Past exam of the quantum condensed matter course of the University of Cambridge / 2005 / Section B / B4 / d / Solution

In a heavy fermion material, correlated low-energy quasiparticles have a large electronic density of states and effective mass. A Kondo lattice with hybridization between localized f-electron states and conduction states is an important setting. The large mass is a low-energy dynamical property, not a change in the electron's bare mass or the ionic mass.

Low-temperature calorimetry measures $C/T\simeq \gamma +\beta T^2$ in a regime where an electronic linear term and a Debye lattice term are appropriate. The large intercept $\gamma =({\pi }^2{k}_B^2/3)D(E_F)$ measures the enhanced quasiparticle density of states, with volume or molar conventions kept consistent. Apply a known heat pulse to a thermally characterized sample platform and measure the temperature rise, then vary the base temperature to separate contributions.

In low-temperature calorimetry and resistivity of CeAl3, measurements below $0.2\mathrm{K}$ gave $\gamma =1.62\mathrm{J}\mathrm{mo}{\mathrm{l}}^{-1}{\mathrm{K}}^{-2}$ and $\rho ={\rho }_0+A{T}^2$ with $A=35\mu \Omega \mathrm{cm}{\mathrm{K}}^{-2}$. The large thermal coefficient and enhanced quadratic transport coefficient are complementary evidence for a strongly renormalized Fermi liquid.^[ref] Enhanced spin susceptibility provides another probe. Where coherent quantum oscillations can be resolved, their thermal damping determines a cyclotron effective mass, giving a band-sensitive comparison with the thermodynamic mass inferred from heat capacity.