Hopping Conduction in Uniaxially Stressed Si:B near the Insulator-Metal Transition

Using uniaxial stress to tune the critical density near that of the sample, we have studied in detail the low-temperature conductivity of p-type Si:B in the insulating phase very near the metal-insulator transition. For all values of temperature and stress, the conductivity collapses onto a single universal scaling curve. For large values of the argument, the scaling function is well fit by the exponentially activated form associated with variable range hopping when electron-electron interactions cause a soft Coulomb gap in the density of states at the Fermi energy. The temperature dependence of the prefactor, corresponding to the T-dependence of the critical curve, has been determined reliably for this system, and is proportional to the square-root of T. We show explicitly that nevlecting the prefactor leads to substantial errors in the determination of the scaling parameters and the critical exponents derived from them. The conductivity is not consistent with Mott variable-range hopping in the critical region nor does it obey this form for any range of the parameters. Instead, for smaller argument of the scaling function, the conductivity of Si:B is well fit by an exponential form with exponent 0.31 related to the critical exponents of the system at the metal- insulator transition.Comment: 13 pages, 6 figure

Scaling theory of two-dimensional metal-insulator transitions

We discuss the recently discovered two-dimensional metal-insulator transition in zero magnetic field in the light of the scaling theory of localization. We demonstrate that the observed symmetry relating conductivity and resistivity follows directly from the quantum critical behavior associated with such a transition. In addition, we show that very general scaling considerations imply that any disordered two dimensional metal is a perfect metal, but most likely not a Fermi liquid.Comment: 4 pages, no figures, REVTEX. Minor corrections adde

Metal-insulator transition at B=0 in a dilute two dimensional GaAs-AlGaAs hole gas

We report the observation of a metal insulator transition at B=0 in a high mobility two dimensional hole gas in a GaAs-AlGaAs heterostructure. A clear critical point separates the insulating phase from the metallic phase, demonstrating the existence of a well defined minimum metallic conductivity sigma(min)=2e/h. The sigma(T) data either side of the transition can be `scaled' on to one curve with a single parameter (To). The application of a parallel magnetic field increases sigma(min) and broadens the transition. We argue that strong electron-electron interactions (rs = 10) destroy phase coherence, removing quantum intereference corrections to the conductivity.Comment: 4 pages RevTex + 4 figures. Submitted to PRL. Originally posted 22 September 1997. Revised 12 October 1997 - minor changes to referencing, figure cations and figure

In-plane Magnetoconductivity of Si-MOSFET's: A Quantitative Comparison between Theory and Experiment

For densities above $n=1.6 \times 10^{11}$ cm$^{-2}$ in the strongly interacting system of electrons in two-dimensional silicon inversion layers, excellent agreement between experiment and the theory of Zala, Narozhny and Aleiner is obtained for the response of the conductivity to a magnetic field applied parallel to the plane of the electrons. However, the Fermi liquid parameter $F_0^\sigma(n)$ and the valley splitting $\Delta_V(n)$ obtained from fits to the magnetoconductivity, although providing qualitatively correct behavior (including sign), do not yield quantitative agreement with the temperature dependence of the conductivity in zero magnetic field. Our results suggest the existence of additional scattering processes not included in the theory in its present form

Universal scaling, beta function, and metal-insulator transitions

We demonstrate a universal scaling form of longitudinal resistance in the quantum critical region of metal-insulator transitions, based on numerical results of three-dimensional Anderson transitions (with and without magnetic field), two-dimensional quantum Hall plateau to insulator transition, as well as experimental data of the recently discovered two-dimensional metal-insulator transition. The associated reflection symmetry and a peculiar logarithmic form of the beta function exist over a wide range in which the resistance can change by more than one order of magnitude. Interesting implications for the two-dimensional metal-insulator transition are discussed.Comment: 4 pages, REVTEX, 4 embedded figures; minor corrections to figures and tex

Sharply increasing effective mass: a precursor of the spontaneous spin polarization in a dilute two-dimensional electron system

