Conductance distribution in quasi-one-dimensional disordered quantum wires

We develop a simple systematic method, valid for all strengths of disorder, to obtain analytically the full distribution of conductances P(g) for a quasi-one-dimensional wire within the model of non-interacting fermions. The method has been used in [Phys. Rev. Lett. 83 (1999) 3013; Ann. Phys. (Leipzig) 8 (1999) 753; Phys. Rev. B 66 (2002) 174204; Europhys. Lett. 61 (2003) 95] to predict sharp features in P(g) near g=1 and the existence of non-analyticity in the conductance distribution in the insulating and crossover regimes, as well as to show how P(g) changes from Gaussian to log-normal behavior as the disorder strength is increased. Here we provide many details of the method, including intermediate results that offer much insight into the nature of the solutions. In addition, we show within the same framework that while for metals P(g) is a Gaussian around 〈g〉?1, there exists a log-normal tail for g?1, consistent with earlier field theory calculations. We also obtain several other results that compare very well with available exact results in the metallic and insulating regimes.     

Interacting quantum wires: A possible explanation for the 0.7 anomalous conductance

We investigate an effective one-dimensional conducting channel considering both the contact umklapp and the Coulomb electron-electron interaction. We show that, at low electronic density, the proximity to the Wigner crystal reproduces the anomaly in conductance at 0.7G₀. The crucial ingredient of our theory is the fact that the gate voltage acts as a bias controlling the intensity of the umklapp term. At large gate voltages, the umklapp vanishes and we obtain a conducting quantum wire with a perfect conductance. At low gate voltages, the Wigner crystal is pinned by the umklapp term, giving rise to an insulating behavior with vanishing conductance. This crossover pattern has a transition point which can be identified with the anomalous conductance around 0.7G₀. This picture is obtained within the framework of a renormalization group calculation. The conductance static regime is achieved by taking first the limit of finite length and then the limit of zero frequency.     

Anticrossing of spin-split subbands in quasi-one-dimensional wires

In quantum Hall systems, both anticrossings and magnetic phase transitions can occur when opposite-spin Landau levels coincide. Our results indicate that both processes are also possible in quasi-1D quantum wires in an in-plane B field, Bparallel. Crossings of opposite-spin 1D subbands resemble magnetic phase transitions at zero dc source-drain bias, but display anticrossings at high dc bias. Our data also imply that the well-known 0.7 structure may evolve into a spin-hybridized state in finite dc bias.     

Universality in quantum chaos and the one-parameter scaling theory

The one-parameter scaling theory is adapted to the context of quantum chaos. We define a generalized dimensionless conductance, g, semiclassically and then study Anderson localization corrections by renormalization group techniques. This analysis permits a characterization of the universality classes associated to a metal (g-->infinity), an insulator (g-->0), and the metal-insulator transition (g-->g(c)) in quantum chaos provided that the classical phase space is not mixed. According to our results the universality class related to the metallic limit includes all the systems in which the Bohigas-Giannoni-Schmit conjecture holds but automatically excludes those in which dynamical localization effects are important. The universality class related to the metal-insulator transition is characterized by classical superdiffusion or a fractal spectrum in low dimensions (d < or = 2). Several examples are discussed in detail.     

Lack of universal one-parameter scaling in the two-dimensional metallic regime

The two-dimensional metallic state is studied in a number of Si-MOS structures with peak mobilities varying by a factor of 8.5. The data show a density dependence and disorder dependence of the major features of the scaling function and thus reveal the absence of universal one-parameter scaling over wide density range in the metallic regime. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 5, 415–419 (10 September 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Crossover scaling behaviour of the quasi-one-dimensional n-vector models

Crossovers in the quasi-one-dimensional n-vector models are discussed by making new scaling hypotheses. Predictions regarding critical point shifts and amplitudes are made for one-to two- and three-dimensional crossovers for 1 ? n ? ∞. Many new scaling functions are obtained exactly and studied by series-expanding methods.     

