# Large contribution of Fermi arcs to the conductivity of topological metals

## TL;DR

This paper demonstrates that Fermi arc surface states in topological metals significantly influence dc conductivity, contributing comparably to bulk effects even in large systems, especially related to the anomalous Hall effect.

## Contribution

It reveals that surface states in topological metals can dominate conductivity contributions, including in time-reversal invariant Weyl semimetals, due to their size-dependent chiral currents.

## Key findings

- Surface states contribute significantly to dc conductivity.
- Large surface contributions occur even in time-reversal invariant Weyl semimetals.
- Resistivity shows size dependence due to surface state effects.

## Abstract

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