The metal–insulator transition (MIT) observed in a two-dimensional dilute electron liquid raises the question about the applicability of the scaling theory of disordered electrons, the approach pioneered by Phil Anderson and his collaborators,8 for the description of this transition. In this context, we review here the scaling theory of disordered electrons with electron–electron interactions. We start with the disordered Fermi liquid, and show how to adjust the microscopic Fermi-liquid theory to the presence of disorder. Then we describe the non-linear sigma model (NLSM) with interactions. This model has a direct relation with the disordered Fermi liquid, but can be more generally applicable, since it is a minimal model for disordered interacting electrons. The discussion is mostly about the general structure of the theory emphasizing the connection of the scaling parameters entering the NLSM with conservation laws. Next, we show that the MIT, as described by the NLSM with interactions, is a quantum phase transition and identify the parameters needed for the description of the kinetics and thermodynamics of the interacting liquid in the critical region of the transition. Finally, we discuss the MIT observed in Si -MOSFETs. We consider it as an example of the Anderson transition in the presence of the electron interactions. We demonstrate that the two-parameter RG equations, which treat disorder in the one-loop approximation but incorporate the full dependence on the interaction amplitudes, describe accurately the experimental data in Si -MOSFETs including the observed non-monotonic behavior of the resistance and its strong drop at low temperatures. The fact that this drop can be reproduced theoretically, together with the argument that Anderson localization should occur at strong disorder, justified the existence of the MIT within the scaling theory.The metal–insulator transition (MIT) observed in a two-dimensional dilute electron liquid raises the question about the applicability of the scaling theory of disordered electrons, the approach pioneered by Phil Anderson and his collaborators,8 for the description of this transition. In this context, we review here the scaling theory of disordered electrons with electron–electron interactions. We start with the disordered Fermi liquid, and show how to adjust the microscopic Fermi-liquid theory to the presence of disorder. Then we describe the non-linear sigma model (NLSM) with interactions. This model has a direct relation with the disordered Fermi liquid, but can be more generally applicable, since it is a minimal model for disordered interacting electrons. The discussion is mostly about the general structure of the theory emphasizing the connection of the scaling parameters entering the NLSM with conservation laws. Next, we show that the MIT, as described by the NLSM with interactions, is a quantum phase transition and identify the parameters needed for the description of the kinetics and thermodynamics of the interacting liquid in the critical region of the transition. Finally, we discuss the MIT observed in Si -MOSFETs. We consider it as an example of the Anderson transition in the presence of the electron interactions. We demonstrate that the two-parameter RG equations, which treat disorder in the one-loop approximation but incorporate the full dependence on the interaction amplitudes, describe accurately the experimental data in Si -MOSFETs including the observed non-monotonic behavior of the resistance and its strong drop at low temperatures. The fact that this drop can be reproduced theoretically, together with the argument that Anderson localization should occur at strong disorder, justified the existence of the MIT within the scaling theory.

International Journal of Modern Physics BMay 20, 201030 citations

Theory of electron-hole liquids in two dimensions

P K Isihara, Yoshinori Nakane, A. Isihara

Journal of Physics C Solid State PhysicsApr 30, 19841 citation

Ground-state properties of the one dimensional electron liquid

Reza Asgari

arXiv:cond-mat/0703359Solid State CommunicationsDec 21, 20067 citations

Interactions and scaling in a disordered two-dimensional metal

Sudip Chakravarty, Lan Yin, Elihu Abrahams

We show that a non-Fermi-liquid state of interacting electrons in two dimensions is stable in the presence of disorder and is a perfect conductor, provided the interactions are sufficiently strong. Otherwise, the disorder leads to localization as in the case of noninteracting electrons. This conclusion is established by examining the replica field theory in the weak-disorder limit, but in the presence of arbitrary electron-electron interaction. Thus, a disordered two-dimensional metal is a perfect metal, but not a Fermi liquid.We show that a non-Fermi-liquid state of interacting electrons in two dimensions is stable in the presence of disorder and is a perfect conductor, provided the interactions are sufficiently strong. Otherwise, the disorder leads to localization as in the case of noninteracting electrons. This conclusion is established by examining the replica field theory in the weak-disorder limit, but in the presence of arbitrary electron-electron interaction. Thus, a disordered two-dimensional metal is a perfect metal, but not a Fermi liquid.

arXiv:cond-mat/9712217Physical review. B, Condensed matterJul 1, 199854 citations

Transport phenomena in disordered interacting electron systems

Karen Michaeli

Jan 1, 20100 citations

Frequency-temperature crossover in the conductivity of disordered Luttinger liquids

Bernd Rosenow, Andreas Glatz, Thomas Nattermann

The temperature $(T)$ and frequency $(\ensuremath{\omega})$ dependent conductivity of weakly disordered Luttinger liquids is calculated in a systematic way both by perturbation theory and from a finite temperature renormalization group (RG) treatment to leading order in the disorder strength. Whereas perturbation theory results in $\ensuremath{\omega}∕T$ scaling of the conductivity, such scaling is violated in the RG treatment. We also determine the nonlinear field dependence of the conductivity, whose power law scaling is different from that of temperature and frequency dependence.The temperature $(T)$ and frequency $(\ensuremath{\omega})$ dependent conductivity of weakly disordered Luttinger liquids is calculated in a systematic way both by perturbation theory and from a finite temperature renormalization group (RG) treatment to leading order in the disorder strength. Whereas perturbation theory results in $\ensuremath{\omega}∕T$ scaling of the conductivity, such scaling is violated in the RG treatment. We also determine the nonlinear field dependence of the conductivity, whose power law scaling is different from that of temperature and frequency dependence.

arXiv:cond-mat/0610426Physical Review BOct 10, 20074 citations

The temperature

(T)

and frequency $(\ensuremath{\omega})$ dependent conductivity of weakly disordered Luttinger liquids is calculated in a systematic way both by perturbation theory and from a finite temperature renormalization group (RG) treatment to leading order in the disorder strength. Whereas perturbation theory results in $\ensuremath{\omega}∕T$ scaling of the conductivity, such scaling is violated in the RG treatment. We also determine the nonlinear field dependence of the conductivity, whose power law scaling is different from that of temperature and frequency dependence.