to the Bragg peaks of the reconstructed surfaces.

Figure 3

Spatial dependence of the conductance ($dI/dV$) at varying locations (shown above by the three different colors in each panel) on the three different surfaces: (a) atomic, (b) ordered, and (c) disordered stripes. Same (different) color corresponds to nearby (farther away) pixel positions where the spectra are acquired. All measurements are carried out at 9.5 K with a set point bias of −200 meV and a set point current of -100 pA.

Figure 4

Temperature dependence of $dI/dV$ conductance spectra on the disordered stripe surface with energy ranges of (a) −200 to 400 meV and (b) −50 to 200 meV. All spectra are taken at the exact same location on the disordered stripe surface with $\mathrm{bias}=–200\mathrm{meV}$ and set $\mathrm{point}\mathrm{current}=–100\mathrm{mA}$.

Figure 5

Temperature dependence of $dI/dV$ conductance spectra on the atomic surface with energy ranges of (a) −200 to 400 meV and (b) −100 to 200 meV. All spectra are taken at the exact same location on the atomic surface with a set point bias of −200 meV and a set point current of −100 pA. Two dashed lines in (b) track the peak positions of the peaks corresponding to the surface state bands, showing the trend of shrinking magnetic gap as temperature increases with the peaks eventually merged together at 19 K, above $T_{\mathrm{N}}$. The black dashed lines correspond to a Gaussian fitting with four Gaussian functions for the B1, S1, S2, and B3 peaks and a quadratic background. The red and green vertical dashed lines guide the eye to the evolution of the peaks. Note that the B1 hump is quite weak since it is composed predominantly of In character (see main text). (c) Energy versus temperature of the four Gaussian peak energies extracted from the fits in (b). The red triangles (S1 and S2) correspond to the left $y$ axis while the bulk bands B1 and B3 correspond to the right $y$ axis. The vertical arrow corresponds to the magnitude of the full bandwidths of the S1 and S2 peaks extracted from the fits.

Figure 6

(a) DFT calculated band structure. (b) DFT calculated band structure along the $M$-Γ-$M$ direction near $E_{\mathrm{F}}$. B1, B2/B3 correspond to Van Hove singularities of the bulk valence and conduction bands, respectively, created as a result of spin-orbit induced band inversion. S1 and S2 correspond to Van Hove singularities of the gapped surface states [44]. (c) The calculated density of states shows peaks [corresponding to Van Hove singularities in (b)] at energies that are in good agreement with the STM spectra observed on the atomic surface [shown in Fig. 3].

Figure 7

(a) Crystal structure of ${\mathrm{EuIn}}_2{\mathrm{As}}_2$ with every other Eu atom missing along the $a$ direction, resulting in the stripe surface. The sites missing the Eu atom are present in each Eu layer; thus the unit cell is doubled along the $a$ direction. (b) The band structure around the Γ point near the Fermi energy. It can be seen that one copy of the band touching point is pushed up to an energy of $\sim 1.3\mathrm{eV}$, while the other copy is pushed down to an energy of $\sim 0.25\mathrm{eV}$ and merged into the Eu $f$ bands. The splitting between these two copies is much larger because the sites missing the Eu atom are present in each Eu layer. This structure represents the case of large splitting due to the stripe order of Eu atoms.

Figure 8

(a) Artificial crystal structure in which one of the Eu atoms is placed closer to its nearby As atom by $h=0.2\AA$. The unit cell is consequently doubled along the $a$ direction. (b) The DFT band structure around the Γ point near the Fermi energy of the artificial crystal structure. The band replication can be clearly seen on the right. In this structure, because Eu atoms are only shifted but not missing from the site, the electrical potential inducing the band replication is much smaller, leading to the smaller band splitting. This structure represents the case of small splitting due to the stripe order of Eu atoms.