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. The transition is characterized by a discontinuous, but not quantized, jump in an off-diagonal transport coefficient. Its sharpness is protected by a symmetry, such as, e.g., particle-hole symmetry, 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.

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We investigate if a sharp topological transition in a metal with a large Fermi surface may be detected in transport measurements. In particular, we address if a skew scattering and a side jump on elastic disorder in the bulk of such a metal masks signatures of the topological transition. We conclude that certain transport coefficients exhibit discontinuous changes across the transition. These discontinuities are not smeared or dwarfed by the bulk metallic transport in a broad range of parameters.