Second wind of the Dulong–Petit Law at a quantum critical point

Renewed interest in $^3$He physics has been stimulated by experimental observation of non-Fermi-liquid behavior of dense $^3$He films at low temperatures. Abnormal behavior of the specific heat $C(T)$ of two-dimensional liquid $^3$He is demonstrated in the occurrence of a $T$-independent $\beta$ term in $C(T)$. To uncover the origin of this phenomenon, we have considered the group velocity of transverse zero sound propagating in a strongly correlated Fermi liquid. For the first time, it is shown that if two-dimensional liquid $^3$He is located in the vicinity of the quantum critical point associated with a divergent quasiparticle effective mass, the group velocity depends strongly on temperature and vanishes as $T$ is lowered toward zero. The predicted vigorous dependence of the group velocity can be detected in experimental measurements on liquid $^3$He films. We have demonstrated that the contribution to the specific heat coming from the boson part of the free energy due to the transverse zero-sound mode follows the Dulong–Petit Law. In the case of two-dimensional liquid $^3$He, the specific heat becomes independent of temperature at some characteristic temperature of a few mK.