Topological nature of the ${\mathrm{FeSe}}_{0.5}{\mathrm{Te}}_{0.5}$ superconductor

We demonstrate, using first-principles calculations, that the electronic structure of ${\mathrm{FeSe}}_{1-x}{\mathrm{Te}}_x(x=0.5)$ is topologically nontrivial and characterized by an odd ${\mathbb{Z}}_2$ invariant and Dirac cone type surface states, in sharp contrast to the end member FeSe $(x=0)$. This topological state is induced by the enhanced three-dimensionality and spin-orbit coupling due to Te substitution (compared to FeSe), and characterized by a band inversion at the $Z$ point of the Brillouin zone, which is confirmed by our ARPES measurements. The results suggest that the surface of ${\mathrm{FeSe}}_{0.5}{\mathrm{Te}}_{0.5}$ may support a nontrivial superconducting channel in proximity to the bulk.

Figure 1

Unit cell of $\mathrm{Fe}X$ ($X$ = ${\mathrm{Se}}_{0.5}{\mathrm{Te}}_{0.5}$), with the $x$ axis pointing along Fe nearest neighbors. (a) Top view. (b) Crystal structure. Gray and green balls represent Fe and $X$ atoms, respectively. (c) Schematic plot of the hybridization along the $z$ axis between the combined orbitals $D_{xy}^{-}$ and $P_z^{-}$ (see details in Appendix pp2), consisting of intralayer $pd$ bonding and interlayer $pp$ bonding.

Figure 2

DFT electronic band structures. (a) Band structure of FeSe with internal parameter $z_X=0.2345$ without SOC. (b) Band structure of ${\mathrm{FeSe}}_{0.5}{\mathrm{Te}}_{0.5}$ ($z_X=0.2719$) without SOC. (c) Band structure of ${\mathrm{FeSe}}_{0.5}{\mathrm{Te}}_{0.5}$ with SOC. (d) Zoom-in view of the solid red box area in (c). The size of the red circles in (a) and (b) indicates the weight of the $p_z$ component of the chalcogen atoms. The two $d_{z^2}$ bands are indicated below $E_F$ in (b). The original ${\mathrm{\Lambda }}_5$ bands split into ${\mathrm{\Lambda }}_6$ and ${\mathrm{\Lambda }}_7$. Along the $\mathrm{\Gamma }-Z$ line, two ${\mathrm{\Lambda }}_6$ bands cross and hybridize to open a SOC gap of about 10 meV. The red dashed line corresponds to a Fermi curve across the gap.

Figure 3

Topological nontrivial 001 surface states and spin-resolved Fermi surface of these states. (a) Surface LDOS on the (001) surface for ${\mathrm{FeSe}}_{0.5}{\mathrm{Te}}_{0.5}$ considering DMFT on-site modification. (b) Fermi surface of the topological state (bright yellow circle beside the projected bulk states). The in-plane spin orientation is indicated by green arrows.

Figure 4

ARPES spectra along the $\mathrm{\Gamma }-M$ direction in the $\sigma$-polarization geometry. (a) ${\mathrm{FeSe}}_{0.5}{\mathrm{Te}}_{0.5}$ before surface evaporation. (b) ${\mathrm{FeSe}}_{0.5}{\mathrm{Te}}_{0.5}$ after 6 minutes of K surface doping. (c), (d) MDCs corresponding to data from the dashed boxes in panels (a) and (b), respectively.

Figure 5

Normal-emission ARPES spectra. First row: Schematic band dispersions. The main feature is the $p_z$ band crossing the $d_{xy}, d_{yz}$, and $d_{xz}$ bands, opening a SOC gap with the $d_{xz}$ band. Second row: ARPES data on ${\mathrm{FeSe}}_{0.5}{\mathrm{Te}}_{0.5}$. Third row: ARPES data on LiFeAs. First column: Dispersion at $k_x=0$ along the $\mathrm{\Gamma }-Z$ direction. Second, third, and fourth columns: Electronic dispersions along cuts indicated in the first column.

Figure 6

Electronic band structure of LiFeAs. The $p_z$ component is highlighted by the size of the red circles.

Figure 7

Electronic band structure along $\mathrm{\Gamma }-Z$. (a) The IRs are labeled in the NSO bands. (b) The parities are labeled in the SOC bands.

Figure 8

Upper panel: LDA+DMFT calculations. Lower panel: SOC band structure only taking the LDA+DMFT on-site modification into consideration.