Metal-Insulator Transition in Disordered Two-Dimensional Electron Systems

We present a theory of the metal-insulator transition in a disordered two-dimensional 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

Branch-cut Singularities in Thermodynamics of Fermi Liquid Systems

The recently measured spin susceptibility of the two dimensional electron gas exhibits a strong dependence on temperature, which is incompatible with the standard Fermi liquid phenomenology. Here we show that the observed temperature behavior is inherent to ballistic two dimensional electrons. Besides the single-particle and collective excitations, the thermodynamics of Fermi liquid systems includes effects of the branch-cut singularities originating from the edges of the continuum of pairs of quasiparticles. As a result of the rescattering induced by interactions, the branch-cut singularities generate non-analyticities in the thermodynamic potential which reveal themselves in anomalous temperature dependences. Calculation of the spin susceptibility in such a situation requires a non-perturbative treatment of the interactions. As in high-energy physics, a mixture of the collective excitations and pairs of quasiparticles can be effectively described by a pole in the complex momentum plane. This analysis provides a natural explanation for the observed temperature dependence of the spin susceptibility, both in sign and magnitude.Comment: 8 pages, 3 figure

Dilute electron gas near the metal-insulator transition in two dimensions

In recent years systematic experimental studies of the temperature dependence of the resistivity in a variety of dilute, ultra clean two dimensional electron/hole systems have revived the fundamental question of localization or, alternatively, the existence of a metal-insulator transition in the presence of strong electron-electron interactions in two dimensions. We argue that under the extreme conditions of ultra clean systems not only is the electron-electron interaction very strong but the role of other system specific properties are also enhanced. In particular, we emphasize the role of valleys in determining the transport properties of the dilute electron gas in silicon inversion layers (Si-MOSFETs). It is shown that for a high quality sample the temperature behavior of the resistivity in the region close to the critical region of the metal-insulator transition is well described by a renormalization group analysis of the interplay of interaction and disorder if the electron band is assumed to have two distinct valleys. The decrease in the resistivity up to five times has been captured in the correct temperature interval by this analysis, without involving any adjustable parameters. The considerable variance in the data obtained from different Si-MOSFET samples is attributed to the sample dependent scattering rate across the two valleys, presenting thereby with a possible explanation for the absence of universal behavior in Si-MOSFET samples of different quality

Suppression of \bbox{T_c} in superconducting amorphous wires

The suppression of the mean field temperature of the superconducting transition, $T_c$, in homogeneous amorphous wires is studied. We develop a theory that gives $T_c$ in situations when the dynamically enhanced Coulomb repulsion competes with the contact attraction. The theory accurately describes recent experiments on $T_c$--suppression in superconducting wires, after a procedure that minimizes the role of nonuniversal mechanisms influencing $T_c$ is applied.Comment: RevTeX, 4 pages, 3 figure

A Single Impurity in Tomonaga-Luttinger Liquids

The problem of a single impurity in one dimensional Tomonaga-Luttinger liquids with a repulsive electron-electron interaction is discussed. We find that the renormalization group flow diagram for the parameters characterizing the impurity is rather complex. Apart from the fixed points corresponding to two weakly connected semi-infinite wires, the flow diagram contains additional fixed points which control the low temperature physics when the bare potential of the impurity is not strong.Comment: To be published in the Philosophical Magazine in the Proceedings of the "MINERVA WORKSHOP on MESOSCOPICS, FRACTALS and NEURAL NETWORKS", Eilat, Israel, March 199

Valley current in graphene through electron-phonon interaction

We discuss valley current, which is carried by quasiparticles in graphene. We show that the valley current arises owing to a peculiar term in the electron-phonon collision integral that mixes the scalar and vector gauge-field-like vertices in the electron-phonon interaction. This mixing makes collisions of phonons with electrons sensitive to their chirality, which is opposite in two valleys. As a result of collisions with phonons, electrons of the different valleys deviate in opposite directions. Breaking the spatial inversion symmetry is not needed for a valley-dependent deviation of the quasiparticle current. The effect exists both in pristine graphene or bilayer graphene samples, and it increases with temperature owing to a higher rate of collisions with phonons at higher temperatures. The valley current carried by quasiparticles could be detected by measuring the electric current using a nonlocal transformer of a suitable design.Comment: 5 pages, 2 figures. To be published as a Rapid Communication in Physical Review

Dephasing time in graphene due to interaction with flexural phonons

We investigate decoherence of an electron in graphene caused by electron-flexural phonon interaction. We find out that flexural phonons can produce dephasing rate comparable to the electron-electron one. The problem appears to be quite special because there is a large interval of temperature where the dephasing induced by phonons can not be obtain using the golden rule. We evaluate this rate for a wide range of density ($n$) and temperature ($T$) and determine several asymptotic regions with temperature dependence crossing over from $\tau_{\phi }^{-1}\sim T^{2}$ to $\tau_{\phi}^{-1}\sim T$ when temperature increases. We also find $\tau_{\phi}^{-1}$ to be a non-monotonous function of $n$. These distinctive features of the new contribution can provide an effective way to identify flexural phonons in graphene through the electronic transport by measuring the weak localization corrections in magnetoresistance.Comment: 13 pages, 8 figure

Odd-frequency spin-triplet instability in disordered electron liquid

We consider a two-dimensional disordered conductor in the regime when the superconducting phase is destroyed by the magnetic field. We observe that the end point of the superconductivity is a quantum critical point separating the conventional superconducting phase from a state with the odd-frequency spin-triplet pairing instability. We speculate that this could shed light on a rather mysterious insulating state observed in strongly disordered superconducting films in a broad region of the magnetic fields.Comment: 27 pages, 8 figure