Pseudogap formation above the superconducting dome in iron pnictides

The nature of the pseudogap (PG) in high transition temperature (high $T_c$) superconducting cuprates has been a major issue in condensed matter physics. It is still unclear whether the high $T_c$ superconductivity can be universally associated with the PG formation. Here we provide direct evidence of the existence of the PG phase via angle-resolved photoemission spectroscopy in another family of high $T_c$ superconductor, iron pnictides. Our results reveal a composition-dependent PG formation in the multiband electronic structure of BaFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$. The PG develops well above the magnetostructural transition for low $x$, persists above the nonmagnetic superconducting dome for optimal $x$, and is destroyed for $x$ ∼ 0.6, thus showing a notable similarity with cuprates. In addition, the PG formation is accompanied by inequivalent energy shifts in the $zx/yz$ orbitals of iron atoms, indicative of a peculiar iron orbital ordering which breaks the fourfold rotational symmetry.

Figure 1

(a) Phase diagram of BaFe${}_2$(As, P)${}_2$. Blue and orange markers indicate the temperatures of the PG formation $T_{\mathrm{PG}}^{*}$ and inequivalent energy shift in the $zx/yz$ orbitals $T_O^{*}$, respectively. (b) Composition dependence of the PG energy Δ_PG obtained by laser ARPES.

Figure 2

(a) FSs of BaFe${}_2$(As, P)${}_2$ for $x$ = 0.30 obtained by first principles band calculations. (b) Vertical cut of the calculated FSs. α, β, γ, δ, and $\varepsilon$ FSs are colored in green, blue, red, light blue, and purple, respectively. (c) FS mapping in the $Z$ plane taken by $p$ polarization of $h$ν = 35 eV around the BZ center and circular polarization of $h$ν = 40 eV around the BZ corner. $X$, $Y$ in $k_X$ and $k_Y$ represent the tetragonal in-plane momentum axes. (d) Orbital characters on the hole and electron FSs obtained by the first principles band calculations. The schematic FSs are based on ARPES results in (c). Intensity of α and β hole FSs is quite weak in (c) due to the matrix element effect. (e) E-k image along cut 1 in (c) taken by circular polarization at 60 K. (f) E-k image along cut 2 in (c) taken by circular polarization at 60 K. (g) E-k image along cut 3 in (c) taken by $p$ polarization at 30 K. (h) E-k image along cut 3 in (c) taken by circular polarization at 30 K. Insets show the schematic band dispersions illustrating each E-k image. Dotted curves represent the band dispersions whose intensity is suppressed due to the matrix element effect. $k_F$ for each band is indicated by the white triangle. ARPES data were taken at PF BL-28A.

Figure 3

(a–d) $T$ dependence of the EDCs for $x$ = 0.30 measured at $k_F$ of the $\varepsilon$ band in Fig. 2, δ band in Fig. 2, γ band in Fig. 2, and the α/β band in Fig. 2, respectively. (e–h) The EDCs in (a–d) symmetrized with respect to $E_F$ and further normalized by the smoothed EDC at 150 K, respectively. Broken lines indicate the PG energy. Note the larger $x$-axis energy scale for γ and α/β bands [panels (c, g) and (d, h)]. ARPES data were taken at PF BL-28A.

Figure 4

(a) Schematics of the in-plane cut of FS sheets in the $Z$ plane of BaFe${}_2$(As, P)${}_2$. Red line indicates the momentum region measured by laser ARPES (ISSP) for 0.07 ≤ $x$ ≤ 0.61. Only for $x$ = 0.00, the measured momentum cut is rotated by 45°. (b) MDCs at $E_F$ for $x$ = 0.45 recorded by s (blue) and $p$ (light blue) polarizations along momentum cut shown in (a). Black triangles indicates $k_F$ for α/β- and γ-hole bands, determined by the peak positions of the MDCs. α- and β-hole bands are nearly degenerate. (c), (d) Hole bands at $x$ = 0.45 measured along the momentum cut shown in (a) by using $p$ and $s$ polarizations, respectively. The γ-hole band can be separately observed by choosing $s$ polarization in the experimental geometry shown in (a). The EDCs in the γ-hole band were obtained at $k_F$, as indicated by broken white line in (d).

Figure 5

(a–c) $T$ dependence of the EDCs at $k_F$ of the γ-hole band measured by laser ARPES (ISSP) for $x$ = 0.07, 0.30, and 0.61, respectively. Inset shows the spectra near $E_F$ in an enlarged energy scale. (d–f) EDCs symmetrized with respect to $E_F$ and further normalized by the smoothed EDC at the highest $T$. Black arrow indicates the crossing point of the spectra with decreasing $T$, representing the PG energy. Note the larger $x$-axis energy scale for $x=0.07$ [panels (a) and (d)].

