Quasiparticle interference above and below $T_c$ in underdoped cuprates

There is considerable debate over the evolution of quasi-particle excitations between the superconducting and pseudogap phases in the underdoped cuprates. In the superconducting phase, dispersive real space modulations are observed [1], which can be explained by quasi-particle interference (QPI), whose location in momentum space is consistent with ARPES. What should happen to these modulations in the pseudogap state, where ARPES indicates a finite arc of gapless Fermi surface? We will present STM data from underdoped $\textrm{Bi}_2\textrm{Sr}_2\textrm{CaCu}_2\textrm{O}_{8+x}$ that investigates the nature of this change and its connection with the non-dispersive features seen above $T_c$ [2]. [1] Kohsaka $\textit{et al. Nature } \textbf{454}$, 1072 (2008). [2] Vershinin $\textit{et al. Science } \textbf{305}$, 1993 (2004).