Nonrigid band shift and nonmonotonic electronic structure changes upon doping in the normal state of the pnictide high-temperature superconductor $\mathrm{Ba}{\left(\mathrm{F}{\mathrm{e}}_{1-x}\mathrm{C}{\mathrm{o}}_x\right)}_2\mathrm{A}{\mathrm{s}}_2$

We report systematic angle-resolved photoemission (ARPES) experiments using different photon polarizations and experimental geometries and find that the doping evolution of the normal state of $\mathrm{Ba}{\left(\mathrm{F}{\mathrm{e}}_{1-x}\mathrm{C}{\mathrm{o}}_x\right)}_2\mathrm{A}{\mathrm{s}}_2$ deviates significantly from the predictions of a rigid band model. The data reveal a nonmonotonic dependence upon doping of key quantities such as band filling, bandwidth of the electron pocket, and quasiparticle coherence. Our analysis suggests that the observed phenomenology and the inapplicability of the rigid band model in Co-doped Ba122 are due to electronic correlations, and not to the either the strength of the impurity potential, or self-energy effects due to impurity scattering. Our findings indicate that the effects of doping in pnictides are much more complicated than currently believed. More generally, they indicate that a deep understanding of the evolution of the electronic properties of the normal state, which requires an understanding of the doping process, remains elusive even for the 122 iron-pnictides, which are viewed as the least correlated of the high-$T_C$ unconventional superconductors.

Figure 1

Experimental methodology. (a) Schematic illustration of the experimental geometry. The directions of the incoming photon $\left(h\nu \right)$ and the outgoing photoelectron $\left(e^{-}\right)$ define the scattering plane, which in our experiment is also a mirror plane of the sample, oriented perpendicular to the sample's $ab$ plane. The analyzer slit, parallel to the sample plane, is contained in the scattering plane. The photon polarization is either parallel (π) or perpendicular (σ) to the scattering plane or, analogously, parallel (σ) or perpendicular (π) to the $ab$ sample plane. (b) A summary of the bands found along the $\mathrm{\Gamma }X$ and $\mathrm{\Gamma }M$ cuts for different polarizations and their notation. Spectra excited with σ and π polarization allow the detection of initial state wave functions with in-plane and out-of-plane character, respectively. HB and EB denote hole and electron bands, respectively. The subscripts σ and π indicate the polarization which selects for the band. For example, $\mathrm{HB}{{\sigma }_{\mathrm{\Gamma }}}_X$ corresponds to a hole band along $\mathrm{\Gamma }X$ observed with σ polarization. The $\mathrm{H}{\mathrm{B}}_{\mathrm{\Gamma }X}$ and $\mathrm{H}{\mathrm{B}}_{\mathrm{\Gamma }M}$ bands are detected in both polarizations (see text).

Figure 2

Fermi surfaces of $\mathrm{Ba}{\left(\mathrm{F}{\mathrm{e}}_{1-x}\mathrm{C}{\mathrm{o}}_x\right)}_2\mathrm{A}{\mathrm{s}}_2$ for different Co concentrations, measured along the $\mathrm{\Gamma }M$ direction. The data were taken in the normal state at $T=28\mathrm{K}$ both with σ and π polarization (left and right panels, respectively) and with an incoming photon energy of 60 eV. The FS maps were generated by integrating the spectra over a window of 10 meV around $E_{\mathrm{F}}$ for better visualization. Higher color brightness corresponds to higher intensity.

Figure 3

Image plots for data collected along the $\mathrm{\Gamma }X$ and $\mathrm{\Gamma }M$ direction, centered at the Γ (0,0) and $M$ (π,π) points. (a)–(d) Image plots of data collected at Γ (hole pocket) along the (a) and (b) $\mathrm{\Gamma }X$ and (c) and (d) $\mathrm{\Gamma }M$ direction with (a) and (c) σ and (b) and (d) π polarization. (e) and (f) Image plots of data collected at Μ (electron pocket) with σ polarization along the (e) $\mathrm{\Gamma }X$ and (f) $\mathrm{\Gamma }M$ direction. Data collected at $M$ with π polarization had extremely low intensity (cf. Fig. 2), and are not shown. The continuous lines denote the renormalized DFT bands (see text for details). Higher color brightness corresponds to higher intensity.

