# 3D Topological metals, 2D surface Fermi arcs and cancelation of the chiral magnetic effect.

## Duncan Haldane

When the Fermi-liquid description is applied to 3D metals with multiple disjoint Fermi surface sheets, it becomes apparent that metallic Fermi-liquids can be classified as “Symmetry-Protected Topological (SPT) states”, which in general support a separate quasiparticle current associated with each disjoint sheet. An exception occurs when the quasiparticle states on a sheet define a “U(1) fiber bundle” with non-vanishing first Chern class (“Chern number”), so its current conservation law exhibits a chiral anomaly, which apparently leads to a “chiral magnetic effecr” (CME) when an applied electric field has a component parallel to an applied magnetic flux density. However, such Fermi surfaces are always connected into groups with vanishing total Chern number by surface Fermi arcs, first discovered in studies of Weyl semimetals, but which are a general feature of topologcally-non-trivial Fermi surfaces. The 2D surface Fermi arcs cancel the bulk CME, and maintain a common chemical potential on the bulk 3D Fermi-surface sheets that they connect. The surface Fermi arcs are supported by non-standard surface states of “Shockley type” that do not form complete bands in the surface Brillouin zone, which is a generic feature of topological surface states.