Ying, Xuzhe2020-10-262020-10-262020-05https://hdl.handle.net/11299/216870University of Minnesota Ph.D. dissertation. May 2020. Major: Physics. Advisors: Alex Kamenev, Jianping Wang. 1 computer file (PDF); x, 89 pages.In this thesis, we investigate the topological phase transitions in metals and the associated transport signatures. We show that sharply defined topological quantum phase transitions are not limited to states of matter with gapped electronic spectra. Such transitions may also occur between two gapless metallic states both with extended Fermi surfaces. Its sharpness is protected by a symmetry, such as particle-hole, which remains unbroken across the transition. We present a simple model of this phenomenon, based on 2D p + ip superconductor with an applied supercurrent, and discuss its geometrical interpretation. The transition is characterized by a discontinuous, but not quantized, jump in an off-diagonal transport coefficient. In particular, these discontinuities are not smeared or dwarfed by the bulk metallic transport due to the skew scattering and side jump on the elastic disorder, in a broad range of parameters.enThesis or Dissertation