Anisotropic superconductivity in the spin-vortex antiferromagnetic superconductor $\mathrm{CaK}{\left({\mathrm{Fe}}_{0.95}{\mathrm{Ni}}_{0.05}\right)}_4{\mathrm{As}}_4$

High critical temperature superconductivity often occurs in systems where an antiferromagnetic order is brought near $T=0$ K by slightly modifying pressure or doping. ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$ is a superconducting, stoichiometric iron-pnictide compound showing optimal superconducting critical temperature with $T_c$ as large as 35 K. Doping with Ni induces a decrease in $T_c$ and the onset of spin-vortex crystal (SVC) antiferromagnetic order, which consists of spins pointing inwards to or outwards from alternating As sites on the diagonals of the in-plane square Fe lattice. Here we study the band structure of $\mathrm{CaK}{\left({\mathrm{Fe}}_{0.95}{\mathrm{Ni}}_{0.05}\right)}_4{\mathrm{As}}_4$ $(T_c=10 \mathrm{K},$ $T_{SVC}=50 \mathrm{K})$ using quasiparticle interference with a scanning tunneling microscope and show how the SVC modifies the band structure and induces a fourfold superconducting gap anisotropy.

Figure 1

(a) Schematic phase diagram of Ni-doped ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$, with a dashed vertical line indicating the Ni concentration discussed here. Crystalline structure of $\mathrm{CaK}{\left({\mathrm{Fe}}_{0.95}{\mathrm{Ni}}_{0.05}\right)}_4{\mathrm{As}}_4$ is shown in the upper left inset. (b) STM topographic image of the surface of $\mathrm{CaK}{\left({\mathrm{Fe}}_{0.95}{\mathrm{Ni}}_{0.05}\right)}_4{\mathrm{As}}_4$. The difference between black and white corresponds to a height change of 0.3 nm. In the inset, we show a view from the top of the structure, indicating Fe (brown) and As (As1 in blue and As2 in green) atoms and with arrows indicating the magnetic moments in the SVC. Note that the magnetic moments point towards As1, giving a finite hyperfine field pointing upwards along the $c$ axis (red circles with a cross), and from As1 atoms, giving a hyperfine field pointing downwards along the $c$ axis (red circle with a dot) [17]. At As2, the field cancels. (c) The temperature dependence of the tunneling conductance is shown as open circles in the main panel (the conductance is normalized to its value at voltages well above the superconducting gap). Curves are taken (from bottom to top) at 0.3, 0.8, 1.4, 4,0, and 7.0 K in the same field of view as in (b) (and in Fig. 1 of the Supplemental Material [28]). Lines are fits using the density of states obtained for a distribution of values of the superconducting gap. Curves are shifted vertically for clarity. The bottom right inset shows as black open circles the temperature dependence of the superconducting gap value, extracted from the maximum in the derivative of the density of states as a function of temperature normalized to $T_c$. The dashed line is a guide to the eye. Bottom left inset provides an image of the vortex lattice taken at 0.3 K and 2.0 T. Color scale shows the normalized zero-bias conductance, which goes from the normal state value (1.0, red) to its value at zero field (0.4, blue). White lines are the Delaunay triangulation of vortex positions, which are shown as black dots. Black scale bar is 30 nm long. Further vortex lattice images and details are provided in the Supplemental Material [28] (see, also, Refs. [13, 39, 40] therein).

Figure 2

(a) Topography of the area where we have made the quasiparticle interference experiment shown in (b)–(k). The colorscale bar is given in the bottom right and the gray scale by the bar at the right. The image has been taken at a bias voltage of 30 mV and a current of 1.0 nA at zero magnetic field and at 0.3 K. (b)–(f) Tunneling conductance normalized to voltages above 40 mV as a function of the position for a few representative bias voltages (given in each panel). The lateral scale bar is provided in (d). The gray scale corresponds to modulations of about 15% of the normalized conductance at each bias voltage. (g)–(k) Fourier transform, symmetrized taking into account the in-plane square lattice, of (b)–(f) shown in the first Brillouin zone. In (g), we mark the outer main scattering vector (black dashed circle) as well as the two inner scattering vectors (purple and green dashed circles). The lateral scale bar is given in (i) and the gray scale goes from low (black) to large (white) scattering intensity.

Figure 3

Scattering intensity for the two main symmetry directions, (a) $\overline{\mathrm{\Gamma }}\text{−}\overline{X}$ and (b) $\overline{\mathrm{\Gamma }}\text{−}\overline{M}$. Open circles mark the evolution of the scattering vectors with bias voltage. Scattering vectors $q_{\alpha }$, $q_{\beta }$, and $q_{\gamma }$ are shown in green, violet, and black. Color scale goes from low (blue) to high (red) scattering intensity. (c) Scattering intensity as a function of the angle with respect to the in-plane $a$ axis for energies close to the Fermi level in $q_{\gamma }$. Color scale goes from blue (about 0.4 in normalized conductance units) to cyan (about 1.0 in normalized conductance units). The black dashed line schematically shows a modulation of the scattering intensity at $q_{\gamma }$ (the modulation represented in the figure is by about 50% of the normalized tunneling conductance, taken at a bias voltages of approximately half the gap). The vertical light-green and orange lines highlight the $\overline{\mathrm{\Gamma }}\text{−}\overline{M}$ and $\overline{\mathrm{\Gamma }}\text{−}\overline{X}$ directions, respectively. The right panel shows a schematic representation of the lattice, with Fe atoms in brown (and their spins represented by arrows), As1 in blue, and As2 in green, and the symmetry directions used in previous figures as light-green and orange lines. The hyperfine field is shown by red circles with a dot and red circles with a cross. Notice that the hyperfine field adds to zero along the orange lines and is finite along the green lines.

Figure 4

Fermi surface of (a) pure ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$ and (b) $\mathrm{CaK}{\left({\mathrm{Fe}}_{0.95}{\mathrm{Ni}}_{0.05}\right)}_4{\mathrm{As}}_4$ in the paramagnetic phase, obtained as described in the text. (c),(d) Band structure and Fermi surface of $\mathrm{CaK}{\left({\mathrm{Fe}}_{0.95}{\mathrm{Ni}}_{0.05}\right)}_4{\mathrm{As}}_4$ in the folded AFM Brillouin zone. Folded bands are shown in blue. Black, violet, and green arrows are the main scattering vectors shown in Fig. 3. The convention for the names of the directions of folded and unfolded Brillouin zones [inset of (c)] follows Ref. [43].