Breakdown of the perturbative renormalization group at certain quantum critical points

It is shown that the presence of multiple time scales at a quantum critical point can lead to a breakdown of the loop expansion for critical exponents, since coefficients in the expansion diverge. Consequently, results obtained from finite-order perturbative renormalization-group treatments may be not be an approximation in any sense to the true asymptotic critical behavior. This problem manifests itself as a non-renormalizable field theory, or, equivalently, as the presence of a dangerous irrelevant variable. The quantum ferromagnetic transition in disordered metals provides an example.Comment: 4pp, 1 eps fi

Density of states and magnetoconductance of disordered Au point contacts

We report the first low temperature magnetotransport measurements on electrochemically fabricated atomic scale gold nanojunctions. As $T \to 0$, the junctions exhibit nonperturbatively large zero bias anomalies (ZBAs) in their differential conductance. We consider several explanations and find that the ZBAs are consistent with a reduced local density of states (LDOS) in the disordered metal. We suggest that this is a result of Coulomb interactions in a granular metal with moderate intergrain coupling. Magnetoconductance of atomic scale junctions also differs significantly from that of less geometrically constrained devices, and supports this explanation.Comment: 5 pages, 5 figures. Accepted to PRB as Brief Repor

Multi-particle effects in non-equilibrium electron tunnelling and field emission

We investigate energy resolved electric current from various correlated host materials under out-of-equilibrium conditions. We find that, due to a combined effect of electron-electron interactions, non-equilibrium and multi-particle tunnelling, the energy resolved current is finite even above the Fermi edge of the host material. In most cases, the current density possesses a singularity at the Fermi level revealing novel manifestations of correlation effects in electron tunnelling. By means of the Keldysh non-equilibrium technique, the current density is calculated for one-dimensional interacting electron systems and for two-dimensional systems, both in the pure limit and in the presence of disorder. We then specialise to the field emission and provide a comprehensive theoretical study of this effect in carbon nanotubes.Comment: 22 pages, 8 figures (eps files