A short review of the recent progresses in the study of the cuprate superconductivity

The last 15 years have witnessed important progresses in our understanding of the mechanism of superconductivity in the high-Tcuprates. There is now strong evidence that the strange metal behavior is induced by the quantum critical fluctuation at the pseudogap end point, where the Fermi surface changes its topology from hole-like to electron-like.However, experiments show that the quantum critical behavior in the high-Tcuprates is qualitatively different from that observed in the heavy Fermion systems and the iron-based superconductors, in both of which the quantum critical behavior can be attributed to the quantum phase transition toward a symmetry breaking phase. The fact that the pseudogap exists as a spectral gap without a corresponding symmetry breaking order, together with the fact that the strange metal behavior occurs as a quantum critical behavior without a corresponding symmetry breaking phase transition, exposes the central difficulty of the field: the lack of a universal low energy effective theory description of the high-Tphenomenology beyond the Landau paradigm. Recent experiments imply that the dualism between the local moment and the itinerant quasiparticle character of the electron in the high-Tcuprates may serve as an organizing principle to go beyond the Landau paradigm and may hold the key to the mystery of the pseudogap phenomena and the strange metal behavior. It is the purpose of this review to provide an introduction to these recent progresses in the study of the high-Tcuprate superconductors and their implications on the construction of a coherent picture for the high-Tproblem.