Transport anomalies in a simplified model for a heavy-electron quantum critical point

We discuss the transport anomalies associated with the development of heavy electrons out of a neutral spin fluid using the large-$N$ treatment of the Kondo-Heisenberg lattice model. At the phase transition in this model the spin excitations suddenly acquire charge. The Higgs process by which this takes place causes the constraint gauge field to loosely “lock” together with the external, electromagnetic gauge field. From this perspective, the heavy-fermion phase is a Meissner phase in which the field representing the difference between the electromagnetic and constraint gauge fields is excluded from the material. We show that at the transition into the heavy-fermion phase, both the linear and Hall conductivities jump together. However, the Drude weight of the heavy-electron fluid does not jump at the quantum critical point, but instead grows linearly with the distance from the quantum critical point, forming a kind of “gossamer” Fermi liquid.

Figure 1

(a) Three-dimensional triangular spin structure for which the uniform RVB phase is stable in the large-$N$ limit. (b) The simpler two-dimensional triangular lattice has the conceptual advantage that spin and diamagnetic parts of the magnetic field can be treated separately by considering fields parallel and perpendicular to the plane.

Figure 2

Diagrams for the conductivities entering into the effective action. Full propagators refer to conduction electron propagators $G_c^{-1}\left(i{\omega }_n\right)=i{\omega }_n-{ϵ}_k+i\mathrm{sgn}\left({\omega }_n\right)∕\left(2{\tau }_1\right)$, and dashed lines refer to $f$-electron propagators $G_f^{-1}\left(i{\omega }_n\right)=i{\omega }_n-j_k+i\mathrm{sgn}\left({\omega }_n\right)∕\left(2{\tau }_2\right)$,

Figure 3

The hybridization $V$ induces a further response to an applied electromagnetic field that leads to an additional term to the physical conductivity illustrated here.