High-energy electronic interaction in the $3d$ band of high-temperature iron-based superconductors

One of the most unique and robust experimental facts about iron-based superconductors is the renormalization of the electronic band dispersion by factor of 3 and more near the Fermi level. Obviously related to the electron pairing, this prominent deviation from the band theory lacks understanding. Experimentally studying the entire spectrum of the valence electrons in iron arsenides, we have found an unexpected depletion of the spectral weight in the middle of the iron-derived band, which is accompanied by a drastic increase of the scattering rate. At the same time, the measured arsenic-derived band exhibits very good agreement with theoretical calculations. We show that the low-energy Fermi velocity renormalization should be viewed as a part of the modification of the spectral function by a strong electronic interaction. Such an interaction with an energy scale of the whole $d$ band appears to be a hallmark of many families of unconventional superconductors.

Figure 1

Theoretically calculated and derived from ARPES band dispersion in NaFeAs. (a) Calculated band dispersion in the $M\mathrm{\Gamma }M$ direction. Color coding of the electronic state orbital composition is indicated in the figure. Orbital polarization of the electronic states in this direction is very strong. (b) Contours of the band dispersion, extracted from an ARPES intensity distribution. Extraction of experimental dispersion curves relies on the data measured at different experimental conditions; typical spectra are shown in (c) and (d). (e)–(h) present the same information for the $MXM$ direction.

Figure 2

Model for the spectral function based on the bare dispersion and electronic interaction with a hypothetical bosonic spectrum of single-peak form. Experimental conditions were chosen to highlight one of the bands and suppress the intensity from all others. (a) Experimental data, recorded at a photon energy of 150 eV with vertical light polarization. (b) Spectral function, obtained for the lower-lying $xz/yz$ band and $\lambda =2$. (c) Spectral function for the bare band. (d) Bosonic spectrum ${\alpha }^{2}F\left(\omega \right)$ and self-energy $\mathrm{\Sigma }\left(\omega \right)$ used in the model. Dashed lines schematically represent the situation where ${\mathrm{\Sigma }}^{{}^{\prime }}$ changes sign and the value of ${\mathrm{\Sigma }}^{{}^{\prime \prime }}$ decreases at high $\omega$—this would further improve the agreement between the model and experiment at the bottom of the iron band. (e) Experimental data, recorded at a photon energy of 159 eV with horizontal light polarization in the second Brillouin zone. (f) Spectral function, obtained for the $z^2$ band and $\lambda =1.6$. (g) Spectral function for the bare band. (h) Corresponding ${\alpha }^{2}F\left(\omega \right)$ and $\mathrm{\Sigma }\left(\omega \right)$.

Figure 3

Experimental data taken from various iron-based superconductors, revealing common signatures of strong electron interactions in the spectral function. (a) Data recorded from NaFeAs, LiFeAs, ${(\mathrm{Ba},\mathrm{Rb})\mathrm{Fe}}_2{\mathrm{As}}_2$, NdFeAs(O,F), and (La,Na)${\mathrm{Fe}}_2{\mathrm{As}}_2$. All spectra were taken along the $\mathrm{\Gamma }M$ direction, Brillouin zone diagonal, exclusively with the light of 80 eV energy and polarization lying in the $ab$ plane. These experimental conditions highlight the spectral function related to the original $xz$ band. Note the similarities in all important aspects for the spectra of different materials and compare to the corresponding model, (b) and (c). (b) Experimental data recorded from NaFeAs, (La,Na)${\mathrm{Fe}}_2{\mathrm{As}}_2$, and hole- and electron-doped ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ along the $\mathrm{\Gamma }M$ direction. Experimental conditions were tuned in order to highlight the spectral weight originating from the original $z^2$ band. The presented data reveal signatures of strong electron interactions and a similar spectral shape (fat letter $\mathsf{M}$) is observed for all studied materials; also see (f) and (g).

Figure 4

Dependence of the scattering rate on the binding energy in different compounds. In the materials with relatively weak electronic interactions, such as ${\mathrm{TaSe}}_2$, ${\mathrm{ZrTe}}_3$, ${\mathrm{TiSe}}_2$, and ${\mathrm{Bi}}_2{\mathrm{Se}}_3$, the spectra are sharp, and the band dispersion remains well discernible down to 5 eV and further from the Fermi level. In contrast, for the materials referred to as “correlated,” or featuring strong electron interactions, such as iron-based, cuprate and ruthenate superconductors, and vanadates, the scattering rate grows very fast, and sharp dispersing features are observed only within several hundreds of meV from the Fermi level. (a) ARPES spectra of ${\mathrm{TaSe}}_2$, ${\mathrm{ZrTe}}_3$, ${\mathrm{TiSe}}_2$, and ${\mathrm{Bi}}_2{\mathrm{Se}}_3$. (b) Scattering rate, determined from the width of energy distribution curves; data for cuprates from Refs. [16, 33]; for ruthenates from Ref. [17]; for vanadates from Ref. [18].