Current and charge distributions of the fractional quantum Hall liquids with edges

An effective Chern-Simons theory for the quantum Hall states with edges is studied by treating the edge and bulk properties in a unified fashion. An exact steady-state solution is obtained for a half-plane geometry using the Wiener-Hopf method. For a Hall bar with finite width, it is proved that the charge and current distributions do not have a diverging singularity. It is shown that there exists only a single mode even for the hierarchical states, and the mode is not localized exponentially near the edges. Thus this result differs from the edge picture in which electrons are treated as strictly one dimensional chiral Luttinger liquids.Comment: 21 pages, REV TeX fil

Bosonization Theory of Excitons in One-dimensional Narrow Gap Semiconductors

Excitons in one-dimensional narrow gap semiconductors of anti-crossing quantum Hall edge states are investigated using a bosonization method. The excitonic states are studied by mapping the problem into a non-integrable sine-Gordon type model. We also find that many-body interactions lead to a strong enhancement of the band gap. We have estimated when an exciton instability may occur.Comment: 4pages, 1 figure, to appear in Phys. Rev. B Brief Report

Universal structure of the edge states of the fractional quantum Hall states

We present an effective theory for the bulk fractional quantum Hall states on the Jain sequences on closed surfaces and show that it has a universal form whose structure does not change from fraction to fraction. The structure of this effective theory follows from the condition of global consistency of the flux attachment transformation on closed surfaces. We derive the theory of the edge states on a disk that follows naturally from this globally consistent theory on a torus. We find that, for a fully polarized two-dimensional electron gas, the edge states for all the Jain filling fractions $\nu=p/(2np+1)$ have only one propagating edge field that carries both energy and charge, and two non-propagating edge fields of topological origin that are responsible for the statistics of the excitations. Explicit results are derived for the electron and quasiparticle operators and for their propagators at the edge. We show that these operators create states with the correct charge and statistics. It is found that the tunneling density of states for all the Jain states scales with frequency as $|\omega|^{(1-\nu)/\nu}$.Comment: 10 page

Randomness at the Edge: Theory of Quantum Hall transport at filling ν=2/3\nu=2/3

Current Luttinger liquid edge state theories for filling $\nu=2/3$ predict a non-universal Hall conductance, in disagreement with experiment. Upon inclusion of random edge tunnelling we find a phase transition into a new disordered-dominated edge phase. An exact solution of the random model in this phase gives a quantized Hall conductance of 2/3 and a neutral mode propagating upstream. The presence of the neutral mode changes the predicted temperature dependence for tunnelling through a point contact from $T^{2/\nu -2}$ to $T^2$.Comment: 12 pages 1 postscript figure appended, REVTEX 3.

Contacts and Edge State Equilibration in the Fractional Quantum Hall Effect

We develop a simple kinetic equation description of edge state dynamics in the fractional quantum Hall effect (FQHE), which allows us to examine in detail equilibration processes between multiple edge modes. As in the integer quantum Hall effect (IQHE), inter-mode equilibration is a prerequisite for quantization of the Hall conductance. Two sources for such equilibration are considered: Edge impurity scattering and equilibration by the electrical contacts. Several specific models for electrical contacts are introduced and analyzed. For FQHE states in which edge channels move in both directions, such as $\nu=2/3$, these models for the electrical contacts {\it do not} equilibrate the edge modes, resulting in a non-quantized Hall conductance, even in a four-terminal measurement. Inclusion of edge-impurity scattering, which {\it directly} transfers charge between channels, is shown to restore the four-terminal quantized conductance. For specific filling factors, notably $\nu =4/5$ and $\nu=4/3$, the equilibration length due to impurity scattering diverges in the zero temperature limit, which should lead to a breakdown of quantization for small samples at low temperatures. Experimental implications are discussed.Comment: 14 pages REVTeX, 6 postscript figures (uuencoded and compressed

Resonant Tunneling Between Quantum Hall Edge States

Resonant tunneling between fractional quantum Hall edge states is studied in the Luttinger liquid picture. For the Laughlin parent states, the resonance line shape is a universal function whose width scales to zero at zero temperature. Extensive quantum Monte Carlo simulations are presented for $\nu = 1/3$ which confirm this picture and provide a parameter-free prediction for the line shape.Comment: 14 pages , revtex , IUCM93-00

Time correlations in 1D quantum impurity problems

We develop in this letter an analytical approach using form- factors to compute time dependent correlations in integrable quantum impurity problems. As an example, we obtain for the first time the frequency dependent conductivity $G(\omega)$ for the tunneling between the edges in the $\nu=1/3$ fractional quantum Hall effect, and the spectrum $S(w)$ of the spin-spin correlation in the anisotropic Kondo model and equivalently in the double well system of dissipative quantum mechanics, both at vanishing temperature.Comment: 4 pages, Revtex and 2 figure

Quantum Transport in Two-Channel Fractional Quantum Hall Edges

We study the effect of backward scatterings in the tunneling at a point contact between the edges of a second level hierarchical fractional quantum Hall states. A universal scaling dimension of the tunneling conductance is obtained only when both of the edge channels propagate in the same direction. It is shown that the quasiparticle tunneling picture and the electron tunneling picture give different scaling behaviors of the conductances, which indicates the existence of a crossover between the two pictures. When the direction of two edge-channels are opposite, e.g. in the case of MacDonald's edge construction for the $\nu=2/3$ state, the phase diagram is divided into two domains giving different temperature dependence of the conductance.Comment: 21 pages (REVTeX and 1 Postscript figure

Spontaneous CP Violating Phase as The CKM Matrix Phase

We propose that the CP violating phase in the CKM mixing matrix is identical to the CP phases responsible for the spontaneous CP violation in the Higgs potential. A specific multi-Higgs model with Peccei-Quinn (PQ) symmetry is constructed to realize this idea. The CP violating phase does not vanish when all Higgs masses become large. There are flavor changing neutral current (FCNC) interactions mediated by neutral Higgs bosons at the tree level. However, unlike general multi-Higgs models, the FCNC Yukawa couplings are fixed in terms of the quark masses and CKM mixing angles. Implications for meson-anti-meson mixing, including recent data on $D-\bar D$ mixing, and neutron electric dipole moment (EDM) are studied. We find that the neutral Higgs boson masses can be at the order of one hundred GeV. The neutron EDM can be close to the present experimental upper bound.Comment: 16 pages, RevTex. Several typos corrected, and one reference adde