We use the coupled two-dimensional spin–three-dimensional fermion model proposed by Rosch et al. [Phys. Rev. Lett. $79,$ 159 (1997)] to study the thermoelectric behavior of a heavy-fermion compound when it is close to an antiferromagnetic quantum critical point. When the low-energy spin fluctuations are quasi-two-dimensional, as has been observed in ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$ and ${\mathrm{CeCu}}_{6-x}{\mathrm{Au}}_x,$ with a typical two-dimensional ordering wave vector and three-dimensional Fermi surface, the “hot” regions on the Fermi surface have a finite area. Due to enhanced scattering with the nearly critical spin fluctuations, the electrons in the hot region are strongly renormalized. We argue that there is an intermediate energy scale where the qualitative aspects of the renormalized hot electrons are captured by a weak-coupling perturbative calculation. Our examination of the electron self-energy shows that the entropy carried by the hot electrons is larger than usual. This accounts for the anomalous logarithmic temperature dependence of specific heat observed in these materials. We show that the same mechanism produces a logarithmic temperature dependence in thermopower. This has been observed in ${\mathrm{CeCu}}_{6-x}{\mathrm{Au}}_x.$ We expect to see the same behavior from future experiments on ${\mathrm{YbRh}}_2{\mathrm{Si}}_2.$

• Received 9 April 2001

DOI:https://doi.org/10.1103/PhysRevB.64.184414