arXiv subjects

George Kirczenow

Publications and source records attributed to George Kirczenow.

68 records · Page 4Linked to original sources

arXiv1998

Fractional Exclusion Statistics and the Universal Quantum of Thermal Conductance: A Unifying Approach

We introduce a generalized approach to one-dimensional (1D) conduction based on Haldane's concept of fractional statistics (FES) and the Landauer formulation of transport theory. We show that the 1D ballistic thermal conductance is independent of the statistics obeyed by the carriers and is governed by the universal quantum $ (π^2 k^2_B T)/(3h) $ in the degenerate regime. By contrast, the electrical conductance of FES systems is statistics-dependent. This work unifies previous theories of electron and phonon systems and explains an interesting commonality in their behavior.

cond-mat.mes-hall↗

arXiv1998

Theoretical Study of Electrical Conduction Through a Molecule Connected to Metallic Nanocontacts

We present a theoretical study of electron transport through a molecule connected to two metallic nanocontacts. The system investigated is 1,4 benzene-dithiolate (BDT) chemically bonded to two Au contacts. The surface chemistry is modeled by representing the tips of the Au contacts as two atomic clusters and treating the molecule-cluster complex as a single entity in an extended Huckel tight binding scheme. We model the tips using several different cluster geometries. An ideal lead is attached to each cluster, and the lead to lead transmission is calculated. The role of the molecule-cluster interaction in transport is analyzed by using single channel leads. We then extend the calculations to multi-channel leads that are a more realistic model of the tip's environment. Using the finite-voltage, finite temperature Landauer formula, we calculate the differential conductance for the different systems studied. The similarities and differences between the predictions of the present class of models and recent experimental work are discussed.

cond-mat.mes-hall↗

arXiv1998

Quantized thermal conductance of dielectric quantum wires

Using the Landauer formulation of transport theory, we predict that dielectric quantum wires should exhibit quantized thermal conductance at low temperatures in a ballistic phonon regime. The quantum of thermal conductance is universal, independent of the characteristics of the material, and equal to $π^2 k^2_B T /3h$ where $k_B$ is the Boltzmann constant, h is Planck's constant and T is the temperature. Quantized thermal conductance should be experimentally observable in suspended nanostructures adiabatically coupled to reservoirs, devices that can be realized at the present time.

cond-mat.mes-hall↗

arXiv1998

Composite fermion edge states, fractional charge and current noise

A composite fermion edge state theory of current fluctuations, fractional quasiparticle charge and Johnson-Nyquist noise in the fractional quantum Hall regime is presented. It is shown that composite fermion current fluctuations and the charges of the associated quasiparticles are strongly renormalized by the interactions between composite fermions. The important interaction is that mediated by the fictitious electric field associated with composite fermion currents. The dressed current fluctuations and quasiparticle charges are calculated self-consistently in a mean field theory for smooth edges. Analytic results are obtained. The values of the fractional quasiparticle charges obtained agree with the predictions of previous theories in the incompressible regions of the 2DEG where those theories apply. In the compressible regions the magnitudes of the quasiparticle charges vary with position. Since Johnson-Nyquist noise arises from the compressible regions, it is due to quasiparticles whose charges differ from the simple fractions of $e$ that apply in the incompressible regions. Never the less, the Nyquist noise formula $S=4{k_B}T G$ is obeyed on fractional quantum Hall plateaus. Some implications for the interpretation of recent shot noise measurements in the fractional quantum Hall regime are briefly discussed.

cond-mat.mes-hall↗

arXiv1997

Resonance Patterns of an Antidot Cluster: From Classical to Quantum Ballistics

We explain the experimentally observed Aharonov-Bohm (AB) resonance patterns of an antidot cluster by means of quantum and classical simulations and Feynman path integral theory. We demonstrate that the observed behavior of the AB period signals the crossover from a low B regime which can be understood in terms of electrons following classical orbits to an inherently quantum high B regime where this classical picture and semiclassical theories based on it do not apply.

cond-mat.mes-hall↗

arXiv1996

Mesoscopic Effects in the Fractional Quantum Hall Regime: Chiral Luttinger versus Fermi Liquid

We study tunneling through an edge state formed around an antidot in the fractional quantum Hall regime using Wen's chiral Luttinger liquid theory extended to include mesoscopic effects. We identify a new regime where the Aharonov-Bohm oscillation amplitude exhibits a distinctive crossover from Luttinger liquid power-law behavior to Fermi-liquid-like behavior as the temperature is increased. Near the crossover temperature the amplitude has a pronounced maximum. This non-monotonic behavior and novel high-temperature nonlinear phenomena that we also predict provide new ways to distinguish experimentally between Luttinger and Fermi liquids.

cond-mat↗

arXiv1996

Composite Fermion Edge States and Transport Through Nanostructures in the Fractional Quantum Hall Regime

A theory of transport through semiconductor nanostructures in the fractional quantum Hall regime is proposed, based on a model of composite fermion edge states. Adiabatic and non-adiabatic constrictions and constrictions containing artificial impurities are studied as examples. The results obtained, including the temperature dependent behavior of Aharonov-Bohm resonances in the fractional regime, are in good agreement with experiments. The temperature dependence predicted by the composite fermion theory for features in the two-terminal conductance of both adiabatic constrictions and constrictions with artificial impurities, is close to that expected from ordinary Fermi liquid phenomenology. However there are significant differences that should be detectable by careful measurements. Some differences between the present results and those obtained from Luttinger liquid models are discussed in the context of the available experimental data.