Anomalous scaling in the Zhang model

We apply the moment analysis technique to analyze large scale simulations of the Zhang sandpile model. We find that this model shows different scaling behavior depending on the update mechanism used. With the standard parallel updating, the Zhang model violates the finite-size scaling hypothesis, and it also appears to be incompatible with the more general multifractal scaling form. This makes impossible its affiliation to any one of the known universality classes of sandpile models. With sequential updating, it shows scaling for the size and area distribution. The introduction of stochasticity into the toppling rules of the parallel Zhang model leads to a scaling behavior compatible with the Manna universality class. Received 8 August 2000 and Received in final form 4 October 2000     

Fermi-energy scaling of the metal-insulator transition temperature in quasi-one-dimensional systems

Several physical properties of four quasi-one-dimensional organic conductors are compared. Assuming that the intermolecular spacing along the conducting stacks and the magnitude of the susceptibility serve as indicators of the degree of electronic overlap, the data indicate that an increase in this overlap enhances the stability of the insulating ground state of these systems. As a result, the metal—insulator transition temperature is found to scale roughly linearly with an effective Fermi energy.     

Coulomb oscillations of the ballistic conductance in a quasi-one-dimensional quantum dot

It is demonstrated that localized states of an open quasi-one-dimensional quantum dot can be charged by the Coulomb blockade mechanism. A new effect—Coulomb oscillations of the ballistic conductance—is observed because of the high sensitivity of the ballistic current to single-electron variations of the self-consistent potential of the dot. The model proposed explains experimental results [C.-T. Liang, M.Y. Simmons, C. G. Smith, et al., Phys. Rev. Lett. 81, 3507 (1998)].     

Four-atom period in the conductance of monatomic Al wires

We present first-principles calculations based on density functional theory for the conductance of monatomic Al wires between Al(111) electrodes. In contrast to the even-odd oscillations observed in other metallic wires, the conductance of the Al wires is found to oscillate with a period of four atoms as the length of the wire is varied. Although local charge neutrality can account for the observed period, it leads to an incorrect phase. We explain the conductance behavior using a resonant transport model based on the electronic structure of the infinite wire.     

Even-odd behavior of conductance in monatomic sodium wires

With the aid of the Friedel sum rule, we perform first-principles calculations of conductances through monatomic Na wires, taking into account the sharp tip geometry and discrete atomic structure of electrodes. We find that conductances (G) depend on the number (L) of atoms in the wires; G is G(0)( = 2e(2)/h) for odd L, independent of the wire geometry, while G is generally smaller than G(0) and sensitive to the wire structure for even L. This even-odd behavior is attributed to the charge neutrality and resonant character due to the sharp tip structure. We suggest that similar even-odd behavior may appear in other monovalent atomic wires.     

Breakdown of one-parameter scaling in quantum critical scenarios for high-temperature copper-oxide superconductors

We show that if the excitations which become gapless at a quantum critical point also carry the electrical current, then a resistivity linear in temperature, as is observed in the copper-oxide high-temperature superconductors, obtains only if the dynamical exponent z satisfies the unphysical constraint, z < 0. At fault here is the universal scaling hypothesis that, at a continuous phase transition, the only relevant length scale is the correlation length. Consequently, either the electrical current in the normal state of the cuprates is carried by degrees of freedom which do not undergo a quantum phase transition, or quantum critical scenarios must forgo this basic scaling hypothesis and demand that more than a single-correlation length scale is necessary to model transport in the cuprates.     

Anomalous dynamic scaling of the non-local growth equations

The anomalous dynamic scaling behavior of the d+1 dimensional non-local growth equations is investigated based on the scaling approach. The growth equations studied include the non-local Kardar-Parisi-Zhang (NKPZ), non-local Sun-Guo-Grant (NSGG), and non-local Lai-Das Sarma-Villain (NLDV) equations. The anomalous scaling exponents in both the weak- and strong-coupling regions are obtained, respectively. Our results show that non-local interactions can affect anomalous scaling properties of surface fluctuations.     

Universal conductance in quantum wires in the presence of Umklapp scattering

The effects of Umklapp scattering on the zero-temperature conductance in one-dimensional quantum wires are reexamined by taking into account both the screening of external potential and the non-uniform chemical potential shift due to electron-electron interaction. It is shown that in the case away from half-filling the conductance is given by the universal value, 2e ² /h, even in the presence of Umklapp scattering, owing to these renormalization effects of external potential. The conclusion is in accordance with the recent claim obtained for the system with non-interacting leads being attached to a quantum wire. Received: 5 February 1998 / Received in final form: 16 March 1998 / Accepted: 17 April 1998