Study of spectral function scaling property of high temperature superconductors

High Temperature Superconductors (HTSCs) were rst discovered in 1986, but despite enormous amount of research for last two decades, these materials are still not yet completely understood. HTSCs exhibit very complicated three dimensional phase diagram parameterized by temperature, magnetic led and carrier concentration. Up to now we do not know how to properly characterize all of their di erent phases, in particular the so-called pseudogap (PG) phase where the system is not macroscopically a superconductor but shows properties similar to the superconducting (SC) state. Angle Resolved Photoemission Spectroscopy (ARPES) that probes the momentum space structure of a system has greatly contributed to our understanding of the electronic structure of HTSCs. In this thesis I will present various ARPES studies on HTSCs. In order to understand the origin of high temperature superconductivity in copper ox- ides, we must understand the normal state from which it emerges. I will present the evolu- tion of the normal state electronic excitations with temperature and carrier concentration in Bi2Sr2CaCu2O8+ using ARPES data. I will show that unlike conventional superconductor, the high temperature superconductors exhibit two additional temperature scales which are pseudo- gap scale T , below which electronic excitations exhibit an energy gap, coherence scale Tcoh, below which sharp spectral features appear due to increased lifetime of the excitations. And T and Tcoh are strongly doping dependent, and cross each other near optimal doping. I will also present ARPES observation of the electronic excitations of the non-superconducting state that exists between the antiferromagnetic Mott insulator at zero doping and the super- conducting state at larger dopings in Bi2Sr2CaCu2O8+ (Bi2212). I will show that the state is a nodal liquid whose excitation gap becomes zero only at points in momentum space, and the material has the same gap structure as the d-wave superconductor despite that it has resistivity characteristic of an insulator and the absence of coherent quasiparticle peaks. And there is a smooth evolution of the spectrum across the insulator-to-superconductor transition At the end I will show our scaling analysis of ARPES data across the phase diagram. From the scaling analysis, we nd that there is a 2-D scaling relation in the pseudogap phase, but not in the normal states in the over-doped phase. Thus the states in the pseudogap phase share the same properties that are di erent from over-doped phase. And also because of the scaling relation, there is quantum critical line along the Fermi-surface in the pseudogap phase.