Figure 1

Fixed polarization Fermi surface mapping: (a) Polarization is kept fixed by moving the analyzer rather than the sample during Fermi surface mapping, and measurements along arbitrary momentum directions are derived from the resulting constant-polarization data matrix. (b) High-symmetry points in the 2D Brillouin zone are labeled on a Fermi surface map. (c) The three-dimensional Fermi surface is constructed from second derivative Fermi surface images measured at momenta spanning the $k_z$ axis Brillouin zone. Polarization is parallel to the $y$ axis for the left column and to the $x\text{−}y$ axis for the right column. A red guide to the eye traces intensity associated with the ${\alpha }_2$ band defined in Fig. 2, and portions of the outermost FS contour are indicated in blue. Linear dimensions for these guides to the eye are increased by 10$\%$ in the $z$-point plane ($k_z=\pi$) relative to the BZ center.Reuse & Permissions

Figure 2

High-symmetry mapping of holelike bands: (a) and (b) Second derivative images (SDIs) of ARPES measurements along the $\Gamma$-$x$ and $\Gamma$-M axes are traced with the approximate dispersion of all three bands found in our measurements. Panel (a) is measured with even polarization and panel (b) with odd polarization. Dispersions over the same energy/momentum window from LDA are shown in the inset using a 50$\%$ renormalization factor as in Ref. 16, with dashed lines used to represent bands that should not be visible because they are in the incorrect symmetry sector for photoemission. (c) and (d) ARPES images along the $\Gamma$-$x$ axis are shown for in-plane polarization oriented 0${}^{\circ }$ (even) and 90${}^{\circ }$ (odd) relative to the measurement axis. (e) and (f) ARPES images are shown for the $\Gamma \text{−}M$ axis.Reuse & Permissions

Figure 3

Circular measurements show intertwined bands: (a) A Fermi surface diagram shows how the band symmetries identified in Fig. 2 can be reconciled with the LDA band structure. The measured (dominant) reflection symmetry for each band at momenta along the high-symmetry axes is labeled with respect to radial measurements intersecting the Brillouin zone center. ARPES intensity along the circular orange contour traced in panel (a) is measured for polarization along (b) the $y$ axis and (c) the $\widehat{x}\text{−}\widehat{y}$ direction. (d) The energies of the (black circles) ${\alpha }_1$ and (white circles) ${\alpha }_2$ bands are obtained based on the point of maximum intensity under symmetry conditions for which only one band is distinctly visible (0${}^{\circ }$ and 90${}^{\circ }$ from the polarization axis). (e)–(g) ARPES intensity is predicted within a two-band $k·p$ model of the $3d_{xz}$ and $3d_{yz}$ orbitals, fitted from the band energy extrema identified in panels (b)–(d). (h) The data from panel (b) are plotted as a polar image, for comparison with (bottom left) the intersecting 2-band model from panel (e) and (bottom right) a scenario in which the ${\alpha }_1$ and ${\alpha }_2$ bands are rotationally isotropic. Intensity from the ${\alpha }_1$ band has been traced in black as a guide to the eye.Reuse & Permissions

Figure 4

Reshaping the Fermi surface: (a) Dispersion of holelike bands along the $\Gamma$-$x$ direction is reproduced from Fig. 2b. (b) LDA band structure is color coded based on the dominant orbital symmetry, and the ${\alpha }_1$/${\alpha }_2$ symmetry inversion point is indicated with an arrow (yellow-red crossing). The color code is blue for $d_{xy}$ (orbital filling $n_{d_{xy}}=0.5500$), green for the ${\alpha }_1$ chirality of $d_{xz/yz}$ and red for the ${\alpha }_2$ chirality (orbital filling $n_{d_{xz/yz}}=0.5815$), and yellow for $d_{3z^2-r^2}$ (orbital filling $n_{d_{3z^2-r^2}}=0.7301$). (c) and (d) The LDA band structure is modified with a small Mott-Hubbard perturbation as described in the text, with Fermi level set to maintain constant carrier density. Cartoons in (e)–(g) illustrate how this and other effects may modify the Fermi surface. (e) Bare LDA results give similar radii for all three Fermi pockets. (f) Perturbing orbital energies with on-site Coulomb interactions increases the anisotropy of ${\alpha }_1$ and ${\alpha }_2$, consistent with the “intertwined” bands observed experimentally. (g) Strong in-plane intersite interactions and correlations may be responsible for the enlarged ${\alpha }_3$ Fermi surface and density of states. Dark circles represent even reflection symmetry and light circles represent odd reflection symmetry, as defined for Fig. 3a.Reuse & Permissions

Figure 5

Bands and orbitals of superconducting electrons: (a) Density of states of the ${\alpha }_1$, ${\alpha }_2$, and ${\alpha }_3$ bands near the Fermi level is obtained from fitting the experimental data in Fig. 2. The approximate gap energies for these bands are labeled based on earlier studies (${\Delta }_1\sim {\Delta }_2\sim 13$ meV, ${\Delta }_3\sim 6$ meV[10, 11]). (b) The orbital-resolved 3D integrated density of states (DOS) is obtained from LDA, and an inset shows electrons near the Fermi level. Total filling is 0.58, consistent with the degree of potassium doping. As in Figs. 4b, 4c, 4d, the color code is blue for $d_{xy}$, green for $d_{xz/yz}$, yellow for $d_{3z^2-r^2}$, and cyan for $d_{x^2-y^2}$. The total density of states is shown in black.Reuse & Permissions