Figure 6

(a–f) Symmetrized and normalized EDCs measured by laser ARPES (ISSP) for $x$ = 0.00, 0.07. 0.24, 0.30, 0.45, and 0.61, respectively. The $T$-dependent depression of the spectral weight is indicated by the black shaded area. Note the larger $x$-axis energy scale for $x$ = 0.0 and 0.07 [panels (a) and (b)]. Dotted lines indicate PG energy. (g–l) $T$ dependence of $S$, the gapped area. $T_{\mathrm{PG}}^{*}$ is defined by the temperature at which $S$ starts to evolve. Twofold oscillation amplitudes of the torque for $x$ = 0.00 and 0.23 (Ref. [27]) are superimposed in (g) and (i), respectively. The background of each panel is colored in light blue for $T_{N,s}$ < $T$ < $T_{\mathrm{PG}}^{*}$, blue for $T_c$ < $T$ < $T_{N,s}$, and yellow for $T$ < $T_c$.

Figure 7

(a) The EDCs of the γ-hole band measured at 5 K ($T$ < $T_c$) and 30 K ($T_c$ < $T$) for $x$ = 0.35 by laser ARPES (ISSP). The black arrow and open circle represent the energy position of the PG and SC gap, respectively. (b) The EDCs symmetrized with respect to $E_F$. Light blue and yellow areas highlight the energy scale of the PG and SC gap, respectively.

Figure 8

(a) Schematics of the FSs obtained by the first principles band calculations for $x$ = 0.30. $k_F$ positions in the α/β hole FSs at which the data in (b) were obtained are plotted by the open circles. (b) Symmetrized EDCs taken at $k_F$ in the α/β hole FSs for $x$ = 0.30 below $T_c$ by using photons of $h$ν = 16 eV, 26 eV (HiSOR BL-9A) and 34 eV, 38 eV (PF BL-28A). Black arrows and open circles represent the energy scale of the PG and SC gap, respectively.

Figure 9

(a) Schematics of the in-plane cut of FS sheets in the $Z$ plane of BaFe${}_2$(As, P)${}_2$. The red line indicates the momentum region measured by helium-lamp ARPES for $x$ = 0.07. (b), (c) Schematic band dispersions above $T_O^{*}$ for detwinned and twinned crystals, respectively, where $T_O^{*}$ represents the temperature at which the $zx/yz$ bands start to show an inequivalent energy shift. Red rectangles represent the E-k region of the ARPES data shown in (f-h). (d), (e) Schematic band dispersions with orbital-dependent energy shift at BZ corners below $T_O^{*}$ for detwinned and twinned crystals, respectively. This picture was originally shown in Ref. [15] for Ba122 parent material. Energy positions of the $zx$ and $yz$ bands in (b–e) are modified, taking into account our ARPES results on $P$-substituted Ba122 system. (f) Band dispersion (second derivative) at the BZ corner near the $Z$ plane measured by Helium discharge lamp ARPES (University of Tokyo) of $h$ν = 40.8 eV at 80 K ($T$ < $T_{N,s}$). (g) The same measured at 120 K ($T_{N,s}$ < $T$ < $T_{\mathrm{PG}}^{*}$). (h) The same measured at 180 K ($T_{\mathrm{PG}}^{*}$ < $T$). (i–k) Schematics of the band dispersions corresponding to (f–h), respectively. Two hole bands (light blue curves) are observed at low $T$. Note that intensity of δ and $\varepsilon$ electron bands crossing $E_F$ is weak in this experimental geometry. (l) $T$ dependence of the EDCs divided by FD function at the momentum cut indicated by the broken white line in (i–k). Linear back ground was subtracted from each spectrum. Red curves represent the fitting functions composed of double Lorentz functions illustrated by gray and light blue curves. Gray and light blue circles represent the peak positions in the EDCs obtained by the fitting procedure, indicating the energy position of upper and lower hole band, respectively.

Figure 10

$T$ dependence of the energy position of the two hole bands below $E_F$ around the BZ corner. Gray and light blue symbols represent the peak positions in the EDCs along a white broken line in Fig. 9 (i–k) for upper and lower hole-bands, respectively. Circles, diamonds, and squares represent the data obtained from different samples. $T_O^{*}$ is estimated to be 160 K ∼ 180 K.