Nesting between hole and electron pockets in $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ $\left(x=0–0.3\right)$ observed with angle-resolved photoemission

We present a comprehensive angle-resolved photoemission study of the three-dimensional electronic structure of $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$. The wide range of dopings covered by this study, $x=0$ to $x=0.3$, allows to extract systematic features of the electronic structure. We show that there are three different hole pockets around the $\Gamma$ point: the two inner ones being nearly degenerate and rather two dimensional, the outer one presenting a strong three-dimensional character. The structure of the electron pockets is clarified by studying high doping contents, where they are enlarged. They are found to be essentially circular and two dimensional. From the size of the pockets, we deduce the number of holes and electrons present at the various dopings. We find that the net number of carriers is in good agreement with the bulk stoichiometry but that the number of each species (holes and electrons) is smaller than predicted by theory. Finally, we discuss the quality of nesting in the different regions of the phase diagram. The presence of the third hole pocket significantly weakens the nesting at $x=0$, so that it may not be a crucial ingredient in the formation of the spin-density wave. On the other hand, superconductivity seems to be favored by the coexistence of two-dimensional hole and electron pockets of similar sizes.

Figure 1

(Color online) Sketch of the BZs corresponding to a Fe square [unfolded BZ (a)] or the unit cell [folded BZ (b)]. Red circles (ovals) indicate 2D hole (electron) pockets, and small blue circle indicates the third hole pocket (see text). Dotted contours in (b) show the folded parts. The dashed blue square represents the AF BZ. Top inset: atoms in real space, $a$ is the side of the unit cell $\left(a=3.96\text{Å}\right)$.

Figure 2

(Color online) Near $E_{\text{F}}$ electronic structure around the $\Gamma$ point for the indicated dopings, measured at 35 eV (left) or 45 eV (right) photon energy and a temperature of 30 K. On the left part, lines sketch the dispersion of inner band A (red) and outer band B (blue). On the right part, black line is a sketch for a cosine dispersion for the two merged bands $\text{A}+\text{B}$ (see text).

Figure 3

(Color online) (a) Fermi surface measured at 35 eV and 30 K, for $x=0.08$. Red points and blue diamonds indicate Fermi-level crossings for A and B bands, respectively, and the circles, the corresponding FS. (b) Fermi wave vector for the two bands as a function of photon energy for $x=0.08$ and $x=0.15$. Vertical dotted line shows positions corresponding to $k_{\text{z}}=1$. Solid lines are guides for the eyes.

Figure 4

(Color online) Detailed variation of $k_{\text{F}}$ with photon energy for $x=0.045$. (a) $k_{\text{F}}$ for A (red points) and B (blue diamonds) bands extracted with linear fits of the dispersion. Solid lines are guides for the eyes. (b) Spectral intensity at a binding energy of $-40\text{meV}$ as a function of photon energy. Red and blue bars indicate the position of the A and B bands at this binding energy. All spectra are normalized to constant area.

Figure 5

(Color online) Near $E_{\text{F}}$ electronic structure of the electron pockets, for $x=0.08$ [(a) and (b)] and $x=0.3$ [(c) and (d)]. (a) and (c): dispersion measured at 30 K and 45 eV photon energy, in the direction indicated as thin black line on the FS (bottom). (b) and (d): Fermi surface measured at 45 eV (b) and 92 eV (d) for the two different dopings. Circles delimit the FS.

Figure 6

(Color online) (a) $k_{\text{F}}$ as a function of photon energy for $x=0.15$ (green) and 0.3 (red). (b) Spectra at $-10\text{meV}$ binding energy for $x=0.3$ at 92 eV (top) and 55 eV (bottom). For 55 eV, the decomposition of each peak into two different peaks is indicated by thin lines.

Figure 7

(Color online) Closed symbols: $k_{\text{F}}$ values as a function of the number of doped electrons determined in this study for the electron pocket and the A and B hole pockets at $k_{\text{z}}=1$. Open symbols: $k_{\text{F}}$ values as a function of the number of doped holes reproduced from Ref. 6. Lines are guides for the eyes. Grey and red hatched areas show SDW and superconducting (SC) regions, respectively (right axis).

Figure 8

(Color online) Number of holes (open blue circles) and electrons (black squares) extracted from the $k_{\text{F}}$ values of Fig. 7. Solid blue circles indicate the number of holes after correction taking into account the warping of the pockets along $k_{\text{z}}$. Black stars are number of electrons deduced from Hall measurements (Ref. 24). Hatched areas indicate likely values for the number of holes and electrons, including possible experimental errors. Thick solid lines are prediction for the evolution of number of holes and electrons reproduced from Ref. 25.