Strong electron pairing at the iron 3$d_{xz,yz}$ orbitals in hole-doped BaFe${}_2$As${}_2$ superconductors revealed by angle-resolved photoemission spectroscopy

Using the angle-resolved photoemission spectroscopy (ARPES) with resolution of all three components of electron momentum and electronic states symmetry, we explicate the electronic structure of hole-doped BaFe${}_2$As${}_2$, and show that widely discussed nesting and dimensionality of Fermi surface (FS) sheets have no immediate relation to the superconducting pairing in iron-based superconductors. Alternatively a clear correlation between the orbital character of the electronic states and their propensity to superconductivity is observed: The magnitude of the superconducting gap maximizes at 10 meV exclusively for iron $3d_{xz,yz}$ orbitals, while for others drops to 3 meV. Presented results imply that the relation between superconducting and magnetostructural transitions goes beyond simple competition for FS, and demonstrate importance of orbital physics in iron superconductors.

Figure 1

$k_z$-dependent superconducting gap at holelike Fermi surface sheets centered at the ($k_x=0$, $k_y=0$) point in optimally doped Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$. (a) Energy-momentum cut, passing through the ($k_x=0$, $k_y=0$) point and capturing spectrum around Fermi crossings of $\Gamma$ FS sheets, recorded at $h\nu$ ranging from 13 to 93 eV (vertical and horizontal polarizations for 33 eV). As discussed in the main text, the two nearly degenerate inner $\Gamma$ barrels are often not resolved. All three $\Gamma$ barrels are clearly resolved at excitation energies around the value of $h\nu =33.5$ eV. Red dashed lines are guides to the eye, located at 0 and 10 meV binding energy. (b) Integrated energy distribution curves (IEDC) fitted to the Dynes function. Inset shows IEDCs for the outer $\Gamma$ barrel at 25 and 27 eV, color coding is preserved. (c) Values of the superconducting gaps at $\Gamma$ barrels as a function of $h\nu$. Underlying fitting curves are described in Ref. [23]. Taking into account that $k_z$ dependence of the gap is observed only for the inner $\Gamma$ barrels and there it possesses large flat regions, the two-gap model still can be sufficient for satisfactory interpretation of many experimental results.

Figure 2

Comparison of the calculated band dispersion, to the band dispersion, extracted from ARPES data. (a) The calculated band dispersion. (b) The band dispersion, extracted from ARPES data, presented in (c) and (d). (c) Energy-momentum cut, passing through the ($k_x=0$, $k_y=0$) point, recorded at 70 eV using horizontal light polarization. (d) Same cut, recorded with vertical polarization. Data recorded from the optimally doped Ba${}_{1-x}$Na${}_x$Fe${}_2$As${}_2$.

Figure 3

Three-dimensional distribution of the superconducting gap and orbital composition of the electronic states at the Fermi level. (a) Distribution of the superconducting gap (plotted as height) and distribution of the orbital composition for the states at the Fermi level (shown in color: $d_{xz,yz}$—red, $d_{xy}$—green, $d_{xz,yz}$ with admixture of other orbitals—orange) as function of $k_x$ and $k_y$ at constant $k_z=0$. (b) The same, only for $k_z=\pi$. (c) Same distributions as function of in-plane momentum, directed along BZ diagonal and $k_z$. Note unambiguous correlation between the orbital composition and superconducting gap magnitude.

Figure 4

Illustration of the $k_z$ dependence of the superconducting gap from peak positions in energy distribution curves. Left column: Energy-momentum cuts passing through the center of the Brillouin zone recorded with various $h\nu$. Right column: $k_{\mathrm{F}}$-EDC corresponding to the inner (red), outer (green), and middle (orange) $\Gamma$ barrels. Data recorded from optimally doped Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$.

Figure 5

Observation of the additional spectral weight presumably related to the iron $3d_{3z^2-r^2}$ orbitals at the Fermi level and superconducting gap on it for optimally doped Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$. (a) Energy-momentum cut, passing through the $(k_x=0,k_y=0)$ point, recorded with $h\nu =33$ meV and vertical polarization of the incoming light. (b) The same cut, recorded with horizontal polarization. (c) EDCs directly from $(k_x=0,k_y=0)$ point recorded with horizontal and vertical polarizations. Comparison of EDCs recorded at different polarization suggests that spectral weight originating from three-dimensional electronic states, seen in spectrum as rather smeared intensity [see (b)], reaches the Fermi level. (d) Energy-momentum cut, passing through the $\Gamma$ point. (e) $\Gamma$-EDC reveals two peaks near the Fermi level: One at binding energy about 17 meV corresponds to the observed in this compound “fusion of bogoliubons” [7], while the one closer to the Fermi level corresponds to the superconducting gap with magnitude about 3 meV.

Figure 6

Calculated band structure of BaFe${}_2$As${}_2$. (a)–(d)The band dispersion and contribution from different iron $3d$ orbitals. (e) The calculated band dispersion cut at 250 meV below the Fermi level. (f) Three-dimensional Brillouin zone. (g) Band dispersion for different $k_z$ values.

Figure 7

(a) Sequence of temperature-dependent measurements, performed on Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$ with $T_{\mathrm{c}}$ of 38 K, for the energy-momentum cut, passing through the $\Gamma$ barrels in the range of 1–43 K. The emergence of superconducting gap shows up as appearance of the “beaks” at Fermi crossings of both inner and outer $\Gamma$ barrels. (b) Temperature dependence of the IEDC, referring to the inner $\Gamma$ barrel, integrated in the range shown in the inset. The spectrum above $T_{\mathrm{c}}$ is nothing but Fermi step, while the coherence peak starts to grow at superconductivity onset. (c) Same as (b), only for the outer $\Gamma$ barrel. (d) Temperature dependence of the superconducting gaps, derived from fit of integrated EDC to Dynes function. (e)–(g) Present data, taken from Ba${}_{1-x}$Na${}_x$Fe${}_2$As${}_2$ with $T_{\mathrm{c}}=34$ K. (e) Fermi surface map. (f) Temperature dependence of the energy-momentum cut passing through the center of the propeller's blade, as shown by a dashed line in (e). (g) Temperature dependence of the integrated EDC, revealing the appearance of prominent coherence peak below $T_{\mathrm{c}}$.

Figure 8

Deterioration of the sample surface with time after cleavage results in reduction of the gap in the surface-related part of the photoemission spectrum. At the same time another bulk component of the signal exhibits a robust time-independent gap value. (a) Energy-momentum cut, passing through the $\Gamma$ point, recorded soon after cleavage. (b) EDC, integrated around the Fermi crossing of the inner $\Gamma$ barrel, as indicated in (a). (c) The same cut, recorded from the same cleave after more than 25 h. (d) Corresponding EDC. (d) Corresponding EDC. (e)–(g) A different data set, where (e) and (f) represent signals from less and more deteriorated surfaces, respectively. (g) Near-$k_{\mathrm{F}}$ EDCs after deconvolution together with fits to two Lorentzians. The peak corresponding to bulk signal remains unchanged, while the peak corresponding to the surface signal with reduced gap shifts towards Fermi level. (h) Third data set: Time evolution of the similar cut, passing through the $\Gamma$ barrels, recorded immediately after cleavage at residue pressure in the measuring chamber of $1.3\times {10}^{-10}$ mbar and using a Janis ST400 cryomanipulator. (i) Time dependence of the leading edge position (LEG) for the outer (gray circles) and inner (blue crosses) $\Gamma$ barrels. All data recorded from optimally doped Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$.