Figure 4

MDC spectra extracted using different integration windows at the Fermi level. The data were collected from the parent compound at Γ (hole pocket) along the $\mathrm{\Gamma }M$ direction with σ polarization. The MDC spectra were extracted using different integration windows at the Fermi level, as indicated in the legend. All of the peaks have been aligned on the left-hand side of the plot in order to show clearly the systematic change of the positions of the peaks on the right-hand side. The zero of the momentum scale has been set to coincide with the center of the peaks on the left-hand side of the plot. Note also the substantial broadening introduced by the use of larger integration windows. The lines through the data points are guides to the eye.

Figure 5

Image plots and MDC analysis for data collected along the $\mathrm{\Gamma }X$ direction, centered at the Γ (0,0) and $M$ (π,π) points. (a)–(d) Image plots, MDC spectra at $E_{\mathrm{F}}$, and fits of data collected at Γ (hole pocket) with (a) and (b) σ and (c) and (d) π polarization. (e) and (f) Image plots, MDC spectra at $E_{\mathrm{F}}$, and fits of data collected at Μ (electron pocket) with σ polarization. Higher color brightness corresponds to higher intensity. A minimum number of peaks were used to fit the MDCs. The continuous lines through the data points are the results of the fits. At Γ (a)–(d), for both polarizations, two bands are always detected: one band visible only in σ polarization $\left(\mathrm{HB}{\sigma }_{\mathrm{\Gamma }X}\right)$, one band visible only in π polarization $\left(\mathrm{HB}{\pi }_{\mathrm{\Gamma }X}\right)$, and one band visible $\left(\mathrm{H}{\mathrm{B}}_{\mathrm{\Gamma }X}\right)$ in both polarizations. For the parent compound there is one additional band visible in the σ polarization. In the HOD compound the $\mathrm{H}{\mathrm{B}}_{\mathrm{\Gamma }X}$ bands lie below $E_{\mathrm{F}}$, and thus only the tails of the bands are visible, and appear as a single peak. (e) and (f) At $M$, two bands are detected, but they cannot be distinguished based on their orbital symmetry. They are labeled as an internal $\left(\mathrm{E}{\mathrm{B}}_{\mathrm{IN}}\right)$ and an external $\left(\mathrm{E}{\mathrm{B}}_{\mathrm{EX}}\right)$ band.

Figure 6

Image plots and MDC analysis for data collected along the $\mathrm{\Gamma }M$ direction centered at the Γ (0,0) and $M$ (π,π) points. (a)–(d) Image plots, MDC spectra at $E_{\mathrm{F}}$, and fits of data collected at Γ (hole pocket) with (a) and (b) σ and (c) and (d) π polarization. (e) and (f) Image plots, MDC spectra at $E_{\mathrm{F}}$, and fits of data collected at Μ (electron pocket) with σ polarization. Higher color brightness corresponds to higher intensity. A minimum number of peaks were used in the fit of the MDCs, resulting in the continuous lines through the data. At Γ (a)–(d), for both polarizations, two bands are always detected: one band visible only in σ polarization (labeled $\mathrm{HB}{\sigma }_{\mathrm{\Gamma }M}$), one band visible only in π polarization (labeled $\mathrm{HB}{\pi }_{\mathrm{\Gamma }M}$ ), and one band visible in both polarizations (labeled $\mathrm{H}{\mathrm{B}}_{\mathrm{\Gamma }M}$ ). For the parent compound there is one small additional band visible in the σ polarization, which originates from the band folding induced by the structural phase transition $T=140\mathrm{K}$. In the HOD compound the $\mathrm{H}{\mathrm{B}}_{\mathrm{\Gamma }M}$ bands lie below $E_{\mathrm{F}}$, and thus only the tails of the bands are visible, appearing as a single peak. (e) and (f) At the $M$ point, two bands are detected, but they cannot be distinguished based on their orbital symmetry. They are labeled as the internal $(\mathrm{E}{\mathrm{B}}_{\mathrm{IN}})$ and external $(\mathrm{E}{\mathrm{B}}_{\mathrm{EX}})$ electron bands.