cond-mat↗

arXiv1995

D.C. Transport Measurements and the Direction of Propagation of Composite Fermion Edge States

Simple and quite general considerations are used to show that the results of d.c. transport experiments on macroscopic Hall bars are inconsistent with Hartree models in which a majority of the branches of single-particle composite fermion edge states at the Fermi level propagate in the direction opposite to that in which non-interacting electrons travel along the edge.

cond-mat↗

arXiv1995

Composite Fermion Theory, Edge Currents and the Fractional Quantum Hall Effect

We present a mean field theory of composite fermion edge channel transport in the fractional and integer quantum Hall regimes. An expression relating the electro-chemical potentials of composite fermions at the edges of a sample to those of the corresponding electrons is obtained and a plausible form is assumed for the composite fermion Landau level energies near the edges. The theory yields the observed fractionally quantized Hall conductances and also explains other experimental results. We also discuss some experiments that are relevant to the question whether fractional edge states in real devices should be described as Fermi or Luttinger liquids.

cond-mat↗

arXiv1995

Composite Fermions, Edge Currents and the Fractional Quantum Hall Effect

We present a theory of composite fermion edge states and their transport properties in the fractional and integer quantum Hall regimes. We show that the effective electro-chemical potentials of composite fermions at the edges of a Hall bar differ, in general, from those of electrons. An expression for the difference is given. Composite fermion edge states of three different types are identified. Two of the three types have no analog in previous theories of the integer or fractional quantum Hall effect. The third type includes the usual integer edge states. The direction of propagation of the edge states agrees with experiment. The present theory yields the observed quantized Hall conductances at Landau level filling fractions p/(mp+-1), for m=0,2,4, p= 1,2,3,... It explains the results of experiments that involve conduction across smooth potential barriers and through adiabatic constrictions, and of experiments that involve selective population and detection of fractional edge channels. The relationship between the present work and Hartree theories of composite fermion edge structure is discussed.

cond-mat↗

arXiv1995

An Electrostatic Model of Split-Gate Quantum Wires

We present a theoretical model of split-gate quantum wires that are fabricated from GaAs-AlGaAs heterostructures. The model is built on the physical properties of donors and of semiconductor surfaces, and considerations of equilibrium in such systems. Based on the features of this model, we have studied different ionization regimes of quantum wires, provided a method to evaluate the shallow donor density, and calculated the depletion and pinchoff voltages of quantum wires both before and after illumination. A real split-gate quantum wire has been taken as an example for the calculations, and the results calculated for it agree well with experimental measurements. This paper provides an analytic approach for obtaining much useful information about quantum wires, as well as a general theoretical tool for other gated nanostructure systems.

cond-mat↗

arXiv1995

Theory of Interacting Parallel Quantum Wires

We present self-consistent numerical calculations of the electronic structure of parallel Coulomb-confined quantum wires, based on the Hohenberg-Kohn-Sham density functional theory of inhomogeneous electron systems. We find that the corresponding transverse energy levels of two parallel wires lock together when the wires' widths are similar and their separation is not too small. This energy level locking is an effect of Coulomb interactions and of the the density of states singularities that are characteristic of quasi- one-dimensional Fermionic systems. In dissimilar parallel wires level lockings are much less likely to occur. Energy level locking in similar wires persists to quite large wire separations, but is gradually suppressed by inter-wire tunneling when the separation becomes small. Experimental implications of these theoretical results are discussed.

cond-mat↗

arXiv1995

Semiconductor Analog of the Large Persistent Currents Observed in Small Gold Rings

The remarkably large persistent currents that are observed in disordered micron-scale gold rings at low temperatures have recently been explained in a theory of non-interacting electrons scattered by crystal grain boundaries. The present article examines the possibility that the basic physics underlying this explanation may also have observable consequences in a different system, a ballistic two-dimensional semiconductor ring with a potential barrier. It is predicted, using computer simulations, that such semiconductor rings can exhibit large persistent currents ~ evF/L (L is the ring circumference), despite the electron transmission probability through the barrier being small, in the regime of quantum-mechanical tunneling of electrons through the barrier. This, like the phenomenon observed in gold rings, is a manifestation of the fundamental dissimilarity of non-equilibrium transport phenomena and equilibrium persistent currents.

cond-mat↗

arXiv1995

Why Are Large Persistent Currents Observed in Small Gold Rings?

It is demonstrated using three-dimensional computer simulations that some simple non-interacting electron models that include electron scattering by grain boundaries, exhibit coexistence of large persistent currents and small conductances, similar to that observed experimentally in isolated micron-scale gold rings. Models with simple grain boundaries, and models with small numbers of regularly stepped or atomically rough dilute grain boundaries have been studied and found to yield similar results, which differ markedly, however, from the predictions of models that assume only random impurity scattering. This difference is due to the fact that equilibrium persistent currents and non-equilibrium transport coefficients are physically different things and depend in different ways on the topology of the defect structure in a conducting ring. Experiments on metal and semiconductor rings that should be able to determine whether this is the explanation of the effects observed by Chandrasekhar et al. (Phys. Rev. Lett. 67, 3578 (1991)) are proposed.

cond-mat↗