Superconductors: Functional-Renormalization-Group Analysis

Recently, complex phase transitions accompanied by the rotational symmetry breaking have been discovered experimentally in cuprate superconductors. To understand the origin of the symmetry breaking, we study various charge susceptibilities in an unbiased way, by applying the functional-renormalization-group method to the realistic d-p Hubbard model [1]. Without assuming the wavevector of the order parameter, we reveal that the most dominant instability is the uniform (q = 0) charge density wave (CDW) on the p orbitals, which possesses the B_1g symmetry. This uniform CDW triggers another nematic p-orbital CDW along the axial (Cu-Cu) direction at Q_a = (π/2,0). It is predicted that uniform CDW is driven by the spin fluctuations in the pseudogap region, and another CDW order at q = Q_a is triggered by the uniform order. The predicted multistage CDW transitions are caused by the Aslamazov-Larkin-type fluctuation-exchange processes. We also revealed that the B_2g symmetry CDW emerges when the density of states near the hot-spots is strongly suppressed by the strong correlation effect. [1] M. Tsuchiizu et al., arXiv:1705.05356; K. Kawaguchi et al., 86, 063707 (2017).