Nonlinear dynamics of two coupled nano-electromechanical resonators

As a model of coupled nano-electromechanical resonantors we study two nonlinear driven oscillators with an arbitrary coupling strength between them. Analytical expressions are derived for the oscillation amplitudes as a function of the driving frequency and for the energy transfer rate between the two oscillators. The nonlinear restoring forces induce the expected nonlinear resonance structures in the amplitude-frequency characteristics with asymmetric resonance peaks. The corresponding multistable behavior is shown to be an efficient tool to control the energy transfer arising from the sensitive response to small changes in the driving frequency. Our results imply that the nonlinear response can be exploited to design precise sensors for mass or force detection experiments based on nano-electromechanical resonators.Comment: 19 pages, 2 figure

Intershell resistance in multiwall carbon nanotubes: A Coulomb drag study

We calculate the intershell resistance R_{21} in a multiwall carbon nanotube as a function of temperature T and Fermi level (e.g. a gate voltage), varying the chirality of the inner and outer tubes. This is done in a so-called Coulomb drag setup, where a current I_1 in one shell induces a voltage drop V_2 in another shell by the screened Coulomb interaction between the shells neglecting the intershell tunnelling. We provide benchmark results for R_{21}=V_2/I_1 within the Fermi liquid theory using Boltzmann equations. The band structure gives rise to strongly chirality dependent suppression effects for the Coulomb drag between different tubes due to selection rules combined with mismatching of wave vector and crystal angular momentum conservation near the Fermi level. This gives rise to orders of magnitude changes in R_{21} and even the sign of R_{21} can change depending on the chirality of the inner and outer tube and misalignment of inner and outer tube Fermi levels. However for any tube combination, we predict a dip (or peak) in R_{21} as a function of gate voltage, since R_{21} vanishes at the electron-hole symmetry point. As a byproduct, we classified all metallic tubes into either zigzag-like or armchair-like, which have two different non-zero crystal angular momenta m_a, m_b and only zero angular momentum, respectively.Comment: 17 pages, 10 figure

Transport Phenomena and Structuring in Shear Flow of Suspensions near Solid Walls

In this paper we apply the lattice-Boltzmann method and an extension to particle suspensions as introduced by Ladd et al. to study transport phenomena and structuring effects of particles suspended in a fluid near sheared solid walls. We find that a particle free region arises near walls, which has a width depending on the shear rate and the particle concentration. The wall causes the formation of parallel particle layers at low concentrations, where the number of particles per layer decreases with increasing distance to the wall.Comment: 14 pages, 14 figure

Orthogonality catastrophe in a one-dimensional system of correlated electrons

We present a detailed numerical study of the orthogonality catastrophe exponent for a one-dimensional lattice model of spinless fermions with nearest neighbor interaction using the density matrix remormalization group algorithm. Keeping up to 1200 states per block we achieve a very great accuracy for the overlap which is needed to extract the orthogonality exponent reliably. We discuss the behavior of the exponent for three different kinds of a localized impurity. For comparison we also discuss the non-interacting case. In the weak impurity limit our results for the overlap confirm scaling behavior expected from perturbation theory and renormalization group calculations. In particular we find that a weak backward scattering component of the orthogonality exponent scales to zero for attractive interaction. In the strong impurity limit and for repulsive interaction we demonstrate that the orthogonality exponent cannot be extracted from the overlap for systems with up to 100 sites, due to finite size effects. This is in contradiction to an earlier interpretation given by Qin et al. based on numerical data for much smaller system sizes. Neverthless we find indirect evidence that the backward scattering contribution to the exponent scales to 1/16 based on predictions of boundary conformal field theory.Comment: 16 pages, Latex, 8 eps figures, submitted to Phys. Rev.

