ARPES view of orbitally resolved quasiparticle lifetimes in iron pnictides

We study with angle-resolved photoemission spectroscopy (ARPES) the renormalization and quasiparticle lifetimes of the $d_{xy}$ and $d_{xz}/d_{yz}$ orbitals in two iron pnictides, LiFeAs and $\mathrm{Ba}({\mathrm{Fe}}_{0.92}{\mathrm{Co}}_{0.08}){}_2{\mathrm{As}}_2$ (Co8). We find that both quantities depend on orbital character rather than on the position on the Fermi surface (for example, hole or electron pocket). In LiFeAs, the renormalizations are larger for $d_{xy}$, while they are similar for both types of orbitals in Co8. The most salient feature, which proved robust against all the ARPES caveats we could think of, is that the lifetimes for $d_{xy}$ exhibit a markedly different behavior than those for $d_{xz}/d_{yz}$. They have smaller values near $E_F$ and exhibit larger $\omega$ and temperature dependences. While the behavior of $d_{xy}$ is compatible with a Fermi-liquid description, that is not the case for $d_{xz}/d_{yz}$. This situation should have important consequences for the physics of iron pnictides, which have not been considered up to now. More generally, it raises interesting questions about how a Fermi-liquid regime can be established in a multiband system with small effective bandwidths.

Figure 1

Lifetime $\hslash /\tau$ (eV) extracted from ARPES linewidths (see Sec. 5) in (a) LiFeAs for hole and electron pockets at 25 K as a function of binding energy $\hslash \omega$, (b) Co8 for electron pockets at 25 K as a function of binding energy $\hslash \omega$, and (c) Co8 for electron pockets at $E_F$ as a function of temperature. As we could never obtain a behavior reversible in temperature for $d_{xy}$, we indicate width measured when warming up (large symbols) and cooling down (small symbols). The lines are fits to simple Fermi-liquid behaviors, as discussed in Sec. 5b. They are calculated from Eq. (1), with the values of $\gamma$ indicated on the figure and adequate offsets.

Figure 2

(a) Fermi surface measured in Co8 at $T=25$ K, with polarization $A$ along the red arrow and photon energy 34 eV. (a1) and (a2) Energy-momentum images of the two different cuts indicated in (a). (b) Sketch of the orbital characters on the two electron pockets expected by calculation. (c) Experimental band dispersion (symbols) compared with calculated bands shifted and renormalized as indicated in Table 1.

Figure 3

(a) Fermi surface measured in LiFeAs at $T=25$ K, with polarization $A$ along the red arrow and photon energy 34 eV. Sketches of the different pockets with orbital characters are indicated as guides to the eye. (a1)–(a5) Energy-momentum images of the different cuts indicated on the FS map. (b) Experimental dispersions of all bands at $k_z=0$ (points). Calculated dispersions are renormalized by a factor of 2 (lines). (c) The same experimental dispersions with calculation shifted and renormalized as indicated in Table 1. (d) Zoom of the dispersion of the different bands near $E_F$. Colored lines are the LDA dispersion of (c), and the black line is a linear fit on the $d_{yz}$ hole.

Figure 4

(a) Spectral weight in LiFeAs integrated in a 5 meV window around $E_F$ for the $d_{xy}$ electron band as a function of photon energy [cut (a2) in Fig. 3]. Lines are theoretical variations for $k_F$. (b) The same for the $d_{xz}/d_{yz}$ electron band [cut (a1) in Fig. 3]. The dotted line is the position of $d_{xy}$. (c) Spectra corresponding to (b). (d) Experimental (points) and calculated (lines) variations of $k_F$ with photon energy in LiFeAs. (e) Same as (d) for Co8. The dotted lines indicate $k_F$ calculated after a shift of 0.1 eV.

Figure 5

MDC half width at half maximum $\delta \nu$ observed at $E_F$ and low temperatures (25–40 K, except ${\mathrm{BaFe}}_2{\mathrm{As}}_2$, 150 K) in different samples of $\mathrm{Ba}({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x){}_2{\mathrm{As}}_2$ (left) and LiFeAs (right). The black line (right axis of the Co panel) shows the residual resistivity in the normal state taken from Ref. [15] and multiplied by the number of electrons from Ref. [23].

Figure 6

MDC half width at half maximum $\delta \nu$ as a function of binding energy in (a) LiFeAs and (b) Co8. Slopes of the dispersion used to compute 1/$\tau$ [Eq. (3)] in (c) LiFeAs and (d) Co8. For electron bands, it is the slope of the renormalized LDA dispersion. For hole bands, it is straight lines, as they give a fit better than or equivalent to that of the LDA [see Fig. 3].