Possible superconductivity in the electron-doped chromium pnictide LaOCrAs

We constructed an effective tight-binding model with five Cr $3d$ orbitals for LaOCrAs according to first-principles calculations. Based on this model, we investigated possible superconductivity induced by interactions in doped LaOCrAs using the functional renormalization group (FRG). We find that there are two domes of superconductivity in electron-doped LaOCrAs. With increasing electron doping, the ground state of the system evolves from G-type antiferromagnetism in the parent compound to an incipient $s_{\pm }\text{−}\mathrm{wave}$ superconducting phase dominated by electron bands derived from the $d_{3z^2-r^2}$ orbital as the filling is above 4.2 electrons per site on the $d$ orbitals of Cr. The gap function has strong octet anisotropy on the Fermi pocket around the zone center and diminishes on the other pockets. In electron over-doped LaOCrAs, the system develops a $d_{x^2-y^2}$-wave superconducting phase and the active band derives from the $d_{xy}$ orbital. In between the two superconducting domes, a time-reversal symmetry breaking $s+id$ SC phase is likely to occur. The typical transition temperature for SC is estimated to lie between that of iron pnictides and cuprates. We also find the $s_{\pm }\text{−}\mathrm{wave}$ superconducting phase in the hole-doped case.

Figure 1

(a) Band structure of LaOCrAs based on the five-band model in the unfolded Brillouin zone. (b) The corresponding density of states. Inset shows the enlarged window near the Fermi level.

Figure 2

The Fermi surface (FS) of LaOCrAs in the unfolded Brillouin zone. From (a)–(d) the width of each FS line is proportional to its spectral weights in $d_{3z^2-r^2},d_{xz},d_{x^2-y^2}$, and $d_{xy}$ components. The arrows in (a) and (d) denote two types of scattering with momentum $\mathbf{Q}$ around $(\pi ,\pi )$. The $\alpha ,\beta$, and $\gamma$ in (b) denote the Fermi pockets around $\mathrm{\Gamma },X$(or $Y)$, and $M$ points, respectively. The pockets around the middle points of the $\mathrm{\Gamma }-M$ lines are denoted by $\delta$.

Figure 3

Results for $n=4.24$ with $U=1.0\mathrm{eV}$ and $J_H=U/4$. (a) FRG flow of $1/S_{\mathrm{SC},\mathrm{SDW}}$, the inverse of the leading attractive interactions, versus the running energy scale $\mathrm{\Lambda }$. Notice that $1/S_{\mathrm{SC},\mathrm{SDW}}\to 0^{-}$ if $S_{\mathrm{SC},\mathrm{SDW}}$ diverges. The inset shows $S_{\mathrm{SDW}}\left(\mathbf{q}\right)$ in the unfolded Brillouin zone at the final energy scale. (b) The Fermi surface and gap function $\mathrm{\Delta }\left(\mathbf{k}\right)$ in the unfolded Brillouin zone (color scale).

Figure 4

The same plot as Fig. 3 but for $n=4.35$. The arrow in (a) indicates the level crossing of the leading pairing channel.

Figure 5

The FRG diverging energy scale ${\mathrm{\Lambda }}_c$ plotted as a function of band filling. The circles, squares, and triangles represent ${\mathrm{\Lambda }}_c$ associated with the G-type AFM, incipient $s_{\pm }\text{−}\mathrm{wave}$ pairing, and $d_{x^2-y^2}$- wave paring states, respectively. $U=1\mathrm{eV},J_H=U/4$ and $U=1.3\mathrm{eV},J_H=U/6$ for solid and dashed lines, respectively.

Figure 6

(a) ${\mathrm{\Delta }}_d/{\mathrm{\Delta }}_s$ versus $V_d/V_s$ with fixed $V_s=-0.3\mathrm{eV}$. The solid and dashed lines are for the real and imaginary parts of ${\mathrm{\Delta }}_d/{\mathrm{\Delta }}_s$. (b) ${\mathrm{\Delta }}_s/{\mathrm{\Delta }}_d$ versus $V_s/V_d$ with fixed $V_d=-0.3\mathrm{eV}$. Notice that we set the imaginary parts of the ratios in both plots to be positive, with the understanding that $s\pm id$ are degenerate.