Non-Fermi-liquid theory for disordered metals near two dimensions

We consider the Finkelstein action describing a system of spin-polarized or spinless electrons in $2+2\epsilon$ dimensions, in the presence of disorder as well as the Coulomb interactions. We extend the renormalization-group analysis of our previous work and evaluate the metal-insulator transition of the electron gas to second order in an $\epsilon$ expansion. We obtain the complete scaling behavior of physical observables like the conductivity and the specific heat with varying frequency, temperature, and/or electron density. We extend the results for the interacting electron gas in $2+2\epsilon$ dimensions to include the quantum critical behavior of the plateau transitions in the quantum Hall regime. Although these transitions have a very different microscopic origin and are controlled by a topological term in the action $(\theta$ term), the quantum critical behavior is in many ways the same in both cases. We show that the two independent critical exponents of the quantum Hall plateau transitions, previously denoted as $\nu$ and p, control not only the scaling behavior of the conductances ${\sigma }_{\mathrm{xx}}$ and ${\sigma }_{\mathrm{xy}}$ at finite temperatures T, but also the non-Fermi-liquid behavior of the specific heat ${(c}_v\propto T^p).\mathrm{}$ To extract the numerical values of $\nu$ and p it is necessary to extend the experiments on transport to include the specific heat of the electron gas.