Magnetic impurity resonance states and symmetry of the superconducting order parameter in iron-based superconductors

We investigate the effect of magnetic impurities on the local quasiparticle density of states in iron-based superconductors. Employing the two-orbital model where $3d$ electron and hole conduction bands are hybridizing with the localized $f$ orbital of the impurity spin, we investigate how various symmetries of the superconducting gap and its nodal structure influence the quasiparticle excitations and impurity bound states. We show that the bound states behave qualitatively different for each symmetry. Most importantly we find that the impurity-induced bound states can be used to identify the nodal structure of the extended $s$-wave symmetry $\left(S^{\pm }\right)$ that is actively discussed in ferropnictides.

Figure 1

(Color online) Fermi surfaces of the two-band model (thick curves) with different symmetry of the superconducting order parameters (nodal lines represented by the dashed lines). (a) Extended $s$-wave symmetry, starting from fully gapped ${\Delta }_{S^{\pm }}\left(k_x,k_y\right)$ [or ${\Delta }_{S_1^{\pm }}\left(k_x,k_y\right)$ with $\alpha =0$]. With increase in the higher harmonics, $\alpha =1,3,6,7,8$ in ${\Delta }_{S_1^{\pm }}\left(k_x,k_y\right)$ this gap becomes more anisotropic and finally has accidental nodes on the electronic pocket around the M point. (b) refers to the other extended nodal $s$-wave gap symmetry ${\Delta }_{S_2^{\pm }}\left(k_x,k_y\right)$ with two separate nodal lines: ${\Delta }_{S_2^{\pm }}\left(k_x,k_y\right)$ for $\alpha =1.2;{\alpha }^{\prime }=0.15$ and $\alpha =1.17;{\alpha }^{\prime }=0.08$). (c) and (d) show $d_{x^2-y^2}$ and $d_{xy}$ gap symmetries with symmetry enforced nodes.

Figure 2

(Color online) Calculated LDOS for the superconducting regime with various superconducting order parameters: (a) $S^{\pm }$: ${\Delta }_{S^{\pm }}\left(k_x,k_y\right)$ and (b)–(f) $S_1^{\pm }$: ${\Delta }_{S_1^{\pm }}\left(k_x,k_y\right)$ (with $\alpha =1,3,6,7,8$, respectively); for ${ϵ}_f=-{\Delta }_0/3$, $V_1=V_2=0$ (solid), $V_1=V_2=0.5{\Delta }_0$ (dashed), and $V_1=V_2={\Delta }_0$ (dotted-dashed).

Figure 3

(Color online) LDOS for the superconducting state with various order parameters: ${\Delta }_{S_2^{\pm }}\left(k_x,k_y\right)$ for $\left(\alpha =1.2;{\alpha }^{\prime }=0.15\right)$ and $\left(\alpha =1.17;{\alpha }^{\prime }=0.08\right)$; for ${ϵ}_f=-{\Delta }_0/3$, $V_1=V_2=0$ (solid), $V_1=V_2=0.5{\Delta }_0$ (dashed), and $V_1=V_2={\Delta }_0$ (dotted-dashed).

Figure 4

(Color online) LDOS for the superconducting regime with order parameters: (a) $d_{x^2-y^2}$ and (b) $d_{xy}$; for ${ϵ}_f=-{\Delta }_0/3$, $V_1=V_2=0$ (solid), $V_1=V_2=0.5{\Delta }_0$ (dashed), and $V_1=V_2={\Delta }_0$ (dotted-dashed).

Figure 5

(Color online) Density plot of the spatial distribution of the LDOS for the superconducting regime with extended $s$-wave order parameter, ${\Delta }_{S^{\pm }}\left(k_x,k_y\right)$, for ${ϵ}_f=-{\Delta }_0/3$, $V_1=V_2={\Delta }_0$, and (a) $\omega ={\omega }_r$, (b) $\omega =-{\omega }_r$. [Maximum intensity is at ($r_x,r_y$) = (0,0)].