A minimal model of quantized conductance in interacting ballistic quantum wires

We review what we consider to be the minimal model of quantized conductance in a finite interacting quantum wire. Our approach utilizes the simplicity of the equation of motion description to both deal with general spatially dependent interactions and finite wire geometry. We emphasize the role of two different kinds of boundary conditions, one associated with local "chemical" equilibrium in the sense of Landauer, the other associated with screening in the proximity of the Fermi liquid metallic leads. The relation of our analysis to other approaches to this problem is clarified. We then use our formalism to derive a Drude type expression for the low frequency AC-conductance of the finite wire with general interaction profile.Comment: 6 pages, 2 figures; extended discussion, references adde

Effects of external radiation on biased Aharonov-Bohm rings

We consider the currents flowing in a solid-state interferometer under the effect of both an Aharonov-Bohm phase and a bias potential. Expressions are obtained for these currents, allowing for electronic or electron-boson interactions, which may take place solely on a quantum dot placed on one of the interferometer arms. The boson system can be out of equilibrium. The results are used to obtain the transport current through the interferometer, and the current circulating around it under the effect of the Aharonov-Bohm flux. The modifications of both currents, brought about by coupling the quantum dot to an incoherent sonic or electromagnetic source, are then analyzed. By choosing the appropriate range of the boson source intensity and its frequency, the magnitude of the interference-related terms of both currents can be controlled.Comment: 18 pages, one figur

Diffusion in infinite and semi-infinite lattices with long-range coupling

We prove that for a one-dimensional infinite lattice, with long-range coupling among sites, the diffusion of an initial delta-like pulse in the bulk, is ballistic at all times. We obtain a closed-form expression for the mean square displacement (MSD) as a function of time, and show some cases including finite range coupling, exponentially decreasing coupling and power-law decreasing coupling. For the case of an initial excitation at the edge of the lattice, we find an approximate expression for the MSD that predicts ballistic behavior at long times, in agreement with numerical results.Comment: 4 pages, 5 figures, submitted for publicatio

The Scaling of the Anomalous Hall Effect in the Insulating Regime

We develop a theoretical approach to study the scaling of anomalous Hall effect (AHE) in the insulating regime, which is observed to be $\sigma_{xy}^{AH}\propto\sigma_{xx}^{1.40\sim1.75}$ in experiments over a large range of materials. This scaling is qualitatively different from the ones observed in metals. Basing our theory on the phonon-assisted hopping mechanism and percolation theory, we derive a general formula for the anomalous Hall conductivity, and show that it scales with the longitudinal conductivity as $\sigma_{xy}^{AH}\sim\sigma_{xx}^{\gamma}$ with $\gamma$ predicted to be $1.38\leq\gamma\leq1.76$, quantitatively in agreement with the experimental observations. Our result provides a clearer understanding of the AHE in the insulating regime and completes the scaling phase diagram of the AHE.Comment: 4 pages, 4 figures, plus the supplementary information. Minor revisions made according to Referee report

Anomalous phase shift in a twisted quantum loop

Coherent motion of electrons in a twisted quantum ring is considered to explore the effect of torsion inherent to the ring. Internal torsion of the ring composed of helical atomic configuration yields a non-trivial quantum phase shift in the electrons' eigenstates. This torsion-induced phase shift causes novel kinds of persistent current flow and an Aharonov-Bohm like conductance oscillation. The two phenomena can occur even when no magnetic flux penetrates inside the twisted ring, thus being in complete contrast with the counterparts observed in untwisted rings.Comment: 13 paes, 5 figure

Random-phase reservoir and a quantum resistor: The Lloyd model

We introduce phase disorder in a 1D quantum resistor through the formal device of `fake channels' distributed uniformly over its length such that the out-coupled wave amplitude is re-injected back into the system, but with a phase which is random. The associated scattering problem is treated via invariant imbedding in the continuum limit, and the resulting transport equation is found to correspond exactly to the Lloyd model. The latter has been a subject of much interest in recent years. This conversion of the random phase into the random Cauchy potential is a notable feature of our work. It is further argued that our phase-randomizing reservoir, as distinct from the well known phase-breaking reservoirs, induces no decoherence, but essentially destroys all interference effects other than the coherent back scattering.Comment: 4 pages,5 figure

Comment on "Order parameter of A-like 3He phase in aerogel"

We argue that the inhomogeneous A-phase in aerogel is energetically more preferable than the "robust" phase suggested by I. A. Fomin, JETP Lett. 77, 240 (2003); cond-mat/0302117 and cond-mat/0401639.Comment: 2 page

Decohering d-dimensional quantum resistance

The Landauer scattering approach to 4-probe resistance is revisited for the case of a d-dimensional disordered resistor in the presence of decoherence. Our treatment is based on an invariant-embedding equation for the evolution of the coherent reflection amplitude coefficient in the length of a 1-dimensional disordered conductor, where decoherence is introduced at par with the disorder through an outcoupling, or stochastic absorption, of the wave amplitude into side (transverse) channels, and its subsequent incoherent re-injection into the conductor. This is essentially in the spirit of B{\"u}ttiker's reservoir-induced decoherence. The resulting evolution equation for the probability density of the 4-probe resistance in the presence of decoherence is then generalised from the 1-dimensional to the d-dimensional case following an anisotropic Migdal-Kadanoff-type procedure and analysed. The anisotropy, namely that the disorder evolves in one arbitrarily chosen direction only, is the main approximation here that makes the analytical treatment possible. A qualitatively new result is that arbitrarily small decoherence reduces the localisation-delocalisation transition to a crossover making resistance moments of all orders finite.Comment: 14 pages, 1 figure, revised version, to appear in Phys. Rev.

On the thermodynamics of first-order phase transition smeared by frozen disorder

The simplified model of first-order transition in a media with frozen long-range transition-temperature disorder is considered. It exhibits the smearing of the transition due to appearance of the intermediate inhomogeneous phase with thermodynamics described by the ground state of the short-range random-field Ising model. Thus the model correctly reproduce the persistence of first-order transition only in dimensions d > 2, which is found in more realistic models. It also allows to estimate the behavior of thermodynamic parameters near the boundaries of the inhomogeneous phase.Comment: 4 page

Landauer Conductance of Luttinger Liquids with Leads

We show that the dc conductance of a quantum wire containing a Luttinger liquid and attached to non-interacting leads is given by $e^2/h$ per spin orientation, regardless of the interactions in the wire. This explains the recent observations of the absence of conductance renormalization in long high-mobility $GaAs$ wires by Tarucha, Honda and Saku (Solid State Communications {\bf 94}, 413 (1995)).Comment: 4 two-column pages, RevTeX + 1 uuencoded figure