Theory of the metal-insulator transition in two-dimensional electron systems

The metal-insulator transition in a two-dimensional disordered electron system (as the carrier concentration decreases) is considered in terms of a percolation theory. The fact that this is a strong-coupling system is substantially taken into account. In our model, the initial structure is taken to be the skeleton of an infinite cluster. Percolation paths are assumed to have regions where two phases having similar energies, namely, liquid (conducting) and solid (nonconducting) phases, can compete with each other. The ratio of these phases changes as a function of the system parameters and temperature. This behavior generates a change in the infinite cluster and results in the conductor-insulator transition. The obtained temperature dependences of resistivity agree qualitatively with experiment. A quantitative comparison of the calculated results with experimental data allows the system parameters to be estimated in each specific case. The temperature dependences of resistivity are mainly determined by the sign of the difference (and also the scatter of) in the initial energies of the phases, and they have a metallic, dielectric, or intermediate (nonmonotonic temperature dependence with a maximum) character. A separatrix can occur only in the case of a sufficiently small scatter of the phase energies.     

Field-induced metal-insulator transition in a two-dimensional organic superconductor

The quasi-two-dimensional organic superconductor beta"-(BEDT-TTF)2SF5CH2CF2SO3 (Tc approximately 4.4 K) shows very strong Shubnikov-de Haas (SdH) oscillations which are superimposed on a highly anomalous steady background magnetoresistance, Rb. Comparison with de Haas-van Alphen oscillations allows a reliable estimate of Rb which is crucial for the correct extraction of the SdH signal. At low temperatures and high magnetic fields insulating behavior evolves. The magnetoresistance data violate Kohler's rule, i.e., cannot be described within the framework of semiclassical transport theory, but converge onto a universal curve appropriate for dynamical scaling at a metal-insulator transition.     

Thermodynamic signature of a two-dimensional metal-insulator transition

We present a study of the compressibility kappa of a two-dimensional hole system which exhibits a metal-insulator phase transition at zero magnetic field. It has been observed that dkappa/dp changes sign at the critical density for the metal-insulator transition. Measurements also indicate that the insulating phase is incompressible for all values of B. Finally, we show how the phase transition evolves as the magnetic field is varied and construct a phase diagram in the density-magnetic field plane for this system.     

Quantum spin-glass transition in the two-dimensional electron gas

We discuss the possibility of spin-glass order in the vicinity of the unexpected metallic state of the two-dimensional electron gas in zero applied magnetic field. An average ferromagnetic moment may also be present, and the spin-glass order then resides in the plane orthogonal to the ferromagnetic moment. We argue that a quantum transition involving the destruction of the spinglass order in an applied in-plane magnetic field offers a natural explanation of some features of recent magnetoconductance measurements. We present a quantum field theory for such a transition and compute its mean field properties.     

Effects of a parallel magnetic field on the metal-insulator transition in a dilute two-dimensional electron system

The temperature dependence of conductivity sigma(T) of a two-dimensional electron system in silicon has been studied in parallel magnetic fields B. At B = 0, the system displays a metal-insulator transition at a critical electron density n(c)(0), and dsigma/dT>0 in the metallic phase. At low fields ( B < or approximately equal to 2 T), n(c) increases as n(c)(B)-n(c)(0) proportional, variant Bbeta ( beta approximately 1), and the zero-temperature conductivity scales as sigma(n(s),B,T = 0)/sigma(n(s),0,0) = f(B(beta)/delta(n)), where delta(n) = [n(s)-n(c)(0)]/n(c)(0) and n(s) is electron density, as expected for a quantum phase transition. The metallic phase persists in fields of up to 18 T, consistent with the saturation of n(c) at high fields.     

Magnetic ratchet effects in a two-dimensional electron gas

The effect of the magnetic field on the generation of an electric current in a two-dimensional electronic ratchet is theoretically studied. Mechanisms of the formation of magnetically induced photocurrent are proposed for a structure with a two-dimensional electron gas (quantum well, graphene, or topological insulator) with a lateral asymmetric superlattice consisting of metallic strips on the external surface of the structure. The ratchet with the spatially oscillating magnetic field generated by the ferromagnetic lattice, as well as the nonmagnetic ratchet placed in the uniform magnetic field both classically weak and strong quantizing, is considered. It is established that the ratio of the amplitude of the magnetic oscillations of photocurrent to the ratchet photocurrent in zero field can exceed two orders of magnitude.     

Surface acoustic wave propagation and inhomogeneities in low-density two-dimensional electron systems near the metal-insulator transition

We have measured the surface acoustic wave velocity shift in a GaAs/AlGaAs heterostructure containing a two-dimensional electron system (2DES) in a low-density regime (<10¹⁰ cm⁻²) at zero magnetic field. The interaction of the surface acoustic wave with the 2DES is not well described by a simple model using low-frequency conductivity measurements. We speculate that this conflict is a result of inhomogeneities in the 2DES, which become very important at low density. This has implications for the putative metal-insulator transition in two dimensions.     

