Effect of impurity substitution on band structure and mass renormalization of the correlated ${\mathrm{FeTe}}_{0.5}{\mathrm{Se}}_{0.5}$ superconductor

Using angle-resolved photoemission spectroscopy (ARPES), we studied the effect of the impurity potential on the electronic structure of ${\mathrm{FeTe}}_{0.5}{\mathrm{Se}}_{0.5}$ superconductor by substituting 10% of Ni for Fe, which leads to an electron doping of the system. We could resolve three hole pockets near the zone center and an electron pocket near the zone corner in the case of ${\mathrm{FeTe}}_{0.5}{\mathrm{Se}}_{0.5}$, whereas only two hole pockets near the zone center and an electron pocket near the zone corner are resolved in the case of ${\mathrm{Fe}}_{0.9}{\mathrm{Ni}}_{0.1}{\mathrm{Te}}_{0.5}{\mathrm{Se}}_{0.5}$, suggesting that the hole pocket having predominantly the $xy$ orbital character is very sensitive to the impurity scattering. Upon electron doping, the size of the hole pockets decreases and the size of the electron pockets increases as compared to the host compound. However, the observed changes in the size of the electron and hole pockets are not consistent with the rigid-band model. Moreover, the effective mass of the hole pockets is reduced near the zone center and of the electron pockets is increased near the zone corner in the doped ${\mathrm{Fe}}_{0.9}{\mathrm{Ni}}_{0.1}{\mathrm{Te}}_{0.5}{\mathrm{Se}}_{0.5}$ as compared to ${\mathrm{FeTe}}_{0.5}{\mathrm{Se}}_{0.5}$. We refer these observations to the changes of the spectral function due to the effect of the impurity potential of the dopants.

Figure 1

ARPES data from ${\mathrm{FeTe}}_{0.5}{\mathrm{Se}}_{0.5}$. In (a), we schematically show our measuring geometry in which we define $s$- and $p$-plane polarized lights with respect to the analyzer entrance slit. (b) Fermi surface map measured using $s$-polarized light with a photon energy $h\nu =81$ eV. (c) and (d) show the energy distribution maps (EDMs) taken close to the high-symmetry points $M$ and $A$ (see text), respectively, measured using $s$-polarized light along cut 1 as showed on the FS map. (e) and (f) show EDMs taken near $\mathrm{\Gamma }$ measured using $p$- and $s$-polarized lights, respectively, along cut 2 as shown on the FS map. (g) and (h) are analogous data to (e) and (f), respectively, but taken near the $Z$ point. (i)–(n) are the second derivatives of (c)–(h). The red colored contours in (b) are guides to the eye schematically representing the Fermi sheets, and the curves in (i)–(n) are guides to the eye schematically representing the band dispersions. In (o) and (p), we show the renormalized DFT-LDA band structure (black curves) overlaid on the experimental (red curves) band dispersions. We have normalized the EDMs by higher orders of the monochromator above the Fermi level.

Figure 2

ARPES spectra of ${\mathrm{Fe}}_{0.9}{\mathrm{Ni}}_{0.1}{\mathrm{Te}}_{0.5}{\mathrm{Se}}_{0.5}$. (a) is the Fermi surface map measured using $s$-polarized light with a photon energy $h\nu =81$ eV. (b) and (c) show the energy distribution maps (EDMs) taken close to the high-symmetry points $M$ and $A$ (see the text), respectively, measured using $s$-polarized light along the cut 1 as shown on the FS map. (d) and (e) are EDMs taken near $\mathrm{\Gamma }$ measured using $p$- and $s$-polarized lights, respectively, along the cut 2 as shown on the FS map. (f) and (g) are analogous data to (d) and (e), respectively, but taken near the $Z$ point. (h)–(m) are the second derivatives of (b)–(g). (n) is the Fermi surface map in the $k_y-k_z$ plane at the zone corner. The black circles are overlaid on the FS map representing the peak positions of the $\beta$ band. (o) shows a stack-plot of momentum distribution curves (MDCs) sampling different $k_z$ (red curves), together with results of a fit using a pair of Lorentzian functions. The red colored contour in (a) is guide to the eye schematically representing the Fermi sheet and the dashed curves in (h)–(m) are guides to the eye schematically representing the band dispersions. We have normalized the EDMs by higher orders monochromator above the Fermi level.

Figure 3

In the figure, the red and blue curves are the band dispersions from ${\mathrm{FeTe}}_{0.5}{\mathrm{Se}}_{0.5}$ and ${\mathrm{Fe}}_{0.9}{\mathrm{Ni}}_{0.1}{\mathrm{Te}}_{0.5}{\mathrm{Se}}_{0.5}$, respectively, resulted from a fit to the MDCs using a pair of Lorentzian functions at $\mathrm{\Gamma }$ for the band ${\alpha }_1$ (a) and for ${\alpha }_2$ (b). Similarly, the band dispersions are shown at $Z$ for ${\alpha }_1$ (c) and for ${\alpha }_2$ (d). (e) and (f) depict the band dispersions from $M$ and $A$, respectively. (g) shows the DFT-LDA (black curves) band structure overlaid with the experimental band dispersions along the $\mathrm{\Gamma }-M$ high-symmetry line. Similarly, (h) shows the band structure overlaid with the experimental band dispersions along the $Z-A$ high-symmetry line.