Deconstruction of the Trap Model for the New Conducting State in 2D

A key prediction of the trap model for the new conducting state in 2D is that the resistivity turns upwards below some characteristic temperature, $T_{\rm min}$. Altshuler, Maslov, and Pudalov have argued that the reason why no upturn has been observed for the low density conducting samples is that the temperature was not low enough in the experiments. We show here that $T_{\rm min}$ within the Altshuler, Maslov, and Pudalov trap model actually increases with decreasing density, contrary to their claim. Consequently, the trap model is not consistent with the experimental trends.Comment: Published version of Deconstructio

Two-Component Scaling near the Metal-Insulator Bifurcation in Two-Dimensions

We consider a two-component scaling picture for the resistivity of two-dimensional (2D) weakly disordered interacting electron systems at low temperature with the aim of describing both the vicinity of the bifurcation and the low resistance metallic regime in the same framework. We contrast the essential features of one-component and two-component scaling theories. We discuss why the conventional lowest order renormalization group equations do not show a bifurcation in 2D, and a semi-empirical extension is proposed which does lead to bifurcation. Parameters, including the product $z\nu$, are determined by least squares fitting to experimental data. An excellent description is obtained for the temperature and density dependence of the resistance of silicon close to the separatrix. Implications of this two-component scaling picture for a quantum critical point are discussed.Comment: 7 pages, 1 figur

Metal-insulator transition in disordered 2DEG including temperature effects

We calculate self-consistently the mutual dependence of electron correlations and electron-defect scattering for a two dimensional electron gas at finite temperature. We employ an STLS approach to calculate the electron correlations while the electron scattering rate off Coulombic impurities and surface roughness is calculated using self-consistent current-relaxation theory. The methods are combined and self-consistently solved. We discuss a metal-insulator transition for a range of disorder levels and electron densities. Our results are in good agreement with recent experimental observations.Comment: 4 pages, RevTeX + epsf, 5 figure

Metallicity and its low temperature behavior in dilute 2D carrier systems

We theoretically consider the temperature and density dependent transport properties of semiconductor-based 2D carrier systems within the RPA-Boltzmann transport theory, taking into account realistic screened charged impurity scattering in the semiconductor. We derive a leading behavior in the transport property, which is exact in the strict 2D approximation and provides a zeroth order explanation for the strength of metallicity in various 2D carrier systems. By carefully comparing the calculated full nonlinear temperature dependence of electronic resistivity at low temperatures with the corresponding asymptotic analytic form obtained in the $T/T_F \to 0$ limit, both within the RPA screened charged impurity scattering theory, we critically discuss the applicability of the linear temperature dependent correction to the low temperature resistivity in 2D semiconductor structures. We find quite generally that for charged ionized impurity scattering screened by the electronic dielectric function (within RPA or its suitable generalizations including local field corrections), the resistivity obeys the asymptotic linear form only in the extreme low temperature limit of $T/T_F \le 0.05$. We point out the experimental implications of our findings and discuss in the context of the screening theory the relative strengths of metallicity in different 2D systems.Comment: We have substantially revised this paper by adding new materials and figures including a detailed comparison to a recent experimen

Two-species percolation and Scaling theory of the metal-insulator transition in two dimensions

Recently, a simple non-interacting-electron model, combining local quantum tunneling via quantum point contacts and global classical percolation, has been introduced in order to describe the observed ``metal-insulator transition'' in two dimensions [1]. Here, based upon that model, a two-species-percolation scaling theory is introduced and compared to the experimental data. The two species in this model are, on one hand, the ``metallic'' point contacts, whose critical energy lies below the Fermi energy, and on the other hand, the insulating quantum point contacts. It is shown that many features of the experiments, such as the exponential dependence of the resistance on temperature on the metallic side, the linear dependence of the exponent on density, the $e^2/h$ scale of the critical resistance, the quenching of the metallic phase by a parallel magnetic field and the non-monotonic dependence of the critical density on a perpendicular magnetic field, can be naturally explained by the model. Moreover, details such as the nonmonotonic dependence of the resistance on temperature or the inflection point of the resistance vs. parallel magnetic are also a natural consequence of the theory. The calculated parallel field dependence of the critical density agrees excellently with experiments, and is used to deduce an experimental value of the confining energy in the vertical direction. It is also shown that the resistance on the ``metallic'' side can decrease with decreasing temperature by an arbitrary factor in the degenerate regime ($T\lesssim E_F$).Comment: 8 pages, 8 figure

The relative importance of electron-electron interactions compared to disorder in the two-dimensional "metallic" state

The effect of substrate bias and surface gate voltage on the low temperature resistivity of a Si-MOSFET is studied for electron concentrations where the resistivity increases with increasing temperature. This technique offers two degrees of freedom for controlling the electron concentration and the device mobility, thereby providing a means to evaluate the relative importance of electron-electron interactions and disorder in this so-called ``metallic'' regime. For temperatures well below the Fermi temperature, the data obey a scaling law where the disorder parameter ($k_{\rm{F}}l$), and not the concentration, appears explicitly. This suggests that interactions, although present, do not alter the Fermi-liquid properties of the system fundamentally. Furthermore, this experimental observation is reproduced in results of calculations based on temperature-dependent screening, in the context of Drude-Boltzmann theory.Comment: 5 pages, 6 figure

Two-Dimensional Wigner Crystal in Anisotropic Semiconductor

We investigate the effect of mass anisotropy on the Wigner crystallization transition in a two-dimensional (2D) electron gas. The static and dynamical properties of a 2D Wigner crystal have been calculated for arbitrary 2D Bravais lattices in the presence of anisotropic mass, as may be obtainable in Si MOSFETs with (110) surface. By studying the stability of all possible lattices, we find significant change in the crystal structure and melting density of the electron lattice with the lowest ground state energy.Comment: 4 pages, revtex, 4 figure

The Parallel Magnetoconductance of Interacting Electrons in a Two Dimensional Disordered System

The transport properties of interacting electrons for which the spin degree of freedom is taken into account are numerically studied for small two dimensional diffusive clusters. On-site electron-electron interactions tend to delocalize the electrons, while long-range interactions enhance localization. On careful examination of the transport properties, we reach the conclusion that it does not show a two dimensional metal insulator transition driven by interactions. A parallel magnetic field leads to enhanced resistivity, which saturates once the electrons become fully spin polarized. The strength of the magnetic field for which the resistivity saturates decreases as electron density goes down. Thus, the numerical calculations capture some of the features seen in recent experimental measurements of parallel magnetoconductance.Comment: 10 pages, 6 figure

Emergence of quasi-metallic state in disordered 2D electron gas due to strong interactions

The interrelation between disorder and interactions in two dimensional electron liquid is studied beyond weak coupling perturbation theory. Strong repulsion significantly reduces the electronic density of states on the Fermi level. This makes the electron liquid more rigid and strongly suppresses elastic scattering off impurities. As a result the weak localization, although ultimately present at zero temperature and infinite sample size, is unobservable at experimentally accessible temperature at high enough densities. Therefore practically there exists a well defined metallic state. We study diffusion of electrons in this state and find that the diffusion pole is significantly modified due to "mixture" with static photons similar to the Anderson - Higgs mechanism in superconductivity. As a result several effects stemming from the long range nature of diffusion like the Aronov - Altshuler logarithmic corrections to conductivity are less pronounced.Comment: to appear in Phys. Rev.