Coherent backscattering near the two-dimensional metal-insulator transition

We have studied corrections to conductivity due to the coherent backscattering in low-disordered two-dimensional electron systems in silicon for a range of electron densities including the vicinity of the metal-insulator transition, where the dramatic increase of the spin susceptibility has been observed earlier. We show that the corrections, which exist deeper in the metallic phase, weaken upon approaching the transition and practically vanish at the critical density, thus suggesting that the localization is suppressed near and at the transition even in zero field.     

Hysteresis and first-order phase transition in the two-dimensional electron gas

We report experimental evidence of the first-order phase transitions in the two-dimensional electron gas formed in a gated wide GaAs/AlGaAs quantum well at even-integer quantum-Hall states. At the filling factor values of ν=2,4 and low temperatures, crossing of Landau levels through the application of the gate bias yields a suppression of the quantum-Hall-state excitation gap and hysteretical behaviour of the diagonal resistivity in up and down sweeps of the magnetic field. Detailed many-body calculations indicate the occurrence of a first-order phase transition and allow the determination of the exact properties of the electron ground states involved in the transition.     

Screening effects in two-dimensional electron gas

The potential produced by a charged impurity at the interface of a highly doped GaAlAs and GaAs is calculated at a finite temperature. The electron gas formed at the interface is described as a two dimensional gas in which the impurity is assumed to be dipped. Temperature dependence of the impurity potential is calculated in the random phase approximation (R.P.A.) as well as in the modified temperature dependent Thomas-Fermi (M.T.T.F.) approximation which is defined to include temperature effects and to reduce to Thomas-Fermi result at zero temperature. The binding energy of the impurity for the ground state is calculated in R.P.A. and in M.T.T.F.. It is shown that at temperature T, much larger than the Fermi temperature, T_F, M.T.T.F. gives binding energies close to R.P.A. results.     

Two-dimensional metal-insulator transition as a percolation transition in a high-mobility electron system

By carefully analyzing the low temperature density dependence of 2D conductivity in undoped high-mobility n-GaAs heterostructures, we conclude that the 2D metal-insulator transition in this 2D electron system is a density inhomogeneity driven percolation transition due to the breakdown of screening in the random charged impurity disorder background. In particular, our measured conductivity exponent of approximately 1.4 approaches the 2D percolation exponent value of 4/3 at low temperatures and our experimental data are inconsistent with there being a zero-temperature quantum critical point in our system.     

Many-body effects in spin-polarized two-dimensional electron gas

Many-body effects on the spin polarization are studied in an n channel inversion layer on Si (1 0 0) surface in a magnetic field parallel to the surface in random phase approximation. The spin polarization exhibits a discrete jump to a full polarization at the critical magnetic field in the low-density regime and the critical field is reduced considerably from that estimated by an extrapolation based on the zero-field susceptibility.     

Spin depolarization and a metal-insulator transition in a two-dimensional system in zero magnetic field

The conditions for spontaneous spin polarization in a two-dimensional system in a zero magnetic field are considered in the case of a partial filling of the lower quantum-well subbands when the energy of exchange interaction of charge carriers exceeds their kinetic energy. The critical density above which the two-dimensional gas of charge carriers undergoes complete spin depolarization is determined in the Hartree-Fock approximation. It is assumed that this process can be due to a transition of the two-dimensional gas to a metallic state.     

Solitons in a two-dimensional electron gas

The non-linear spectrum of a two-dimensional electron gas (2-DEG) formed at the interface of a heterostructure is investigated. This spectrum is found to contain a new type of localized excitation exhibiting soliton behavior. A matrix formulation of the model equations permits the extraction of the equation of evolution in space for these excitations. Results are presented for the boundary value problem excited by temporal Gaussian pulses.     

Elastic electron tunneling study of the metal-insulator transition in TTF-TCNQ

Using a single crystal of TTF-TCNQ as a moving electrode and by approaching to to an oxidized Al counter-electrode we realized tunnel junctions in the temperature range of about 30 to 295 K. By selecting junctions with minimum thermionic background current and measuring the tunnel conductance by a standard constant voltage lock-in detection we observed a deepening of the zero bias conductance abruptly reaching zero at about 53 K. We suggest that this reflects a progressive depletion of the electron density of states at the Fermi level and gives a direct image of the opening of a Peierls gap at the transition temperature.     

Features of the conductivity and magnetoresistance of doped two-dimensional structures near a metal-insulator transition

Theoretical and experimental studies of the conductivity and magnetoresistance of selectively doped structures of GaAs/AlGaAs quantum well structures near a metal-insulator phase transition have been reviewed. Special attention is focused on the role of the structure of impurity bands, which are narrow in the absence of intentional compensation and, in the case of doping of barriers, include the partially filled upper Hubbard band. It has been shown that the indicated structures exhibit (i) specific mixed conductivity, which can, in particular, include the contribution from delocalized states in the impurity band; (ii) the virtual Anderson transition, which is suppressed with an increase in disorder owing to compensation or with an increase in the concentration of a dopant; (iii) slow relaxations of the hopping magnetoresistance caused by the Coulomb glass effects, including, in particular, the states of the upper Hubbard band; and (iv) the suppression of the negative interference magnetoresistance owing to the spin effects.