Quantum corral effects on competing orders and electronic states in chiral d + id or f-wave superconductors

Self-consistent calculations are performed to characterize the quantum corral effects on the electronic states of chiral d + id or f-wave superconductors in this paper. A variety of spatial structures of competing orders are revealed in the presence of ferromagnetic nano-corrals, and superconducting islands are found to be absent in the case of small corrals while being seen for large corrals. Compared with the local suppression of superconductivity by a magnetic impurity inside the corral, surprisingly, an additional remarkable feature, i.e., obvious oscillations or enhancement of superconductivity around a non-magnetic impurity, is observed inside the magnetic corral. This is important in view of applications, especially in view of the demand for devices to locally produce strong superconductivity. Meanwhile, the charge density displays obvious modulations due to quantum confinement but in contrast, the spin density pattern exhibits its robustness against the corral effect. Furthermore, we explore the local density of states so as to be directly checked by experiments. We demonstrate that a magnetic corral can suppress the formation of quasi-particle bound states induced by an impurity inside the corral in the chiral d + id state while the f-wave case shows different behaviors. These results also propose a new route to make a distinction between the two competing pairing states in triangular-lattice superconductors.