Quasiparticles beyond the Fermi liquid and heavy fermion criticality

We give a self-consistent theory of the scale-dependent effective mass enhancement $m^{*}/m$ of quasiparticles by three-dimensional (3D) antiferromagnetic (AFM) spin fluctuations in the presence of disorder at an AFM quantum critical point. The coupling of fermionic and bosonic degrees of freedom in the critical regime is described in terms of a critical quasiparticle theory. Using the fact that even in the “non-Fermi liquid” regime the quasiparticle width does not exceed the quasiparticle energy, we adopt relations from Fermi liquid theory to determine the dependence of the spin fluctuation spectrum on $m^{*}/m$, from which the self-energy and hence $m^{*}/m$ may be calculated. The self-consistent equation for $m^{*}/m$ has a strong coupling solution provided the initial value is sufficiently large. We argue that in YbRh${}_2$Si${}_2$, quasi-2D AFM and/or 3D ferromagnetic Gaussian fluctuations existing over a wide range drive the system into the 3D strongly coupled fluctuation regime. We find critical exponents of the temperature dependence of the specific heat coefficient $\gamma \propto T^{-1/4}$ and of the resistivity $\rho (T)=\rho (0)+{\mathit{AT}}^{3/4}$ in good agreement with experiments on YbRh${}_2$Si${}_2$ in the temperature range $T<0.3\hspace{0.5em}\text{K}$.

Figure 1

Specific heat: Comparison of theory, Eq. (6), and data of Ref. 17 at the critical magnetic field and below the critical temperature for quantum critical scaling.

Figure 2

Resistivity: Comparison of theory, Eq. (7), and data of Ref. 19 at the critical magnetic field and below the critical temperature for quantum critical scaling.