Quasi One-dimensional Systems Research Articles

Size and boundary effects on the diffusive behavior of elongated colloidal particles in a strongly confined dense dispersion

In very recent experimental work, diffusive motion of individual particles in a dense columnar phase of colloidal suspension of filamentous virus particles probed by means of fluorescence video microscopy [S. Naderi, E. Pouget, P. Ballesta, P. van der Schoot, M. P. Lettinga, and E. Grelet, Phys. Rev. Lett. 111, 037801 (2013)]. Rare events were observed in which the minority fluorescently labeled particles engage in sudden, jump-like motion along the director. The jump length distribution turned out to be biased towards a half and a full particle length. We suggest these events may be indicative of two types of particle motion, one in which particles overtake other particles in the same column and the other where a column re-equilibrates after a particle leaves a column either to enter into another column or into a void defect on the lattice. Our Brownian dynamics simulations of a quasi one-dimensional system of semi-flexible particles, subject to a Gaussian confinement potentials mimicking the effects of the self-consistent molecular field in the columnar phase, support this idea. We find that the frequency of overtaking depends on the linear fraction of particles and the steepness of the confining potential. The re-equilibration time of a column after a particle is removed from it is much shorter than the self-diffusion timescale. For the case of large system sizes and periodic boundary conditions, overtaking events do not present themselves as full-length jumps. Only if the boundary conditions are reflecting and the system is sufficiently small, full length jumps are observed in particle trajectories. The reason is that only then the amplitude of the background fluctuations is smaller than a particle length. Increasing the bending flexibility of the particles on the one hand enhances the ability of particles to overtake each other but on the other it enhances fluctuations that wash out full jumps in particle trajectories.

Kitaev-Ising model and the transition between topological and ferromagnetic order

We study the Kitaev-Ising model, where ferromagnetic Ising interactions are added to the Kitaev model on a lattice. This model has two phases which are characterized by topological and ferromagnetic order. Transitions between these two kinds of order are then studied on a quasi-one dimensional system, a ladder, and on a two dimensional periodic lattice, a torus. By exactly mapping the quasi-one dimensional case to an anisotropic XY chain we show that the transition occurs at zero $\lambda$ where $\lambda$ is the strength of the ferromagnetic coupling. In the two dimensional case the model is mapped to a 2D Ising model in transverse field, where it shows a transition at finite value of $\lambda$. A mean field treatment reveals the qualitative character of the transition and an approximate value for the transition point. Furthermore with perturbative calculation, we show that expectation value of Wilson loops behave as expected in the topological and ferromagnetic phases.

Three dimensional elongation method for large molecular calculations

Three dimensional elongation (3D-ELG) method is introduced to perform the calculations on real large systems based on regionally localized molecular orbitals. The settings are firstly justified by a quasi-one dimensional system calculations at HF/STO-3G basis set. Then two model systems are employed and calculated to validate the accuracy of 3D-ELG method at HF/6-31G basis set. The average deviation of the total energy between elongation and conventional calculations is 4.7×10−7au/atom for these two model systems. This small deviation indicates the feasibility of 3D-ELG scheme for the large molecular calculations. Finally, the further development of 3D-ELG method is pointed out.

Magnetic and electric properties in the distorted tetrahedral spin chain system Cu3Mo2O9

We study the multiferroic properties in the distorted tetrahedral quasi-one dimensional spin system Cu3Mo2O9, in which the effects of the low dimensionality and the magnetic frustration are expected to appear simultaneously. We clarify that the antiferromagnetic order is formed together with ferroelectric properties at TN = 7.9 K under zero magnetic field and obtain the magnetic-field-temperature phase diagram by measuring dielectric constant and spontaneous electric polarization. It is found that the antiferromagnetic phase possesses a spontaneous electric polarization parallel to the c axis when the magnetic field H is applied parallel to the a axis. On the other hand, there are three different ferroelectric phases in the antiferromagnetic phase for H parallel to the c axis.