Figure 7

Co concentration dependence of the Fermi momenta and comparison to DFT results. The Fermi momenta $k_{\mathrm{F}}$, identified by the position of the peaks fitting the MDC shown in Figs. 5 and 6, are plotted for the different Co concentrations indicated on the left vertical scales. The right vertical scales indicate the corresponding shift of the chemical potential as calculated with DFT (see text). The lines through the data points are guides to the eye. The error bars on the Fermi momenta are comparable to the symbols size. (a) and (b) Result from the fitting of the MDC at the hole pocket along the (a) $\mathrm{\Gamma }X$ and (b) $\mathrm{\Gamma }M$ directions. (c) and (d) Result from the fitting of the MDC at the electron pocket along the (c) $\mathrm{\Gamma }X$ and (d) $\mathrm{\Gamma }M$ directions. The continuous lines are the DFT bands for the P compound. According to the DFT calculations, the band structure of the doped compounds is obtained by raising the chemical potential μ corresponding to the value of the chemical shift indicated on the right vertical scale in the figures.

Figure 8

Energy distribution curve (EDC) stacks, corresponding to the data shown in Figs. 5 and 6. (a)–(d) EDCs of data collected at the Γ point (hole pocket) along the (a) and (b) $\mathrm{\Gamma }X$ and (c) and (d) $\mathrm{\Gamma }M$ directions. The photon polarization is indicated in the figure. (e) and (f) EDCs of data collected in σ polarization at the $M$ point (electron pocket) along the (e) $\mathrm{\Gamma }X$ and (f) $\mathrm{\Gamma }M$ directions. The highlighted spectra denote the EDC at the Fermi momenta $k_{\mathrm{F}}$. The outer EDC corresponds to the $k_{\mathrm{F}}\text{"}\mathrm{s}$ of the (a) $\mathrm{HB}{{\sigma }_{\mathrm{\Gamma }}}_X$, (b) $\mathrm{HB}{{\pi }_{\mathrm{\Gamma }}}_X$, (c) $\mathrm{HB}{{\sigma }_{\mathrm{\Gamma }}}_M$, (d) $\mathrm{HB}{{\pi }_{\mathrm{\Gamma }}}_M$, and (e) and (f) $\mathrm{E}{\mathrm{B}}_{\mathrm{EX}}$ bands. In (a)–(d), the inner EDC corresponds to $k_{\mathrm{F}}$ for the (a) and (b) $\mathrm{H}{\mathrm{B}}_{\mathrm{\Gamma }X}$ and (c) and (d) $\mathrm{H}{\mathrm{B}}_{\mathrm{\Gamma }M}$ bands. In (e) and (f), the inner and outer EDCs correspond to the $k_{\mathrm{F}}$'s for the $\mathrm{E}{\mathrm{B}}_{\mathrm{IN}}$ and $\mathrm{E}{\mathrm{B}}_{\mathrm{EX}}$ bands, respectively. The highlighted spectra at the center of the EDC stack denote the EDC taken at the $M$ point (bottom of electron pocket).

Figure 9

Co concentration dependence and fits of the EDCs at $M$. EDCs extracted from the data at the $M$ point (bottom of electron pocket) along the (a) and (b) $\mathrm{\Gamma }X$ and (c) and (d) $\mathrm{\Gamma }M$ directions in σ polarization. In (a) and (c) the EDC spectra are fit with the Doniach-Šunjić (DS) line shape, while the spectra shown in (b) and (d) are fit with Lorentzian (L) peaks and an additional Gaussian peak denoted as G, after subtraction of a Shirley background. Peak B denotes a broad holelike band that never crosses $E_{\mathrm{F}}$, but intersects the $\mathrm{E}{\mathrm{B}}_{\mathrm{IN}}$ and $\mathrm{E}{\mathrm{B}}_{\mathrm{EX}}$ bands close to the $M$ point. The narrow peak (BF) visible in the spectra along the $\mathrm{\Gamma }X$ direction in the P and UD compounds accounts for the band folding due to the orthorhombic distortion. In (b), the dashed line denotes an additional background necessary to fit the longer tail of the spectra. The use of the DS line shape does not produce satisfactory fits. For clarity, the spectra in the figures were normalized to the same height, so overall intensities cannot be directly compared.

