Metal-Insulator Transition Tuned by External Gates in Hall Systems with Constrictions

The nature of a metal-insulator transition tuned by external gates in quantum Hall (QH) systems with point constrictions, as reported in recent experiments of Roddaro et al [1], is examined. We attribute this phenomenon to a splitting of the integer edge into conducting and insulating stripes, the latter wide enough to allow for the stability of the edge structure. Inter-channel impurity scattering and inter-channel Coulomb interactions do not destabilize this picture.Comment: 4 pages, 6 figure

Interactions suppress Quasiparticle Tunneling at Hall Bar Constrictions

Tunneling of fractionally charged quasiparticles across a two-dimensional electron system on a fractional quantum Hall plateau is expected to be strongly enhanced at low temperatures. This theoretical prediction is at odds with recent experimental studies of samples with weakly-pinched quantum-point-contact constrictions, in which the opposite behavior is observed. We argue here that this unexpected finding is a consequence of electron-electron interactions near the point contact.Comment: 4 page

Edge Magnetoplasmons in Quantum Hall Line Junction Systems

A quantum Hall line junction system consists of a one-dimensional Luttinger liquid (LL) and two chiral channels that allow density waves incident upon and reflected by the LL to be measured separately. We demonstrate that interactions in a quantum Hall line junction system can be probed by studying edge magnetoplasmon absorption spectra and their polarization dependences. Strong interactions in the junction lead to collective modes that are isolated in either Luttinger liquid or contact subsystems.Comment: 4 pages, 3 figures, submitted to Phys. Rev. B Rapid Communicatio

Edge State Tunneling in a Split Hall Bar Model

In this paper we introduce and study the correlation functions of a chiral one-dimensional electron model intended to qualitatively represent narrow Hall bars separated into left and right sections by a penetrable barrier. The model has two parameters representing respectively interactions between top and bottom edges of the Hall bar and interactions between the edges on opposite sides of the barrier. We show that the scaling dimensions of tunneling processes depend on the relative strengths of the interactions, with repulsive interactions across the Hall bar tending to make breaks in the barrier irrelevant. The model can be solved analytically and is characterized by a difference between the dynamics of even and odd Fourier components. We address its experimental relevance by comparing its predictions with those of a more geometrically realistic model that must be solved numerically.Comment: 13 pages, including 4 figures,final version as publishe

Exact Results for Thermodynamics of the Classical Field Theories: Sine- and Sinh-Gordon Models

Using the recently obtained exact results for the expectation values of operators in the sine- and sinh-Gordon models [A. B. Zamolodchikov and S. Lukyanov, Nucl. Phys. B{\bf 493}, 571 (1997), V. Fateev, S. Lukyanov, A. B. Zamolodchikov and Al. B. Zamolodchikov, Phys. Lett. B{\bf 406}, 83 (1997)] we calculate the specific heat of the corresponding two dimensional Euclidean (classical) models. We show that the temperature dependence of the specific heat of the sine-Gordon model, in the commensurate phase, has a maximum well below the Kosterlitz-Thouless transition and that the sinh-Gordon model is thermodynamically unstable in the strong coupling regime. We give also the temperature dependence of the specific heat in the incommensurate phase of the sine-Gordon model.Comment: 14 pages, including 6 figures; updated version; submitted to Phys. Rev.

Scaling Exponents in the Incommensurate Phase of the Sine-Gordon and U(1) Thirring Models

In this paper we study the critical exponents of the quantum sine-Gordon and U(1) Thirring models in the incommensurate phase. This phase appears when the chemical potential $h$ exceeds a critical value and is characterized by a finite density of solitons. The low-energy sector of this phase is critical and is described by the Gaussian model (Tomonaga-Luttinger liquid) with the compactification radius dependent on the soliton density and the sine-Gordon model coupling constant $\beta$. For a fixed value of $\beta$, we find that the Luttinger parameter $K$ is equal to 1/2 at the commensurate-incommensurate transition point and approaches the asymptotic value $\beta^2/8\pi$ away from it. We describe a possible phase diagram of the model consisting of an array of weakly coupled chains. The possible phases are Fermi liquid, Spin Density Wave, Spin-Peierls and Wigner crystal.Comment: 10pages; Improved version; Submitted to Physical Review

Electrostatics of Edge States of Quantum Hall Systems with Constrictions: Metal--Insulator Transition Tuned by External Gates

The nature of a metal--insulator transition tuned by external gates in quantum Hall (QH) systems with point constrictions at integer bulk filling, as reported in recent experiments of Roddaro et al. [1], is addressed. We are particularly concerned here with the insulating behavior--the phenomena of backscattering enhancement induced at high gate voltages. Electrostatics calculations for QH systems with split gates performed here show that observations are not a consequence of interedge interactions near the point contact. We attribute the phenomena of backscattering enhancement to a splitting of the integer edge into conducting and insulating stripes, which enable the occurrence of the more relevant backscattering processes of fractionally charged quasiparticles at the point contact. For the values of the parameters used in the experiments we find that the conducting channels are widely separated by the insulating stripes and that their presence alters significantly the low-energy dynamics of the edges. Interchannel impurity scattering does not influence strongly the tunneling exponents as they are found to be irrelevant processes at low energies. Exponents of backscattering at the point contact are unaffected by interchannel Coulomb interactions since all channels have same chirality of propagation.Comment: 19 pages; To appear in Phys. Rev.