Entanglement of Two Charged Bosons in Strongly Anisotropic Traps

Examination of the ground-state correlation properties of two Coulombically interacting bosons confined in strongly anisotropic harmonic potentials is carried out within the framework of the single-mode approximation of the transverse components. The linear entropy of the quasi-one dimensional systems is discussed in dependence on the confinement anisotropy and the interaction strength. A comparison with a strictly one-dimensional limit is performed.

Quantum phase transition from a spin-liquid state to a spin-glass state in the quasi-one-dimensional spin-1system Sr1−xCaxNi2V2O8

We report a quantum phase transition from a spin-liquid state to a spin-glass state in the quasi-one dimensional (1D) spin-1 system Sr1-xCaxNi2V2O8, induced by a small amount of Ca-substitution at Sr site. The ground state of the parent compound (x = 0) is found to be a spin-liquid type with a finite energy gap of 26.6 K between singlet ground state and triplet excited state. Both dc-magnetization and ac-susceptibility studies on the highest Ca-substituted compound (x = 0.05) indicate a spin-glass type magnetic ground state. With increasing Ca-concentration, the spin-glass ordering temperature increases from 4.5 K (for the x = 0.015 compound) to 6.25 K (for the x = 0.05 compound). The observed results are discussed in the light of the earlier experimental reports and the theoretical predictions for a quasi-1D spin-1 system.

Implementation of the SU(2) Hamiltonian symmetry for the DMRG algorithm

In the Density Matrix Renormalization Group (DMRG) algorithm (White, 1992, 1993) [1,2], Hamiltonian symmetries play an important rôle. Using symmetries, the matrix representation of the Hamiltonian can be blocked. Diagonalizing each matrix block is more efficient than diagonalizing the original matrix. This paper explains how the the DMRG++ code (Alvarez, 2009) [3] has been extended to handle the non-local SU(2) symmetry in a model independent way. Improvements in CPU times compared to runs with only local symmetries are discussed for the one-orbital Hubbard model, and for a two-orbital Hubbard model for iron-based superconductors. The computational bottleneck of the algorithm and the use of shared memory parallelization are also addressed.Program summaryProgram title: DMRG++Catalog identifier: AEDJ_v2_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEDJ_v2_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Special license. See http://cpc.cs.qub.ac.uk/licence/AEDJ_v2_0.htmlNo. of lines in distributed program, including test data, etc.: 211560No. of bytes in distributed program, including test data, etc.: 10572185Distribution format: tar.gzProgramming language: C++.Computer: PC.Operating system: Multiplatform, tested on Linux.Has the code been vectorized or parallelized?: Yes. 1 to 8 processors with MPI, 2 to 4 cores with pthreads.RAM: 1GB (256MB is enough to run the included test)Classification: 23.Catalog identifier of previous version: AEDJ_v1_0Journal reference of previous version: Comput. Phys. Comm. 180(2009)1572External routines: BLAS and LAPACKNature of problem:Strongly correlated electrons systems, display a broad range of important phenomena, and their study is a major area of research in condensed matter physics. In this context, model Hamiltonians are used to simulate the relevant interactions of a given compound, and the relevant degrees of freedom. These studies rely on the use of tight-binding lattice models that consider electron localization, where states on one site can be labeled by spin and orbital degrees of freedom. The calculation of properties from these Hamiltonians is a computational intensive problem, since the Hilbert space over which these Hamiltonians act grows exponentially with the number of sites on the lattice.Solution method:The DMRG is a numerical variational technique to study quantum many body Hamiltonians. For one-dimensional and quasi one-dimensional systems, the DMRG is able to truncate, with bounded errors and in a general and efficient way, the underlying Hilbert space to a constant size, making the problem tractable.Running time:Varies. The test suite provided takes about 10 min to run on a serial machine.

Coherent electron transport in quasi one-dimensional carbon-based systems

This Colloquium discusses the coherent electron transport properties of non-ideal quasi-one-dimensional carbon-based systems, i.e. graphene nanoribbons, carbon nanotubes and linear chains. Results are based on numerical simulations that implement Schroedinger/Poisson as well as non-equilibrium polaronic methodologies for the calculation of quantities relative to the conduction. Attention is paid on the role of localized or extended modifications of the structural and electronic symmetry within atomistic descriptions that go beyond phenomenological approaches. Three different types of perturbations are considered: (a) perturbations induced by defects/impurities in the atomic lattice, (b) perturbations induced by the coupling with the metallic contacts, and (c) perturbations induced by the application of bias. The objective is to elucidate the potentiality as well as the possible drawbacks of future all-carbon-based electronics.

