Nematic superconductivity in LiFeAs

The role of nematic order for the mechanism of high-temperature superconductivity is highly debated. In most iron-based superconductors (IBSs) the tetragonal symmetry is broken already in the normal state, resulting in orthorhombic lattice distortions, static stripe magnetic order, or both. Superconductivity then emerges, at least at weak doping, already from the state with broken $C_4$ rotational symmetry. One of the few stoichiometric IBSs, lithium iron arsenide superconducts below 18 K and does not display either structural or magnetic transition in the normal state. Here we demonstrate, using angle-resolved photoemission spectroscopy, that even the superconducting state in LiFeAs is also a nematic one. We observe spontaneous breaking of the rotational symmetry in the gap amplitude on all Fermi surfaces, as well as unidirectional distortion of the Fermi pockets. Remarkably, these deformations are hardly visible above superconducting $T_c$. Our results demonstrate the realization of the phenomenon of superconductivity-induced nematicity in IBSs, emphasizing the intimate relation between them. We suggest a theoretical explanation based on the emergence of a secondary instability inside the superconducting state, which leads to the nematic order and $s-d$ mixing in the gap function.

Figure 1

Superconducting gaps from ARPES. (a) Overview Fermi surface map taken using 80-eV photons. (b) Intensity plots corresponding to the dashed line in (a) measured as a function of temperature with 21-eV photons. All spectra are divided by the Fermi function to enhance the signal above the Fermi level. (c) Exemplary EDCs from the $k$ points marked in (a) by red and magenta dots. The 2D intensity plot corresponds to the area limited by the square brackets in the bottom panel of (b).

Figure 2

Gap anisotropy and distortions of the holelike FS pockets and dispersions. (a) High-resolution FS map measured at 7 K with 25-eV photons, which approximately corresponds to $k_z=0$. (b) Intensity distributions along the $k_x$ and $k_y$ cuts. White curves are $E_F$-MDCs. Vertical dashed lines help to compare the peak positions. (c) Gap function of the large hole pocket. Here the angle is counted counterclockwise from the $k_y$ direction. Fitting function is mostly $cos2\theta$ with a small ($\sim 6\%$) admixture of higher harmonics. (d) Dispersions corresponding to the large hole pocket extracted from (b). The inset shows the behavior of the distortion coefficient. (e) Gap function of the small hole pocket. (f) Temperature dependence of the dispersions corresponding to the $k_y$ cut. (g) Distortion coefficient for the $xz$ and $yz$ dispersions in the center of the BZ. (h) The same as (g), but measured at 23 K. Insets show EDCs from $k$ points indicated by crosses and dots on the map in the energy scale with zero at the minimal leading-edge position. The error bars in the corners of (c) and (e) indicate standard error.

Figure 3

Gap anisotropy and distortions of the electronlike FS pockets. (a) and (b) FS map of electron pockets measured with 25 eV ($k_z\sim 0$) and 23 eV photons, respectively. (c) and (d) Gap functions corresponding to (a) and (b). Here angle is counted counterclockwise from the $k_y$ direction. Insets show EDCs from the points on the maps marked by the crosses of the same color in the energy scale with zero at the minimal leading-edge position. (e) and (f) $E_F$-MDCs corresponding to (a) and (b). Dashed lines indicate the different positions of the peaks. (g) Dispersions supporting the inner electron pocket from (b). The inset shows the distortion coefficient and its average value. (h) FS map at 21 eV, which roughly corresponds to $k_z=\pi$. (i) Intensity distribution along $k_x$ and $k_z$ cuts from (h) together with the corresponding $E_F$-MDCs. (j) Dispersions corresponding to the inner electron pocket from (h). (k) Temperature dependence of the dispersions along the $k_x$ cut. The inset shows the temperature-induced size variation of the inner (green markers) and outer (purple markers) electron pockets, similar to the distortion coefficient. (l) Temperature dependence of the dispersions of the inner pocket along the $k_y$ cut. No matching of the zero position has been done in (j)–(l). The error bars in the corners of (c) and (d) indicate standard error.

Figure 4

(a) Schematic Fermi surface contours of LiFeAs from the experiments in the normal state. The dashed contour represents the $yz$ states which do not cross the Fermi level. (b) Qualitative sketch of the distortions and gap anisotropies consistent with the experimental data. Red (blue) arrows indicate squeezing (stretching) of the FSs. Question marks indicate uncertainty in regard to the distortion of the outer electron pocket.

Figure 5

Gap fitting.

Figure 6

${\mathrm{k}}_z$ dispersion. (a) A set of EDCs which were obtained through the center of the holelike dispersion ($k_y=0$) for different photon energies. (b) $k_z$ map.

Figure 7

(a) MDC dispersions of the $d_{xy}$ bands forming the largest hole pocket obtained from spectra measured in the normal state (red curves) and superconducting state (blue curves). (b) Size variation caused by temperature. (c) Dispersions within the close vicinity of the Fermi level along two perpendicular cuts parallel to $k_x$ (red curves) and $k_y$ (blue curves) obtained from the data set measured at temperature above $T_c$. (d) Dispersions along the $k_x$ (yellow curves) and $k_y$ (blue curves) directions obtained from a different sample.