Comparing the three characteristic electronic excitations in the pseudogap state of underdoped Bi$_{2}$Sr$_{2}$Ca$_{0.8}$Dy$_{0.2}$Cu$_{2}$O$_{8+\delta }$

We investigate the quasiparticle interference processes as a function of temperature for heavily underdoped Bi$_{2}$Sr$_{2}$Ca$_{0.8}$Dy$_{0.2}$Cu$_{2}$O$_{8 }$ (T$_{c}$=42K). We demonstrate that three types of electronic excitations exist in the pseudogap phase: (1) metallic excitations on the Fermi Arc, (2) the Bogoliubov quasiparticle excitations of what appears to be a phase incoherent d-wave superconductor in the confined area in momentum space (Jhinhwan Lee \textit{et al} (2009)) and (3) the high energy pseudogap excitations seen in the anti-nodal region outside the $\surd $2X$\surd $2 Brillouin zone (Y. Kohsaka \textit{et al}. Nature 454, 1072 (2008 ). We discuss the relationship of these three components of the electronic structure to the thermodynamic and transport characterization of this phase.