Controlled potential electrodeposition of a microcrystalline thin film of the charge transfer material tetrathiafulvalene–polyoxometalate of approximate composition (TTF)5.3(Bu4N)0.7[P2W18O62]·3H2O

Electrocrystallisation provides a systematic approach to the preparation of tetrathiafulvalene (TTF)–polyoxometalate materials in the form of films having significant conductivity. In this study, a highly uniform microcrystalline thin film derived from TTF+ and the Dawson–Wells anion [α-P2W18O62]6− has been deposited onto glassy carbon, gold and indium tin oxide surfaces by controlled potential oxidative electrolysis of TTF in the presence of K6[P2W18O62] in acetonitrile (0.1 M [Bu4N][PF6]). Elemental analytical data are consistent with the formation of this conducting charge transfer salt having the approximate composition (TTF)5.3(Bu4N)0.7[P2W18O62]·3H2O. Spectroscopic data support this conclusion. Mechanistic aspects of the electrocrystallisation process have been monitored by cyclic voltammetry, electrochemical quartz crystal microbalance and chronoamperometric methods. A less crystalline form of this material with a slightly different composition also can be produced by bulk electrolysis of TTF to TTF+ followed by addition of K6[P2W18O62]. The conductivity of the film at room temperature is in the semiconducting range. The EPR spectra, together with the field strength and temperature dependence of the magnetic susceptibility, suggest that regions of film behave as a quasi one-dimensional system, with antiferromagnetic and spin-flop behaviour at low temperatures. The Raman spectra are consistent with an average TTF charge state of +1, while voltammetry confirms the presence of [P2W18O62]6−. The morphology and crystallinity of the electrocrystallised and chemically prepared materials were investigated by scanning electron microscopy and X-ray diffraction, respectively.

Symmetry Breaking in Quasi-1D Coulomb Systems

Quasi one-dimensional systems are systems of particles in domains which are of infinite extent in one direction and of uniformly bounded size in all other directions, e.g. on a cylinder of infinite length. The main result proven here is that for such particle systems with Coulomb interactions and neutralizing background, the so-called "jellium", at any temperature and at any finite-strip width there is translation symmetry breaking. This extends the previous result on Laughlin states in thin, two-dimensional strips by Jansen, Lieb and Seiler (2009). The structural argument which is used here bypasses the question of whether the translation symmetry breaking is manifest already at the level of the one particle density function. It is akin to that employed by Aizenman and Martin (1980) for a similar statement concerning symmetry breaking at all temperatures in strictly one-dimensional Coulomb systems. The extension is enabled through bounds which establish tightness of finite-volume charge fluctuations.

Ab initio vibrations in nonequilibrium nanowires

We review recent results on electronic and thermal transport in two different quasi one-dimensional systems: Silicon nanowires (SiNW) and atomic gold chains. For SiNW's we compute the ballistic electronic and thermal transport properties on equal footing, allowing us to make quantitative predictions for the thermoelectric properties, while for the atomic gold chains we evaluate microscopically the damping of the vibrations, due to the coupling of the chain atoms to the modes in the bulk contacts. Both approaches are based on the combination of density-functional theory, and nonequilibrium Green's functions.

DIFFRACTION FROM NANOTUBES AND QUASI ONE-DIMENSIONAL CRYSTALS

Quasi one-dimensional systems, including bio-polymers, nanotubes, nanowires, etc., are in focus of material science and technology for more than two decades. Using recently found quasi one-dimensional conformation classes, which are elementary building blocks of all quasi one-dimensional crystals, we make symmetry based study of their diffraction patterns. In particular, we single out the features distinguishing between the classes, thus enabling to characterize each of them. It turns out that this analysis suffices to find out chiral indices of carbon nanotubes.

