Local electronic structure of the superconducting interface ${\text{LaAlO}}_3/{\text{SrTiO}}_3$

Motivated by the recent discovery of superconductivity on the heterointerface ${\text{LaAlO}}_3/{\text{SrTiO}}_3$, we theoretically investigate its local electronic structures near an impurity considering the influence of Rashba-type spin-orbit interaction (RSOI) originated in the lack of inversion symmetry. We find that local density of states near an impurity exhibits the in-gap resonance peaks due to the quasiparticle scattering on the Fermi surface with the reversal sign of the pairing gap caused by the mixed singlet and RSOI-induced triplet superconducting state. We also analyze the evolutions of density of states and local density of states with the weight of triplet pairing component determined by the strength of RSOI, which will be widely observed in thin films of superconductors with surface or interface-induced RSOI, or various noncentrosymmetric superconductors in terms of point contact tunneling and scanning tunneling microscopy, and thus reveal an admixture of the spin singlet and RSOI-induced triplet superconducting states.

Figure 1

(Color online) Fermi surfaces for ${\mathbf{g}}_{\mathbf{k}}=\left(-\text{sin}{k}_y,\text{sin}{k}_x,0\right)$ with reversal spin orientation at $\lambda /t=0.1$. The solid and dotted double arrows denote the Cooper pairing within each Fermi surface.

Figure 2

(Color online) Evolution of DOS with the ratio $\alpha =d_0/{\Delta }_s$ between singlet $s$-wave and triplet pairing gaps. The dashed and dotted curve denotes the contribution of the different bands and the solid curve refers to the total DOS.

Figure 3

(Color online) Mixed singlet and triplet pairing gap functions for ${\Delta }_s-\left|{\mathbf{d}}_{\mathbf{k}}\right|$ in the first Brillouin zone at (a) $\alpha =0.5$ and (b) $\alpha =1$. The solid line denotes Fermi surface of band ${\xi }_{\mathbf{k}-}$, and the dashed line in (b) indicates the formation of the line of node.

Figure 4

(Color online) Evolution of LDOS near a nonmagnetic impurity with $\alpha$ for various scattering strengths $V_0$.

Figure 5

(Color online) Evolution of DOS for various ratio $\alpha =d_0/{\Delta }_s$ between singlet $d_{x^2-y^2}$-wave and triplet Cooper-pairing states in (a), (b), and (c). The dashed and dotted curve denotes the contribution of the different bands and the solid curve refers to the total DOS. The corresponding singlet and triplet pairing gap functions in the first Brillouin zone at $\alpha =0$ for ${\Delta }_{+}$ (d) and ${\Delta }_{-}$ (e), and $\alpha =1$ for ${\Delta }_{+}$ (f) and ${\Delta }_{-}$ (g), where the solid line denotes corresponding Fermi surface of band ${\xi }_{\mathbf{k}+}$ in (d) and (f), and band ${\xi }_{\mathbf{k}-}$ in (e) and (g), and the dashed line indicates the node line.

Figure 6

(Color online) LDOS near an impurity for $\alpha =0$ and $\alpha =1$ with various scattering strengths $V_0$.