arXiv subjects

C. L. Kane

Publications and source records attributed to C. L. Kane.

69 records · Page 4Linked to original sources

arXiv2000

A Crossed Sliding Luttinger Liquid Phase

We study a system of crossed spin-gapped and gapless Luttinger liquids. We establish the existence of a stable non-Fermi liquid state with a finite-temperature,long-wavelength, isotropic electric conductivity that diverges as a power law in temperature $T$ as $T\to 0$. This two-dimensional system has many properties characteristic of a true isotropic Luttinger liquid, though at zero temperature it becomes anisotropic. This model can easily be extended to three dimensions.

cond-mat.str-el↗

arXiv1999

Broken Symmetries in Scanning Tunneling Images of Carbon Nanotubes

Scanning tunneling images of carbon nanotubes frequently show electron distributions which break the local sixfold symmetry of the graphene sheet. We present a theory of these images which relates these anisotropies to the off diagonal correlations in the single particle density matrix, and allows one to extract these correlations from the observed images. The theory is applied to images of the low energy states reflected at the end of a tube or by point defects, and to states propagating on defect free semiconducting tubes. The latter exhibit a novel switching of the anisotropy in the tunneling image with the sign of the tunneling bias.

cond-mat.mes-hall↗

arXiv1998

Resonant Tunneling between quantum Hall states at filling ν= 1 and ν= 1/3

We study the problem of resonant tunneling between a Fermi liquid and the edge of a $ν=1/3$ fractional quantum Hall state. In the limit of weak coupling, the system is adequately described within the sequential tunneling approximation. At low temperatures, however, the system crosses over to a strong coupling phase, which we analyze using renormalization group techniques. We find that at low temperatures a "perfect" can be achieved by tuning two parameters. This resonance has a peak conductance $G = e^2/2h$ and is a realization of the weak backscattering limit of the $g=1/2$ Luttinger liquid, as well as the non Fermi liquid fixed point of the two channel Kondo problem. We discuss several regimes which may be experimentally accessible as well as the implications for resonances recently observed in cleaved edge overgrowth structures.

cond-mat.mes-hall↗

arXiv1997

Temperature Dependent Resistivity of Single Wall Carbon Nanotubes

Nonchiral single wall carbon nanotubes with an "armchair" wrapping are theoretically predicted to be conducting, and high purity samples consisting predominantly of these tubes exhibit metallic behavior with an intrinsic resistivity which increases approximately linearly with temperature over a wide temperature range. Here we study the coupling of the conduction electrons to long wavelength torsional shape fluctuations, or twistons. A one dimensional theory of the scattering of electrons by twistons is presented which predicts an intrinsic resistivity proportional to the absolute temperature. Experimental measurements of the temperature dependence of the resistivity are reported and compared with the predictions of the twiston theory.

cond-mat↗

arXiv1996

Line Junctions in the Quantum Hall Effect

A long skinny gate across a fractional quantum Hall fluid at filling $ν=1/m$ with odd integer $m$, creates a novel one-dimensional (1d) system which is isomorphic to a disordered 1d electron gas with {\it attractive} interactions. By varying the gate potential along such a line junction, it should be possible to tune through the 1d localization transition, predicted for an attractively interacting electron gas. The key signature of this 1d metal-insulator transition is the temperature dependence of the conductivity, which diverges as a power of temperature in the metallic phase, and vanishes rapidly in the insulator. We show that the 1d conductivity can be extracted from a standard Hall transport measurement, in the regime where the Hall conductance is close to its quantized value. A line junction in a $ν=2/3$ quantized Hall fluid is predicted to exhibit a similar localization transition.

cond-mat↗

arXiv1996

Size, Shape and Low Energy Electronic Structure of Carbon Nanotubes

A theory of the long wavelength low energy electronic structure of graphite-derived nanotubules is presented. The propagating $π$ electrons are described by wrapping a massless two dimensional Dirac Hamiltonian onto a curved surface. The effects of the tubule size, shape and symmetry are included through an effective vector potential which we derive for this model. The rich gap structure for all straight single wall cylindrical tubes is obtained analytically in this theory, and the effects of inhomogeneous shape deformations on nominally metallic armchair tubes are analyzed.

cond-mat↗

arXiv1996

Quantized Thermal Transport in the Fractional Quantum Hall Effect

We analyze thermal transport in the fractional quantum Hall effect (FQHE), employing a Luttinger liquid model of edge states. Impurity mediated inter-channel scattering events are incorporated in a hydrodynamic description of heat and charge transport. The thermal Hall conductance, $K_H$, is shown to provide a new and universal characterization of the FQHE state, and reveals non-trivial information about the edge structure. The Lorenz ratio between thermal and electrical Hall conductances {\it violates} the free-electron Wiedemann-Franz law, and for some fractional states is predicted to be {\it negative}. We argue that thermal transport may provide a unique way to detect the presence of the elusive upstream propagating modes, predicted for fractions such as $ν=2/3$ and $ν=3/5$.

cond-mat↗

arXiv1996

Quantum Brownian Motion in a Periodic Potential and the Multi Channel Kondo Problem

