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Surface-state contributions to the dc conductivity of most homogeneous metalsexposed to uniform electric fields are usually as small as the system size islarge compared to the lattice constant. In this work, we show that surfacestates of topological metals can contribute with the same order of magnitude asthe bulk even in large systems. This effect is intimately related to theintrinsic anomalous Hall effect, in which an applied voltage induces chiralsurface-state currents proportional to the system size. Unlike the anomalousHall effect, the large contribution of surface states to the dc conductivity isalso present in time-reversal invariant Weyl semimetals, where the surfacestates come in counter-propagating time-reversed pairs. While the Hall voltagevanishes in the presence of time-reversal symmetry, the twinned chiral surfacecurrents develop similarly as in the time-reversal broken case. For this effectto occur, the relaxation length associated with scattering betweentime-reversed partner states needs to be larger than the separation ofcontributing surfaces, which results in a characteristic size dependence of theresistivity and a highly inhomogeneous current-density profile across thesample.

Large contribution of Fermi arcs to the conductivity of topological metals