We have measured the effective mass, m, and Lande g-factor in very dilute two-dimensional electron systems in silicon. Two independent methods have been used: (i) measurements of the magnetic field required to fully polarize the electrons' spins and (ii) analysis of the Shubnikov-de Haas oscillations. We have observed a sharp increase of the effective mass with decreasing electron density while the g-factor remains nearly constant and close to its value in bulk silicon. The corresponding strong rise of the spin susceptibility may be a precursor of a spontaneous spin polarization; unlike in the Stoner scenario, it originates from the enhancement of the effective mass rather than the increase of g-factor. Furthermore, using tilted magnetic fields, we have found that the enhanced effective mass is independent of the degree of spin polarization and, therefore, its increase is not related to spin exchange effects, in contradiction with existing theories. Our results show that the dilute 2D electron system in silicon behaves well beyond a weakly interacting Fermi liquid.Comment: This paper summarizes results reported in our recent publications on the subjec

Conducting phase in the two-dimensional disordered Hubbard model

We study the temperature-dependent conductivity $\sigma(T)$ and spin susceptibility $\chi(T)$ of the two-dimensional disordered Hubbard model. Calculations of the current-current correlation function using the Determinant Quantum Monte Carlo method show that repulsion between electrons can significantly enhance the conductivity, and at low temperatures change the sign of $d\sigma/dT$ from positive (insulating behavior) to negative (conducting behavior). This result suggests the possibility of a metallic phase, and consequently a metal-insulator transition,in a two-dimensional microscopic model containing both interactions and disorder. The metallic phase is a non-Fermi liquid with local moments as deduced from a Curie-like temperature dependence of $\chi(T)$.Comment: 4 pages; 4 postscript figures; added (1) a new figure showing temperature dependence of spin susceptibility; (2) more references. accepted for publication in Phys. Rev. Let

Non-perturbative saddle point for the effective action of disordered and interacting electrons in 2D

We find a non-perturbative saddle-point solution for the non-linear sigma model proposed by Finkelstein for interacting and disordered electronic systems. Spin rotation symmetry, present in the original saddle point solution, is spontaneously broken at one-loop, as in the Coleman-Weinberg mechanism. The new solution is singular in both the disorder and triplet interaction strengths, and it also explicitly demonstrates that a non-trivial ferromagnetic state appears in a theory where the disorder average is carried out from the outset.Comment: 4 pages, 1 figur

On large deviation properties of Erdos-Renyi random graphs

We show that large deviation properties of Erd\"os-R\'enyi random graphs can be derived from the free energy of the $q$-state Potts model of statistical mechanics. More precisely the Legendre transform of the Potts free energy with respect to $\ln q$ is related to the component generating function of the graph ensemble. This generalizes the well-known mapping between typical properties of random graphs and the $q\to 1$ limit of the Potts free energy. For exponentially rare graphs we explicitly calculate the number of components, the size of the giant component, the degree distributions inside and outside the giant component, and the distribution of small component sizes. We also perform numerical simulations which are in very good agreement with our analytical work. Finally we demonstrate how the same results can be derived by studying the evolution of random graphs under the insertion of new vertices and edges, without recourse to the thermodynamics of the Potts model.Comment: 38 pages, 9 figures, Latex2e, corrected and extended version including numerical simulation result

The metallic resistance of a dilute two-dimensional hole gas in a GaAs quantum well: two-phase separation at finite temperature?

We have studied the magnetotransport properties of a high mobility two-dimensional hole gas (2DHG) system in a 10nm GaAs quantum well (QW) with densities in range of 0.7-1.6*10^10 cm^-2 on the metallic side of the zero-field 'metal-insulator transition' (MIT). In a parallel field well above B_c that suppresses the metallic conductivity, the 2DHG exhibits a conductivity g(T)~0.3(e^2/h)lnT reminiscent of weak localization. The experiments are consistent with the coexistence of two phases in our system: a metallic phase and a weakly insulating Fermi liquid phase having a percolation threshold close to B_c