Quasi One-dimensional Systems Research Articles

SO(4) Theory of Antiferromagnetism and Superconductivity in Bechgaard Salts

Motivated by recent experiments with Bechgaard salts, we investigate the competition between antiferromagnetism and triplet superconductivity in quasi-one-dimensional electron systems. We unify the two orders in an SO(4) symmetric framework, demonstrating the existence of such symmetry in one-dimensional Luttinger liquids. SO(4) symmetry strongly constrains the phase diagram, leading to coexistence regions of antiferromagnetic, superconducting, and normal phases, as observed in (TMTSF)(2)PF(6). We predict a sharp neutron scattering resonance in superconducting samples.

Flux and chemical vapor transport growth and characterization of [formula omitted]- and [formula omitted]-VO[formula omitted] single crystals

Differential thermal and thermogravimetric analysis investigations of VO(PO3)2 at elevated temperatures shows that the substance melts at 1035∘C incongruently with decomposition in two condensed phases and evolution of gaseous oxygen. In order to grow single crystals at lower temperature two techniques were used: flux and chemical vapor growth. α- and β-VO(PO3)2 single crystals were grown from V–P–O flux and by vapor transport mediated by TeCl4. Because of a high viscosity of the flux the crystallized material contains inclusions of flux. Vapor transport growth leads to crystals of a higher quality. The crystals contain no inclusions of foreign phases and contaminations of Te and Cl which might be introduced by transport agent. Magnetic susceptibility measurements of β-VO(PO3)2 single crystals indicate a quasi one-dimensional system with weak antiferromagnetic interactions. The temperature dependence of the magnetic susceptibility shows the parameters of the interaction (intra and interchain) to be essentially similar with the previously published parameters of α-phase.

Magnetic ordering in a doped frustrated spin-Peierls system

Based on a model of a quasi-one dimensional spin-Peierls system doped with nonmagnetic impurities, an effective two-dimensional Hamiltonian of randomly distributed $S=1∕2$ spins interacting via long-range pairwise interaction is studied using a stochastic series expansion quantum Monte Carlo method. The susceptibility shows Curie-like behavior at the lowest temperatures reached although the staggered magnetisation is found to be finite for $T\ensuremath{\rightarrow}0$. The doping dependance of the corresponding three-dimensional N\'eel temperature is also computed.

Linear stability analysis of rapid granular flow down a slope and density wave formation

The linear stability of rapid granular flow on a slope under gravity against the longitudinal perturbation is analyzed using hydrodynamic equations. It is demonstrated that the steady flow uniform along the flow direction becomes unstable against the long-wavelength perturbations longitudinal to the flow direction for certain parameter ranges to form the density wave, in contrast with the finite wavelength instability against the transverse perturbation (Forterre & Pouliquen 2002). It is shown that the instability can be understood as the the long-wave instability of the kinematic waves in a quasi-one dimensional system. The results are compared with our previous molecular dynamics simulations (Mitarai & Nakanishi 2001), where the spontaneous density wave formation has been found.

Spatial correlations of trapped one-dimensional bosons in an optical lattice

We investigate a quasi-one dimensional system of trapped cold bosonic atoms in an optical lattice by using the density matrix renormalization group to study the Bose-Hubbard model at T=0 for experimentally realistic numbers of lattice sites. It is shown that a properly rescaled one-particle density matrix characterizes superfluid versus insulating states just as in the homogeneous system. For typical parabolic traps we also confirm the widely used local density approach for describing correlations in the limit of weak interaction. Finally, we note that the superfluid to Mott-insulating transition is seen most directly in the half width of the interference peak.

Magnetization of GaAs quantum wires with quasi one-dimensional electron systems

We have investigated experimentally the magnetization of low-dimensional electron systems in quantum wire arrays fabricated in modulation-doped AlGaAs/GaAs heterostructures. Periodic arrays with different electronic width of the wires ranging from 160 to 380 nm have been studied. We observe magnetization oscillations which are surprisingly close to a sawtooth profile, however exhibit an increasing width of the negative flanks for the narrow wires. We argue that this profile directly reflects the effective screening of the external confinement potential due to the electron–electron interaction and the E −1/2 density of states in the quantum wires, respectively.