We study the motion of a particle in a periodic potential with Ohmic dissipation. In $D=1$ dimension it is well known that there are two phases depending on the dissipation: a localized phase with zero temperature mobility $μ=0$ and a fully coherent phase with $μ$ unaffected by the periodic potential. For $D>1$, we find that this is also the case for a Bravais lattice. However, for non symmorphic lattices, such as the honeycomb lattice and its $D$ dimensional generalization, there is a new intermediate phase with a universal mobility $μ^*$. We study this intermediate fixed point in perturbatively accessible regimes. In addition, we relate this model to the Toulouse limit of the $D+1$ channel Kondo problem. This mapping allows us to compute $μ^*$ exactly using results known from conformal field theory. Experimental implications are discussed for resonant tunneling in strongly coupled Coulomb blockade structures and for multi channel Luttinger liquids.

cond-mat↗

arXiv1996

Coulomb Blockade in a Quantum Dot Coupled Strongly to a Lead

We study theoretically a quantum dot in the quantum Hall regime that is strongly coupled to a single lead via a point contact. We find that even when the transmission through the point contact is perfect, important features of the Coulomb blockade persist. In particular, the tunneling into the dot via a second weakly coupled lead is suppressed, and shows features which can be ascribed to elastic or inelastic cotunneling through the dot. When there is weak backscattering at the point contact, both the tunneling conductance and the differential capacitance are predicted to oscillate as a function of gate voltage. We point out that the dimensionless ratio $ξ$ between the fractional oscillations in $G$ and $C$ is an intrinsic property of the dot, which, in principle, can be measured. We compute $ξ$ within two models of electron-electron interactions. In addition, we discuss the role of additional channels.

cond-mat↗

arXiv1995

Thermal transport in a Luttinger liquid

We study thermal transport in a one-dimensional (1d) interacting electron gas, employing the Luttinger liquid model. Both thermal conductance and thermopower are analyzed for a pure 1d gas and with impurities. The universal ratio of electrical to thermal conductance in a Fermi-liquid - the Wiedeman-Franz law - is modified, whereas the thermopower is still linear in temperature. For a single impurity the Lorenz number is given by $L(T \rightarrow 0) = 3L_0/(2g+g^2)$ - with $L_0$ the Fermi liquid value - and the conductance $1/2 < g < 1$. For $g<1/2$ the Lorenz number {\it diverges} as $T \rightarrow 0$. Possible relevance to thermal transport in conducting polymer systems is discussed.

cond-mat↗

arXiv1995

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 $ν=2/3$, 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 $ν=4/5$ and $ν=4/3$, 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.

cond-mat↗

arXiv1994

Impurity scattering and transport of fractional Quantum Hall edge state

We study the effects of impurity scattering on the low energy edge state dynamic s for a broad class of quantum Hall fluids at filling factor $ν=n/(np+1)$, for integer $n$ and even integer $p$. When $p$ is positive all $n$ of the edge modes are expected to move in the same direction, whereas for negative $p$ one mode moves in a direction opposite to the other $n-1$ modes. Using a chiral-Luttinger model to describe the edge channels, we show that for an ideal edge when $p$ is negative, a non-quantized and non-universal Hall conductance is predicted. The non-quantized conductance is associated with an absence of equilibration between the $n$ edge channels. To explain the robust experimental Hall quantization, it is thus necessary to incorporate impurity scattering into the model, to allow for edge equilibration. A perturbative analysis reveals that edge impurity scattering is relevant and will modify the low energy edge dynamics. We describe a non-perturbative solution for the random $n-$channel edge, which reveals the existence of a new disorder-dominated phase, characterized by a stable zero temperature renormalization group fixed point. The phase consists of a single propagating charge mode, which gives a quantized Hall conductance, and $n-1$ neutral modes. The neutral modes all propagate at the same speed, and manifest an exact SU(n) symmetry. At finite temperatures the SU(n) symmetry is broken and the neutral modes decay with a finite rate which varies as $T^2$ at low temperatures. Various experimental predictions and implications which follow from the exact solution are described in detail, focusing on tunneling experiments through point contacts.

cond-mat↗

arXiv1994

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

Current Luttinger liquid edge state theories for filling $ν=2/3$ 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 $T^{2/ν-2}$ to $T^2$.

cond-mat↗

arXiv1993

Fermi Edge Singularities and Backscattering in a Weakly Interacting 1D Electron Gas

The photon-absorption edge in a weakly interacting one-dimensional electron gas is studied, treating backscattering of conduction electrons from the core hole exactly. Close to threshold, there is a power-law singularity in the absorption, $I(ε) \propto ε^{-α}$, with $α= 3/8 + δ_+/π- δ_+^2/2π^2$ where $δ_+$ is the forward scattering phase shift of the core hole. In contrast to previous theories, $α$ is finite (and universal) in the limit of weak core hole potential. In the case of weak backscattering $U(2k_F)$, the exponent in the power-law dependence of absorption on energy crosses over to a value $α= δ_+/π- δ_+^2/2π^2$ above an energy scale $ε^* \sim [U(2k_F)]^{1/γ}$, where $γ$ is a dimensionless measure of the electron-electron interactions.

cond-mat↗

arXiv1993

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 $ν= 1/3$ which confirm this picture and provide a parameter-free prediction for the line shape.

cond-mat↗