Figure 10

Co concentration dependence of the Fermi momenta and binding energy of the $\mathrm{E}{\mathrm{B}}_{\mathrm{IN}}$ and $\mathrm{E}{\mathrm{B}}_{\mathrm{EX}}$ bands obtained from fitting the EDCs at the $M$ point. The Fermi momenta, identified by the position of the peaks in the MDCs fits, are plotted as a function of Co concentration. The error bars $(\pm 0.005{\AA }^{-1})$ are smaller than the size of the symbols. The continuous lines through the data points are a guide to the eye. (a) and (b) Result from the fitting of the MDCs at the hole pocket along the (a) $\mathrm{\Gamma }X$ and (b) $\mathrm{\Gamma }M$ directions. (c) and (d) Result from the fitting of the MDCs at the electron pocket along the (c) $\mathrm{\Gamma }X$ and (d) $\mathrm{\Gamma }M$ directions. (e) and (f) Doping dependence of the binding energy of the $\mathrm{E}{\mathrm{B}}_{\mathrm{IN}}$ and $\mathrm{E}{\mathrm{B}}_{\mathrm{EX}}$ bands obtained from fitting the EDCs at the $M$ point (bottom of the electron pocket). The error bars are comparable to the size of the symbols. For lower Co concentrations, the bottom of the $\mathrm{E}{\mathrm{B}}_{\mathrm{EX}}$ band shifts toward $E_{\mathrm{F}}$, while the bottom of the $\mathrm{E}{\mathrm{B}}_{\mathrm{IN}}$ band exhibits an irregular, nonmonotonic shift. For different Co concentrations, only in the HOD sample does the bottom of the $\mathrm{E}{\mathrm{B}}_{\mathrm{IN}}$ and $\mathrm{E}{\mathrm{B}}_{\mathrm{EX}}$ bands shifts to higher BE. This behavior is clearly at odds with a rigid shift of the band structure, since in this case the bottom of the bands would drift progressively away from $E_{\mathrm{F}}$. Also shown, denoted with the triangle symbol, is the position of peak B in Fig. 9, i.e., the maximum of the band that never crosses $E_{\mathrm{F}}$ (see text).

Figure 11

Schematic illustration of the Co concentration dependence of the electronic structure at the $M$ point (electron pocket). The positions of the Fermi momenta from the MDC analysis [cf. Figs. 10 and 10] and the BE of the bottom of the electron pocket obtained from the fitting of the EDC spectra [cf. Figs. 10 and 10] for the (a) $\mathrm{\Gamma }X$ and (b) $\mathrm{\Gamma }M$ directions are plotted for different Co concentration. Also shown, denoted with the diamond symbol, is the position of the maximum of the band that never crosses $E_{\mathrm{F}}$ [cf. peak B in Figs. 9, 10, and 10]. The continuous lines are guides for the eye.

Figure 12

Co concentration dependence of the EDCs at the Fermi momenta $\left(k_{\mathrm{F}}\right)$ for the bands at Γ (hole pocket). (a)–(d) Outer band EDCs extracted from the image plots corresponding to $k_{\mathrm{F}}$ for cuts along the (a) and (b) $\mathrm{\Gamma }X$ and (c) and (d) $\mathrm{\Gamma }M$ directions. (e)–(h) Inner band EDCs extracted from the image plots corresponding to $k_{\mathrm{F}}$ for cuts along the (e) and (f) $\mathrm{\Gamma }X$ and (g) and (h) $\mathrm{\Gamma }M$ directions. The photon polarization is indicated on top of the panels. For clarity, the spectra in the figures were normalized to the same height, so a comparison of the intensities is meaningless.

Figure 13

Co concentration dependence of the EDCs at the Fermi momenta $\left(k_{\mathrm{F}}\right)$ for the bands at $M$ (electron pocket). EDCs extracted from the image plots corresponding to $k_{\mathrm{F}}$ for cuts along the (a) and (b) $\mathrm{\Gamma }X$ and (c) and (d) $\mathrm{\Gamma }M$ directions. All of the spectra have been taken with σ polarization. The spectra sharpen in correspondence of optimal doping. For clarity, the spectra in the figures were normalized to the same height, so a comparison of the intensities is meaningless.

Figure 14

Results of the DFT calculations in the parent compound. The calculations are pertinent to the plane containing the $Z$ point, i.e., the zone boundary along the vertical $k_z$ direction. As explained in the text, we refer to the high symmetry directions $Za$ and $Zb$ as $\mathrm{\Gamma }X$ and $\mathrm{\Gamma }M$, respectively. In each panel the size of the markers indicate the amount of orbital character contributed to each band. (a) $xy$, (b) $xz,yz$, (c) $x^2-y^2$, and (d) $z^2$.