Particle-Hole Pair Excitations in a Quasi-Zero-Dimensional Mott Insulator

We investigate momentum dependence of charge excitations across the effective Mott gap in a quasi-zero dimensional (q-ZD) model cuprate Li 2 CuO 2, using high resolution inelastic X-ray scattering by working near a resonance. In comparison to quasi-one dimensional (q-1D) systems such as Sr 2 CuO 3 or SrCuO 2, momentum dependence is much weaker in Li 2 CuO 2. Particle-hole pair excitations at the gap edge in these low dimensional Mott systems are found to be strongly dependent on the effective dimensionality (or topology) of the lattice and the strength of electron–electron interaction.

Structural properties and melting of a quasi-one dimensional classical Wigner crystal

The structural and melting properties of a quasi-one dimensional system of charged particles, interacting through a screened Coulomb potential are investigated. Depending on the density and the screening length, the system crystallizes in different lattice structures. The structural phase transitions between them are of first or second order. The melting of the system is studied through Monte Carlo simulations and reentrant behavior as a function of density is observed as well as evidence of anisotropic melting.

Finite‐temperature quantum transfer‐matrix simulations of the frustrated spin 1/2 chains: comparison with experiment

AbstractThis article presents the thermodynamical properties of quasi‐one dimensional magnetic systems CuGeO3 and new obtained Pb[Cu(SO4)(OH)2] evaluated by the numerically exact quantum transfer‐matrix method. Numerical results calculated for an infinite system and for a finite‐chain structure are compared successfully with experimental magnetic susceptibility data.

One-dimensional statistical mechanics models with application to peapods

Quasi one-dimensional systems of molecules of C60 encapsulated in (10/10) nanotubes were studied by both lattice-gas and Takashi–Gursey configurational integral methods of statistical mechanics for both open and capped finite nanotubes as well as infinite nanotubes. From well-established potentials, the energy, heat capacity compressibility, equation of state and absorption isotherms were computed as a function of temperature and molecular density. The existing theories were extended to include the calculation of clustering, and the number of clusters as a function of size was computed for a variety of temperatures and densities. For both models, all molecules are frozen into a single cluster, and increasing the temperature results in a break-up into smaller clusters. The corresponding heat capacity has a broad maximum, which is lower for the T–G model than for the lattice-gas model. The equations of state have a similar form in both models and are identical at low temperatures. The absorption isotherms show that filling of the tubes can take place at all temperatures of practical interest. Peapods are nearly ideal realizations of one-dimensional systems whose thermodynamic and structural properties can be accurately obtained by statistical mechanics.

Field-dependent conductivity at low electric fields in pressed pellets of doped poly(3-methylthiophene): evidence of charge-density wave depinning

Field-dependent conductivity at low electric fields was observed from low to room temperature in pressed pellets of doped poly(3-methylthiophene). The room temperature data showed good agreement with Bardeen's theory of charge-density wave depinning and the values of the parameters obtained are consistent with a strong electron–phonon interaction as expected for quasi-one dimensional systems.

Orbital Order in a Quasi-One-Dimensional Spin-Orbital Model

Quantum spin systems with orbital degrees of freedom in low dimensions have attracted much interest recently. In order to understand such orbital effects, one-dimensional (1D) spin-orbital models have been investigated extensively. Theoretical studies have been so far focused on 1D systems, and the instability to ordered phases in quasione-dimensional (Q1D) systems has not been investigated systematically, though the stability of the SU(4)-singlet phase was discussed for a two-leg SU(4) ladder and a 2D SU(4) model. In this short note, we show that a staggered-orbital order is stabilized in a Q1D spin-orbital system when weak interchain couplings are introduced to the 1D system. We consider the following Hamiltonian, which is a Q1D extension of the SU(4) spin-orbital model,

Glass transition in charge-density-wave systems o-TaS3 and K0.3MoO3

We present experimental evidence for the glass transition in charge density wave (CDW) superstructure of two quasi one-dimensional systems, o-TaS3 and K0.3MoO3. Low frequency dielectric response of both systems exhibits typical glass-like phenomenology, featuring the splitting of the relaxational spectrum into two processes on decreasing the temperature and the subsequent freezing of primary or a process at finite temperature of glass transition Tg. Below Tg secondary, or β process becomes dominant. Activation energies obtained from the temperature evolution of the characteristic relaxation times of a and β processes correspond to the activation energies of the temperature evolution of the DC conductivity above and below Tg respectively. The results are discussed in respect to the relevant theories of low frequency CDW dynamics, with the emphasis on the Coulomb hardening of CDW in absence of screening by free carriers. An attempt to understand observed differences in freezing of CDW in o-TaS3 and K0.3MoO3 is made.

