Valentin Peschansky and puzzles of magnetotransport

Starting from the 1950s, the Kharkov school of theoretical physics was one of the world leaders in the theory of metals. In particular, the research by V.G. Peschansky for many years was focused on studying the relationship between magnetic field dependence of resistivity components and the electron energy spectrum. V.G. Peschansky elaborated an elegant theory of magnetoresistance that took into account surface scattering of electrons. The physics of bulk 3D metals was almost exhausted by the end of 1970s and Peschansky extended his research to the low-dimensional electron systems. Through all his scientific life, V.G. Peschansky advocated the idea that magnetoresistance is a powerful tool that can be used to explore rich physics of electron systems. By now, numerous experimental and theoretical studies of magnetoresistance behavior in various systems, from simple to the most complex ones, confirm the fruitfulness of this idea

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

David Shoenberg and the beauty of quantum oscillati

The quantum oscillation effect was discovered in Leiden, in 1930, by W.J. de Haas and P.M. van Alphen in magnetization measurement, and by L.W. Shubnikov and de Haas — in magnetoresistance. Studying single crystals of bismuth, they observed oscillatory variations of magnetization and magnetoresistance with magnetic field. Shoenberg, whose first research in Cambridge had been on bismuth, found that much stronger oscillations are observed when a bismuth sample is cooled to liquid helium rather than to liquid hydrogen, which had been used by de Haas. In 1938 Shoenberg came from Cambridge to Moscow to study these oscillations at Kapitza Institute where liquid helium was available at that time. In 1947, J. Marcus observed similar oscillations in zinc, that persuaded Shoenderg to return to this research, and, since then, the dHvA effect had been one of his main research topic. In particular, he developed techniques for quantitative measurements of the effect in many metals. Theoretical explanation of quantum oscillations was given by L. Onsager in 1952, and the analytical quantitative theory by I.M. Lifshitz and A.M. Kosevich in 1955. These theoretical advancements seemed to provide a comprehensive description of the effect. Since then, quantum oscillations were commonly considered as a tool for measuring Fermi surface extremal cross-sections and all-angle electron scattering times. However, in his pioneering experiments in 1960s, Shoenberg revealed the richness and deep essence of the quantum oscillation effect and showed how the beauty of the effect is disclosed under nonlinear conditions imposed by interactions in the system under study. It was quite unexpected, that under «magnetic interaction» conditions, the apparently weak effect of quantum oscillations may lead to such strong consequences as breaking the sample into magnetic (now called «Shoenberg») domains and the formation of an inhomogeneous magnetic state. Owing to his contribution to the field of quantum oscillations and superconductivity, Shoenberg is no doubt one of the 20th century's foremost experts. We describe the experiments on finding the quantitative parameters of electron–electron interaction, which are in line with the Shoenberg ideas that the quantum oscillations are modified by interactions and, hence, their analysis enables one to extract the quasiparticle interaction parameters

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

Hall Coefficient in an Interacting Electron Gas

The Hall conductivity in a weak homogeneous magnetic field, $\omega_{c}\tau \ll 1$, is calculated. We have shown that to leading order in $1/\epsilon_{F}\tau$ the Hall coefficient $R_{H}$ is not renormalized by the electron-electron interaction. Our result explains the experimentally observed stability of the Hall coefficient in a dilute electron gas not too close to the metal-insulator transition. We avoid the currently used procedure that introduces an artificial spatial modulation of the magnetic field. The problem of the Hall effect is reformulated in a way such that the magnetic flux associated with the scattering process becomes the central element of the calculation.Comment: 23 pages, 15 figure

Phase separation in the two-dimensional electron liquid in MOSFETs

We show that the existence of an intermediate phase between the Fermi liquid and the Wigner crystal phases is a generic property of the two-dimensional pure electron liqd in MOSFET's at zero temperature. The physical reason for the existence of these phases is a partial separation of the uniform phases. We discuss properties of these phases and a possible explanation of experimental results on transport properties of low density electron gas in Si MOSFET's. We also argue that in certain range of parameters the partial phase separation corresponds to a supersolid phas e discussed in [AndreevLifshitz].Comment: 11 pages, 3 figure

Sharp increase of the effective mass near the critical density in a metallic 2D electron system

We find that at intermediate temperatures, the metallic temperature dependence of the conductivity \sigma(T) of 2D electrons in silicon is described well by a recent interaction-based theory of Zala et al. (Phys. Rev. B 64, 214204 (2001)). The tendency of the slope d\sigma/dT to diverge near the critical electron density is in agreement with the previously suggested ferromagnetic instability in this electron system. Unexpectedly, it is found to originate from the sharp enhancement of the effective mass, while the effective Lande g factor remains nearly constant and close to its value in bulk silicon

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

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

"Forbidden" transitions between quantum Hall and insulating phases in p-SiGe heterostructures

We show that in dilute metallic p-SiGe heterostructures, magnetic field can cause multiple quantum Hall-insulator-quantum Hall transitions. The insulating states are observed between quantum Hall states with filling factors \nu=1 and 2 and, for the first time, between \nu=2 and 3 and between \nu=4 and 6. The latter are in contradiction with the original global phase diagram for the quantum Hall effect. We suggest that the application of a (perpendicular) magnetic field induces insulating behavior in metallic p-SiGe heterostructures in the same way as in Si MOSFETs. This insulator is then in competition with, and interrupted by, integer quantum Hall states leading to the multiple re-entrant transitions. The phase diagram which accounts for these transition is similar to that previously obtained in Si MOSFETs thus confirming its universal character