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Emergence of strongly correlated electronic states driven by the Andreev bound state in d-wave superconductors

As the surface Andreev bound state (ABS) forms at the open ($1,1$) edge of a $d_{x^2-y^2}$-wave superconductor, the local density of states (LDOS) increases. Therefore, a strong electron correlation and drastic phenomena may occur. However, a theoretical study on the effects of the ABS on the electron correlation has not been performed yet. To understand these effects, we study large cluster Hubbard model with an open ($1,1$) edge in the presence of a bulk $d$-wave gap. We calculate the site-dependent spin susceptibility by performing random-phase-approximation (RPA) and modified fluctuation-exchange (FLEX) approximation in the real space. We find that near the ($1,1$) edge, drastic ferromagnetic (FM) fluctuations occur owing to the ABS. In addition, as the temperature decreases, the system rapidly approaches a magnetic-order phase slightly below the transition temperature of the bulk $d$-wave superconductivity (SC). In this case, the FM fluctuations are expected to induce interesting phenomena such as edge-induced triplet SC and quantum critical phenomena.