Interlamellar Coupling of Phospholipid Bilayers in Liposomes: An Emergent Property of Lipid Rearrangement

The thermal phase behaviors of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) large unilamellar vesicles (LUVs) and multilamellar vesicles (MLVs) were compared by fluorescence spectroscopy, using PPDPC (1-palmitoyl-2[10-(pyren-1-yl)]decanoyl-sn-glycero-3-phosphocholine) as a reporter, in parallel with differential scanning calorimetry (DSC). A striking difference is seen between MLVs and LUVs in the lateral organizational dynamics of PPDPC, in particular, below the main phase transition temperature T(m), with efficient clustering of PPDPC into fluid microdomains in the L(beta') and P(beta') (ripple) phases of DPPC MLVs. In the P(beta') phase of MLVs, the probe is likely to become enriched in linear line defects, restricting intermolecular collisions to occur in a quasi one-dimensional system. In contrast, fluorescence and DSC data both suggest that the P(beta') phase is not well-defined in LUVs. Fluorescence anisotropy for 1-palmitoyl-2-[3-(diphenylhexatrienyl)propanoyl]-sn-glycero-3-phosphocholine (DPH-PC) revealed similar acyl chain order for both LUVs and MLVs in the L(beta') and P(beta') phases. However, for MLVs with this probe, T(m) determined from anisotropy was elevated by 0.7 degrees, with higher anisotropy evident in the L(alpha) phase compared to LUVs. These differences in the thermal phase behavior of the two types of liposomes are likely to derive from the augmented acyl chain order due to cooperative coupling of the lamellae of DPPC MLVs, thus manifesting in new, emerging material properties in the latter type of bilayer membrane assembly, as reflected in the organizational dynamics of the pyrene-labeled analogue.

Evidence of Water Adsorption in Hydrophobic Nanospaces of Highly Pure Double-Walled Carbon Nanotubes

Highly pure double-walled carbon nanotubes synthesized by a catalytic chemical vapor deposition method have a quasi one-dimensional nanopore system. We determined these nanotubes' nanopore structures by means of molecular probe adsorption using N(2) at 77 K, CO(2) at 273 K, and water at 298, 308, and 318 K, as well as high-resolution transmission electron microscopy. The water vapor adsorption behavior of this system was quite unusual. At a lower relative pressure of P/P(0) = 0.3-0.65, water filled the interstitial nanopores, and at relative pressures higher than this range, water also filled the interbundle nanopores. This study is the first to our knowledge that has provided direct evidence of water adsorption in hydrophobic nanospaces of highly pure double-walled carbon nanotubes.

Theory of confined plasmonic waves in coaxial cylindrical cables fabricated of metamaterials

We report on the theoretical investigation of the plasmonic wave propagation in the coaxial cylindrical cables fabricated of both right-handed medium (RHM) [with $\epsilon >0$, $\mu >0$] and left-handed medium (LHM) [with $\epsilon(\omega) <0$, $\mu(\omega) <0$], using a Green-function (or response function) theory in the absence of an applied magnetic field. The Green-function theory generalized to be applicable to such quasi-one dimensional systems enables us to derive explicit expressions for the corresponding response functions (associated with the EM fields), which can in turn be used to derive various physical properties of the system. The confined plasmonic wave excitations in such multi-interface structures are characterized by the electromagnetic fields that are localized at and decay exponentially away from the interfaces. A rigorous analytical diagnosis of the general results in diverse situations leads us to reproduce exactly the previously well-known results in other geometries, obtained within the different theoretical frameworks. As an application, we present several illustrative examples on the dispersion characteristics of the confined (and extended) plasmonic waves in single- and double-interface structures made up of dispersive metamaterials interlaced with conventional dielectrics. These dispersive modes are also substantiated through the computation of local as well as total density of states. It is observed that the dispersive components enable the system to support the simultaneous existence of s- and p-polarization modes in the system. Such effects as this one are solely attributed to the negative-index metamaterials and are otherwise impossible...

