Large Temperature Dependence of the Number of Carriers in Co-Doped ${\mathrm{BaFe}}_2{\mathrm{As}}_2$

Using angle-resolved photoemission spectroscopy, we study the evolution of the number of carriers in $\mathrm{Ba}({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$ as a function of Co content and temperature. We show that there is a $k$-dependent energy shift compared to density functional calculations, which is large below 100 K at low Co contents and reduces the volume of hole and electron pockets by a factor 2. This $k$ shift becomes negligible at high Co content and could be due to interband charge or spin fluctuations. We further reveal that the bands shift with temperature, changing significantly the number of carriers they contain (up to 50%). We explain this evolution by thermal excitations of carriers among the narrow bands, possibly combined with a temperature evolution of the $k$-dependent fluctuations.

Figure 1

(a) Calculated LDA band structure along $\Gamma X$ at $k_z=0$ and $x=0$. Colors indicate the main orbital character. Arrows indicate the direction of the $k$ shift observed at low $T$ in experiments. (b) $k_F$ measured as a function of Co content for the two electron bands, deep and shallow. The thin lines are guides for the eye. Solid lines are $k_F$ obtained in VCA DFT calculations for $k_z$ corresponding to experimental conditions [22]. (c) Shifts compared to LDA calculations at $x=0$ needed to obtain the experimental $k_F$. Solid line indicates the expectations from the VCA calculations.

Figure 2

Temperature dependence for 8% Co (a)–(c) and 30% Co (d)–(f). (a), (d) Spectral weight integrated over 10 meV around $\mu$ for the shallow electron band. White dashed lines indicate $k_F$ at $T=0$. The last row (20 K) was measured after cooling back from 300 K. (b), (e) $k_F$ as a function of $T$ for the two electron bands at $X$ (shallow and deep) and for one band at $\Gamma$ (holes for $x=0.08$, electrons for $x=0.3$). (c), (f) Shift as a function of $T$ for the different bands.

Figure 3

(a) Thick lines: DOS considered for the two bands model. The Fermi edge is sketched at 300 K, dashed areas indicate the occupied parts for holes and electrons before shifting the chemical potential $\mu$. Arrows indicate the directions in which the bands will shift with increasing $T$ with respect to $\mu$. (b) Number of carriers (holes or electrons) obtained as a function of temperature for the two bands model. (c) DOS calculated in LDA, $\mathrm{LDA}+\mathrm{DMFT}$, and $\mathrm{LDA}+\mathrm{DMFT}$ including a $k$ shift. The Fermi levels for $x=0$ and $x=0.3$ are indicated by vertical lines. (d) Shift of $\mu$ obtained within band theory from the DOS of various models (see text and caption).

Figure 4

Number of electrons as a function of Co content for different temperatures (left) and as a function of $T$ for different Co content (right). The lowest $T$ is shown as filled symbol. The solid orange thick line indicates the number of electrons expected from LDA calculation.