We present a theory of the metal-insulator transition in a disordered twodimensional electron gas. A quantum critical point, separating the metallic phase which is stabilized by electronic interactions, from the insulating phase where disorder prevails over the electronic interactions, has been identified.The existence of the quantum critical point leads to a divergence in the density of states of the underlying collective modes at the transition, causing the thermodynamic properties to behave critically as the transition is approached.We show that the interplay of electron-electron interactions and disorder can explain the observed transport properties and the anomalous enhancement of the spin susceptibility near the metal-insulator transition.

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The transport and complex optical properties of the electron-doped iron-arsenic superconductor BaFe 1.85 Co 0.15 As 2 with T c = 25 K have been examined in the Fe-As planes above and below T c . A BlochGrüneisen analysis of the resistivity yields a weak electron-phonon coupling constant ph Ӎ 0.2. The lowfrequency optical response in the normal state appears to be dominated by the electron pocket and may be described by a weakly interacting Fermi liquid with a Drude plasma frequency of p,D Ӎ 7840 cm −1 ͑Ӎ0.972eV͒ and scattering rate 1 / D Ӎ 126 cm −1 ͑Ӎ15 meV͒ just above T c . The frequency-dependent scattering rate 1 / ͑͒ has kinks at Ӎ12 and 55 meV that appear to be related to bosonic excitations. Below T c the majority of the superconducting plasma frequency originates from the electron pocket and is estimated to be p,S Ӎ 5200 cm −1 ͑ 0 Ӎ 3000 Å͒ for T Ӷ T c , indicating that less than half the free carriers in the normal state have collapsed into the condensate, suggesting that this material is not in the clean limit. Supporting this finding is the observation that this material falls close to the universal scaling line for a Bardeen, Cooper, and Schrieffer dirty-limit superconductor in the weak-coupling limit. There are two energy scales for the superconductivity in the optical conductivity and photoinduced reflectivity at ⌬ 1 ͑0͒Ӎ3.1Ϯ 0.2 meV and ⌬ 2 ͑0͒ Ӎ 7.4Ϯ 0.3 meV. This corresponds to either the gapping of the electron and hole pockets, respectively, or an anisotropic s-wave gap on the electron pocket; both views are consistent with the s Ϯ model.

The discovery of the metal-insulator transition (MIT) in two-dimensional (2D) electron systems [1] challenged the veracity of one of the most influential conjectures [2] in the physics of disordered electrons, which states that "in two dimensions, there is no true metallic behaviour"; no matter how weak the disorder, electrons would be trapped and unable to conduct a current. However, that theory did not account for interactions between the electrons. Here we investigate the interplay between the electron-electron interactions and disorder near the MIT using simultaneous measurements of electrical resistivity and magnetoconductance. We show that both the resistance and interaction amplitude exhibit a fan-like spread as the MIT is crossed. From these data we construct a resistance-interaction flow diagram of the MIT that clearly reveals a quantum critical point, as predicted by the two-parameter scaling theory [3]. The metallic side of this diagram is accurately described by the renormalization group theory [4] without any fitting parameters. In particular, the metallic temperature dependence of the resistance sets in when the interaction amplitude reaches γ 2 ≈ 0.45 -a value in remarkable agreement with the one predicted by theory [4].The low amount of disorder in high mobility silicon metal-oxide-semiconductor field-effect transistors (Si MOSFETs) allows measurements to be made in the regime of very low electron densities where correlation effects due to electron-electron interactions become especially important. (Ratios r s ≡ E C /E F > 10 between Coulomb and Fermi energies are easily reached with Fermi energies of the order 0.7 meV.) This material system has the additional advantage that its electron spectrum has two almost degenerate valleys, which further enhances the correlation effects. Indeed, the lowtemperature drop of the resistance on the metallic side of the transition (Fig.