Unexpected Fermi-surface nesting in the pnictide parent compounds ${\text{BaFe}}_2{\text{As}}_2$ and ${\text{CaFe}}_2{\text{As}}_2$ revealed by angle-resolved photoemission spectroscopy

We use angle-resolved photoemission spectroscopy to study the band structure of ${\text{BaFe}}_2{\text{As}}_2$ and ${\text{CaFe}}_2{\text{As}}_2$, two of the parent compounds of the iron arsenic high-temperature superconductors. Our high quality data reveals that although the Fermi surface is strongly three-dimensional, it does indeed have long parallel segments along the $k_z$ direction that can lead to the emergence of magnetic order. More interestingly, we find very unusual incommensurate nesting of the Fermi surface in the $a\text{−}b$ plane that is present only at low temperatures. We speculate that this is a signature of a failed charge density wave state that was predicted by renormalization-group studies.

Figure 1

(Color online) (a)–(c) ${\text{BaFe}}_2{\text{As}}_2$ and (d) ${\text{CaFe}}_2{\text{As}}_2$ data. FS map along $a\text{−}b$ (a1) above and (a2) below $T_N$. (b1) FS map along $k_{\left(001\right)}$ and $k_{\left(100\right)}$ [horizontal pink arrow in (a2)]. (Inner potential: $V_0\equiv 13\text{eV}$) (b3) MDCs of (b1). (b2) FS plots of ${\alpha }_1$ band extracted from peak positions of the MDCs. Blue dashed arrow indicates the parallel segment. (c1) MDC of (c2) at the Fermi energy and the fitting curve (yellow dashed curve). (c2) Band dispersion map along a diagonal cut [diagonal blue arrow in (a2)]. (c3) EDCs within a white arrow range in (c2). Circles follow hole bands (${\alpha }_1$ and ${\alpha }_2$) and electron bands (${\beta }_1$ and ${\beta }_2$). (d1)–(d2) MDCs at Fermi level of (d3)–(d4) and these fits (dashed yellow curves). Band dispersion map along a diagonal cut (d3) below and (d4) above $T_N$. Green dashed line is a guide to the eye for the electron band.

Figure 2

(Color online) (a) Model calculation, (b)–(e) ${\text{BaFe}}_2{\text{As}}_2$, and (f) ${\text{CaFe}}_2{\text{As}}_2$ data. (a1) Model FSs in nonmagnetic phase. Reconstructed FSs for ${\Delta }_{\text{AF}}$ of (a2) 10, (a3) 30, and (a4) 50 meV. ARPES intensity about the Fermi energy and $E=-20\text{meV}$ obtained at (b1)–(b2) $h\nu =49\text{eV}$ (near $\Gamma$) and (c1)–(c2) $h\nu =35\text{eV}$ (near $Z$). (d1) FS and (d2) energy contour plots at $E=-20\text{meV}$ for $h\nu =35\text{eV}$ data. (e) MDCs along arrow directions in (c1). FS map close to the zone center along $a\text{−}b$ plane (f1) below and (f2) above $T_N$. Dimension arrows indicate nesting vector $q\left({\alpha }_1\right)=\left(0.16\pi /a,0.16\pi /a\right)$ and $q\left({\alpha }_2\right)=\left(0.33\pi /a,0.33\pi /a\right)$ for hole band ${\alpha }_1$ and ${\alpha }_2$, respectively.

Figure 3

(Color online) ${\text{CaFe}}_2{\text{As}}_2$ data below $T_N$. (a) Schematic FSs along $k_{\left(001\right)}$. (b) FS map along $a\text{−}b$ plane. (c1)–(f1) MDC of (c2)–(f2) at the Fermi level. (c2)–(f2) Band dispersion map measured along a red arrow in (c3)–(f3). ARPES intensity about (c3)–(f3) Fermi level, (c4)–(f4) $-30$, (c5)–(f5) $-60$, (c6)–(f6) $-90$, and (c7)–(f7) $-120\text{meV}$. (g1)–(g5) FS and energy contour plots extracted from (c)–(f). Only stronger peaks between $k_F\left({\alpha }_1\right)$ and $k_F\left({\alpha }_2\right)$ are plotted. Dimension arrows indicate a nesting vector $q\left({\alpha }_1\right)=\left(0.15\pi /a,0.15\pi /a\right)$ and $q\left({\alpha }_2\right)=\left(0.31\pi /a,0.31\pi /a\right)$ of hole band ${\alpha }_1$ and ${\alpha }_2$, respectively. (c8)–(d8) MDCs within a blue line indicators in (c3) and (d3). (h) $\left|q\left({\alpha }_1\right)\right|$ and $\left|q\left({\alpha }_2\right)\right|$ for ${\text{CaFe}}_2{\text{As}}_2$ (Ca122) and ${\text{BaFe}}_2{\text{As}}_2$ (Ba122) at various $k_z\text{s}$ indicated with arrows in (a). [Inner potential: $V_0\equiv 13\text{eV}$ for Ba122 and 20eV for Ca122]