Anomalous Fermi-liquid phase in metallic skyrmion crystals

In noncentrosymmetric crystals such as MnSi, magnetic order can take the form of a skyrmion crystal (SkX). In this phase, conduction electrons coupled to the local magnetic moments acquire a Berry phase, leading to an emergent electromagnetism. Motivated by experimental reports of a non-Fermi-liquid phase in MnSi, in which resistivity is observed to scale as Δρ~T3/2, here we examine the effect of coupling phonons of an incommensurate SkX to electrons. Despite the formal similarity to a system consisting of a Fermi surface coupled to an electromagnetic field, the Berry phase fluctuations do not lead to non-Fermi-liquid behavior. Instead, we propose a different mechanism in which electrons scatter off columnar fluctuation in a three-dimensional SkX. When the effects of lattice-induced anisotropy are neglected, these fluctuations are ultrasoft and induce an ``anomalous Fermi liquid'' in which Landau quasiparticles survive but with an anomalous Δρ(T)~T7/4 resistivity perpendicular to the columns, and a Fermi-liquid resistivity along them.