Apparent Violation of the Wiedemann-Franz law near a magnetic field tuned metal-antiferromagnetic quantum critical point

The temperature dependence of the interlayer electrical and thermal resistivity in a layered metal are calculated for Fermi liquid quasiparticles which are scattered inelastically by two-dimensional antiferromagnetic spin fluctuations. Both resistivities have a linear temperature dependence over a broad temperature range. Extrapolations to zero temperature made from this linear-$T$ range give values that appear to violate the Wiedemann-Franz law. However, below a low-temperature scale, which becomes small close to the critical point, a recovery of this law occurs. Our results describe recent measurements on CeCoIn$_5$ near a magnetic field-induced quantum phase transition. Hence, the experiments do not necessarily imply a non-Fermi liquid ground state.