Quantum Phase Transition in a Resonant Level Coupled to Interacting Leads

An interacting one-dimensional electron system, the Luttinger liquid, is distinct from the "conventional" Fermi liquids formed by interacting electrons in two and three dimensions. Some of its most spectacular properties are revealed in the process of electron tunneling: as a function of the applied bias or temperature the tunneling current demonstrates a non-trivial power-law suppression. Here, we create a system which emulates tunneling in a Luttinger liquid, by controlling the interaction of the tunneling electron with its environment. We further replace a single tunneling barrier with a double-barrier resonant level structure and investigate resonant tunneling between Luttinger liquids. For the first time, we observe perfect transparency of the resonant level embedded in the interacting environment, while the width of the resonance tends to zero. We argue that this unique behavior results from many-body physics of interacting electrons and signals the presence of a quantum phase transition (QPT). In our samples many parameters, including the interaction strength, can be precisely controlled; thus, we have created an attractive model system for studying quantum critical phenomena in general. Our work therefore has broadly reaching implications for understanding QPTs in more complex systems, such as cold atoms and strongly correlated bulk materials.Comment: 11 pages total (main text + supplementary

Kondo effect in crossed Luttinger liquids

We study the Kondo effect in two crossed Luttinger liquids, using Boundary Conformal Field Theory. We predict two types of critical behaviors: either a two-channel Kondo fixed point with a nonuniversal Wilson ratio, or a new theory with an anomalous response identical to that found by Furusaki and Nagaosa (for the Kondo effect in a single Luttinger liquid). Moreover, we discuss the relevance of perturbations like channel anisotropy, and we make links with the Kondo effect in a two-band Hubbard system modeled by a channel-dependent Luttinger Hamiltonian. The suppression of backscattering off the impurity produces a model similar to the four-channel Kondo theory.Comment: 7 pages, RevteX, to be published in Physical Review

Coulomb drag of Luttinger liquids and quantum-Hall edges

We study the transconductance for two coupled one-dimensional wires or edge states described by Luttinger liquid models. The wires are assumed to interact over a finite segment. We find for the interaction parameter $g=1/2$ that the drag rate is finite at zero temperature, which cannot occur in a Fermi-liquid system. The zero temperature drag is, however, cut off at low temperature due to the finite length of the wires. We also consider edge states in the fractional quantum Hall regime, and we suggest that the low temperature enhancement of the drag effect might be seen in the fractional quantum Hall regime.Comment: 5 pages, 2 figures; to appear in Phys. Rev. Let

Exact Fermi-edge singularity exponent in a Luttinger liquid

We report the exact calculation of the Fermi-edge singularity exponent for correlated electrons in one dimension (Luttinger liquid). Focusing on the special interaction parameter g=1/2, the asymptotic long-time behavior can be obtained using the Wiener-Hopf method. The result confirms the previous assumption of an open boundary fixed point. In addition, a dynamic k-channel Kondo impurity is studied via Abelian bosonization for k=2 and k=4. It is shown that the corresponding orthogonality exponents are related to the orthogonality exponent in a Luttinger liquid.Comment: 8 Pages RevTeX, no figure

Electronic Transport in a Three-dimensional Network of 1-D Bismuth Quantum Wires

The resistance R of a high density network of 6 nm diameter Bi wires in porous Vycor glass is studied in order to observe its expected semiconductor behavior. R increases from 300 K down to 0.3 K. Below 4 K, where R varies approximately as ln(1/T), the order-of-magnitude of the resistance rise, as well as the behavior of the magnetoresistance are consistent with localization and electron-electron interaction theories of a one-dimensional disordered conductor in the presence of strong spin-orbit scattering. We show that this behaviour and the surface-enhanced carrier density may mask the proposed semimetal-to-semiconductor transition for quantum Bi wires.Comment: 19 pages total, 4 figures; accepted for publication in Phys. Rev.

Kondo Problems in Tomonaga-Luttinger liquids

Quantum impurity problems in Tomonaga-Luttinger liquids (TLLs) are reviewed with emphasis on their analogy to the Kondo problem in Fermi liquids. First, the problem of a static impurity in a spinless TLL is considered, which is related to the model studied in the context of the macroscopic quantum coherence. In the low-energy limit the TLL is essentially cut into two pieces when interaction is repulsive. The orthogonality catastrophe in a TLL is then discussed. Finally, the Kondo effect of a spin-1/2 impurity in a one-dimensional repulsively interacting electron liquids (a spinful TLL) is reviewed. Regardless of the sign of the exchange coupling, the impury spin is completely screened in the ground state. The leading low-temperature contributions to thermodynamic quantities come from boundary contributions of a bulk leading irrelevant operator.Comment: 7 pages, submitted to a special edition of JPSJ "Kondo Effect -- 40 Years after the Discovery"; corrected typos, added reference