Abstract

We study a two-dimensional metallic system close to an antiferromagnetic critical point within the framework of the spin-fermion model. The model describes fermionic quasiparticles interacting with bosonic collective spin modes close to the antiferromagnetic wave vector Q.
Since Q is a large momentum scale, in first order of the spin-fermion coupling, low-energy fermions are only coupled to spin fluctuations at “hot spots” of the Fermi surface which are connected by Q. However, at second order a fermion at an arbitrary point of a generic Fermi surface can be scattered successively by two spin fluctuations via an intermediate high-energy state and, in total, suffer only a small momentum transfer. This gives rise to an interference of critical spin fluctuations and diffusive excitations of the disordered metal.
Integrating out the fermionic high-energy modes above a certain low-energy cutoff, we derive an effective critical low-energy action which exhibits a local interaction vertex for low-energy fermions on the entire Fermi surface. This interaction is mediated by a composite propagator composed of two bare bosonic propagators.
Using a diagrammatic approach, we calculate the temperature-dependent interaction correction to dc-conductivity induced by the composite propagator in the presence of disorder and find that the appearing integral over diffusion poles give rise to a log^2(T) behaviour.