Thermodynamic and statistical properties of charged topological defects

We focus on the statistical and thermodynamic properties of systems with competing long-range interactions. The studies are based on the physics of quasi-one dimensional system with special interest towards their topological defects, the so-called solitons. We have been considering ensembles of solitons resulting from the degeneracy of the ground state of the system. This is the case of various charge density-wave systems such as polyacetylene-like polymers where the solitons are the non-trivial excitations connecting different ground-states. We have been interested in particular with a one component plasma with $3D$ Coulomb interactions of such defects, mainly in 2 space dimensions. The $3D$ case has also been considered. The quasi-one dimensional nature of the system is responsible for the confinement of the solitons. This competition between confinement and Coulomb has been formulated and some of its non-trivial effects analyaed. This led us to study the statistical properties of charged interfaces: strings or domain walls in $3D$. We have found that shape instabilities, due to the competing interactions, play a fundamental role. The obtained results show similarities with experimental work in the field of stripe phases in cuprate oxides.

Electron transport in a quasi-one-dimensional channel on suspended helium films

Quasi-one dimensional electron systems have been created using a suspended helium film on a structured substrate. The electron mobility along the channel is calculated by taking into account the essential scattering processes of electrons by helium atoms in the vapor phase, ripplons, and surface defects of the film substrate. It is shown that the last scattering mechanism may dominate the electron mobility in the low temperature limit changing drastically the temperature dependence of the mobility in comparison with that controlled by the electron-ripplon scattering.

Theory of local optical spectroscopy of quantum wires with interface fluctuations

We present a theory of local optical spectroscopy in quantum wires taking into account structural disorder. The calculated spatially resolved spectra show the individual spectral lines due to the exciton states localized by the disordered potential in agreement with experimental findings. We investigate systematically the influence of the potential profile and of the spatial resolution on the local optical spectra. Several line scans along the wire axis are obtained for different spatial correlations and strength of the disorder potential and for different spatial resolutions ranging from the subwavelength to the diffraction limit. Lowering the spatial resolution causes the disappearance of many spectral lines due to destructive spatial interference. However, our results show that information on the individual eigenstates of this quasi one-dimensional quantum system can be obtained at also resolutions significantly lower than the correlation length of interface fluctuations.

EFFECTS OF INTERACTION FOR THE QUANTUM DIFFUSION IN COUPLED CHAINS

Effects of electron–electron interaction for the quantum diffusion is investigated numerically in quasi one-dimensional systems (coupled chains) with a few particles. We have observed localization even with the interaction after sufficient time evolution. The localization length ξ increases by the interactions in the weak coupling region. Also significant enhancement of the localization length ξ is observed by the increase of the chain numbers.

Bounded Fluctuations and Translation Symmetry Breaking: A Solvable Model

The variance of the particle number (equivalently the total charge) in a domain of length \(\mathcal{L}\) of a one-component plasma (OCP) on a cylinder of circumference W at the reciprocal temperature β=2, is shown to remain bounded as \(\mathcal{L}\)→∞. This exactly solvable system with average density ρ has a density profile which is periodic with period (ρW)−1 along the axis of the infinitely long cylinder. This illustrates the connection between bounded variance and periodicity in (quasi) one-dimensional systems.(1) When W→∞ the system approaches the two-dimensional OCP and the variance in a domain Λ grows like its perimeter |∂Λ|. In this limit, the system is translation invariant with rapid decay of correlations.

Thermodynamics and optical conductivity of unconventional spin density waves

We consider the possibility of formation of an unconventional spin density wave (USDW) in quasi-one dimensional electronic systems. In analogy with unconventional superconductivity, we develop a mean field theory of SDW allowing for the momentum dependent gap $\Delta({\bf k})$ on the Fermi surface. Conditions for the appearence of such a low temperature phase are investigated. The excitation spectrum and basic thermodynamic properties of the model are found to be very similar to those of d-wave superconductors in spite of the different topology of their Fermi surfaces. Several correlation functions are calculated, and the frequency dependent conductivity is evaluated for various gap functions. The latter is found to reflect the maximum gap value, however with no sharp onset for absorbtion.

Tomonaga-Luttinger features in the resonant Raman spectra of quantum wires

The differential cross section for resonant Raman scattering from the collective modes in a one dimensional system of interacting electrons is calculated non-perturbatively using the bosonization method. The results indicate that resonant Raman spectroscopy is a powerful tool for studying Tomonaga-Luttinger liquid behaviour in quasi-one dimensional electron systems.