Consequences of Broken Translational Symmetry in ${\mathrm{FeSe}}_x{\mathrm{Te}}_{1-x}$

We investigate the consequences of broken translational symmetry in the superconductor ${\mathrm{FeSe}}_x{\mathrm{Te}}_{1-x}$ using angle-resolved photoemission spectroscopy. We find that the intensity does not follow the periodicity dictated by the crystal structure, owing to the form of the perturbing potential and the symmetries of the Fe $d$ orbitals. Their interplay leads to substantial differences in the orbital character and spectral features observed at nominally equivalent locations in the reciprocal space. Such differences cannot be accounted for by the usual dipole matrix element effects and are due instead to the structure factor, which must be explicitly considered whenever more than one atom is present in the unit cell.

Figure 1

(a) Three dimensional view of the ${\mathrm{FeSe}}_x{\mathrm{Te}}_{1-x}$ crystal structure, where nearest neighbor chalcogen atoms alternate above and below the Fe plane. (b) Projection onto the $xy$ (Fe) plane. The size of the atoms is representative of the distance from the observer. The orange (red) square is the 1-Fe (2-Fe) unit cell. The corresponding Brillouin zones are shown in (c) with the same color code. (d) ARPES Fermi surface (FS) map of ${\mathrm{Fe}}_{1.03}{\mathrm{Se}}_{0.26}{\mathrm{Te}}_{0.74}$ measured at 20 K with 140 eV photons and $p$ polarization (for details see Ref. [4]). (e) Wide range FS map measured in the same experimental conditions as in (d), but after a 45° azimuthal rotation of the sample. Higher intensity is darker. No intensity normalization has been applied to the data.

Figure 2

(a) The spectral function $A(k,\omega )$, decomposed into the different orbital contributions. (b) Same as (a) for $\tilde{A}(k,\omega )$ unfolded from $A(k,\omega )$ onto the 1-Fe BZ. A constant lifetime is artificially included in the plot for visualization purposes, and the orbital character of each band is indicated by different colors. The computed bandwidth overestimates by a factor of $\sim 5$ the measured one due to well-known limitations of LDA. (c) FS for the 2-Fe unit cell (left) and 1-Fe unit cell (right), correspondent to the band structure in (a) and (b), respectively. The dashed lines indicate the corresponding BZ boundaries. Close-ups at $\mathrm{\Gamma }$ and $M$ after unfolding onto the 1-Fe BZ are shown in [(d), left] and [(e), left], respectively. At $\mathrm{\Gamma }$, the light polarization and experimental geometry select the $d_{xz}$ component and generate the twofold butterfly [(d), right], at $M$ they select the $d_{3z^2-r^2}$ character, and generate the fourfold cloverleaf [(e), right]. For a detailed discussion see Ref. [4]. In [(c), right] and (e), the $d_{3z^2-r^2}$ weight is amplified by a factor of 5.