Freezing light with cold atoms

The impact of disorder and localisation in electronic conduction was introduced more than half a century ago by Philip Anderson. In a much broader context of disorder-mediated wave dynamics it remains an important research area, and surprises abound. Meanwhile, research in ultracold atomic physics has led to phenomenally detailed elucidation of properties, including changes in phase, of quantum degenerate Bosonic and Fermionic gases. For example, beautiful experiments have recently demonstrated, in quasi one-dimensional systems, Anderson localisation of matter waves. In this brief essay, we describe and discuss research on wave localisation in the context of ultracold atomic physics, with a particular emphasis on light localisation in ultracold and high-density atomic gases. Essential ideas are reviewed, along with the current experimental status of the field, and promising avenues for future research are discussed.

Tight-binding Calculations of Band Structure and Conductance in Graphene Nano-ribbons

We suggest a general approach based on the nearest-neighbor tight-binding approximation (TB) to investigate the band structure and conductance of a quasi-one dimensional system. Numerical calculations carried out for Graphene nanoribbons (GNRs) with different widths and edge conditions (zigzag and armchair) reveal the well-known results that the electronic properties of GNRs depend strongly on the size and geometry of the sample.

The density matrix renormalization group for strongly correlated electron systems: A generic implementation

The purpose of this paper is (i) to present a generic and fully functional implementation of the density-matrix renormalization group (DMRG) algorithm, and (ii) to describe how to write additional strongly-correlated electron models and geometries by using templated classes. Besides considering general models and geometries, the code implements Hamiltonian symmetries in a generic way and parallelization over symmetry-related matrix blocks. Program summary Program title: DMRG++ Catalogue identifier: AEDJ_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEDJ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: See file LICENSE No. of lines in distributed program, including test data, etc.: 15 795 No. of bytes in distributed program, including test data, etc.: 83 454 Distribution format: tar.gz Programming language: C++, MPI Computer: PC, HP cluster Operating system: Any, tested on Linux Has the code been vectorized or parallelized?: Yes RAM: 1 GB (256 MB is enough to run included test) Classification: 23 External routines: BLAS and LAPACK Nature of problem: Strongly correlated electrons systems, display a broad range of important phenomena, and their study is a major area of research in condensed matter physics. In this context, model Hamiltonians are used to simulate the relevant interactions of a given compound, and the relevant degrees of freedom. These studies rely on the use of tight-binding lattice models that consider electron localization, where states on one site can be labeled by spin and orbital degrees of freedom. The calculation of properties from these Hamiltonians is a computational intensive problem, since the Hilbert space over which these Hamiltonians act grows exponentially with the number of sites on the lattice. Solution method: The DMRG is a numerical variational technique to study quantum many body Hamiltonians. For one-dimensional and quasi one-dimensional systems, the DMRG is able to truncate, with bounded errors and in a general and efficient way, the underlying Hilbert space to a constant size, making the problem tractable. Running time: The test program runs in 15 seconds.

Semiclassical spectral correlator in quasi one-dimensional systems

We investigate the spectral statistics of chaotic clean quasi one-dimensional systems. To do so we represent the spectral correlation function R(ϵ) through derivatives of a generating function and semiclassically approximate the latter in terms of periodic orbits. In contrast to previous work we obtain both non-oscillatory and oscillatory contributions to the correlation function. Both types of contributions are evaluated to leading order in 1/ϵ for systems with and without time-reversal invariance. Our results agree with predictions from the nonlinear sigma model for disordered systems.

Quantum Effects of Capacitance in Nano-Scale Devices

We explore quantum effects of capacitance in nano-scale systems, by using a first-principles calculation of a carbon nanotube (CNT) capacitor. We show that the capacitance exhibits two principal quantum effects: First, the capacitance shows a large bias dependence, reflecting the density of states structure of the CNT with the divergent-type Van-Hove singularities peculiar to quasi-one dimensional systems. Second, the capacitance is larger than what the classical electromagnetism predicts with the tube-wall radius, according to a quantum spill of the stored charge density from the tube wall. We argue that these two quantum effects in the capacitance become more prominent when the system size gets smaller, which will open a new possibility for a design and control of nanometer scale devices.