Quasi One-dimensional Electron Systems Research Articles

Pattern Formation and Aggregation in Ensembles of Solitons in Quasi One-Dimensional Electronic Systems

Broken symmetries of quasi one-dimensional electronic systems give rise to microscopic solitons taking roles of carriers of the charge or spin. The double degeneracy gives rise to solitons as kinks of the scalar order parameter A; the continuous degeneracy for the complex order parameter Aexp(iθ) gives rise to phase vortices, amplitudes solitons, and their combinations. These degrees of freedom can be controlled or accessed independently via either the spin polarization or the charge doping. The long-range ordering in dimensions above one imposes super-long-range confinement forces upon the solitons, leading to a sequence of phase transitions in their ensembles. The higher-temperature T transition enforces the confinement of solitons into topologically bound complexes: pairs of kinks or the amplitude solitons dressed by exotic half-integer vortices. At a second lower T transition, the solitons aggregate into rods of bi-kinks or into walls of amplitude solitons terminated by rings of half-integer vortices. With lowering T, the walls multiply, passing sequentially across the sample. Here, we summarize results of a numerical modeling for different symmetries, for charged and neutral soliton, in two and three dimensions. The efficient Monte Carlo algorithm, preserving the number of solitons, was employed which substantially facilitates the calculations, allowing to extend them to the three-dimensional case and to include the long-range Coulomb interactions.

Reprint of : Scattering theory approach to bosonization of non-equilibrium mesoscopic systems

Between many prominent contributions of Markus Büttiker to mesoscopic physics, the scattering theory approach to the electron transport and noise stands out for its elegance, simplicity, universality, and popularity between theorists working in this field. It offers an efficient way to theoretically investigate open electron systems far from equilibrium. However, this method is limited to situations where interactions between electrons can be ignored, or considered perturbatively. Fortunately, this is the case in a broad class of metallic systems, which are commonly described by the Fermi liquid theory. Yet, there exist another broad class of electron systems of reduced dimensionality, the so-called Tomonaga–Luttinger liquids, where interactions are effectively strong and cannot be neglected even at low energies. Nevertheless, strong interactions can be accounted exactly using the bosonization technique, which utilizes the free-bosonic character of collective excitations in these systems. In the present work, we use this fact in order to develop the scattering theory approach to the bosonization of open quasi-one dimensional electron systems far from equilibrium.

Reprint of : Scattering theory approach to bosonization of non-equilibrium mesoscopic systems

Between many prominent contributions of Markus Büttiker to mesoscopic physics, the scattering theory approach to the electron transport and noise stands out for its elegance, simplicity, universality, and popularity between theorists working in this field. It offers an efficient way to theoretically investigate open electron systems far from equilibrium. However, this method is limited to situations where interactions between electrons can be ignored, or considered perturbatively. Fortunately, this is the case in a broad class of metallic systems, which are commonly described by the Fermi liquid theory. Yet, there exist another broad class of electron systems of reduced dimensionality, the so-called Tomonaga–Luttinger liquids, where interactions are effectively strong and cannot be neglected even at low energies. Nevertheless, strong interactions can be accounted exactly using the bosonization technique, which utilizes the free-bosonic character of collective excitations in these systems. In the present work, we use this fact in order to develop the scattering theory approach to the bosonization of open quasi-one dimensional electron systems far from equilibrium.

Scattering theory approach to bosonization of non-equilibrium mesoscopic systems

Between many prominent contributions of Markus Büttiker to mesoscopic physics, the scattering theory approach to the electron transport and noise stands out for its elegance, simplicity, universality, and popularity between theorists working in this field. It offers an efficient way to theoretically investigate open electron systems far from equilibrium. However, this method is limited to situations where interactions between electrons can be ignored, or considered perturbatively. Fortunately, this is the case in a broad class of metallic systems, which are commonly described by the Fermi liquid theory. Yet, there exist another broad class of electron systems of reduced dimensionality, the so-called Tomonaga–Luttinger liquids, where interactions are effectively strong and cannot be neglected even at low energies. Nevertheless, strong interactions can be accounted exactly using the bosonization technique, which utilizes the free-bosonic character of collective excitations in these systems. In the present work, we use this fact in order to develop the scattering theory approach to the bosonization of open quasi-one dimensional electron systems far from equilibrium.

Collapse of Charge Ordering Due to Disorder in Quasi One-Dimensional Electron Systems

Effects of disorder on charge ordering (CO) is investigated for one-dimensional (1D) and quasi 1D extended Hubbard model with infinite on-site repulsion at quarter filling. Only the forward scattering due to disorder is taken into account. In the 1D model, the resistivity due to Umklapp scattering that is an origin of CO is shown to be suppressed by the forward scattering. In addition, we obtain that the CO transition temperature TCO for quasi 1D model becomes smaller with increasing strength of the forward scattering.

Quantized current in carbon nanotube quantum dots by surface acoustic waves

Single charge effects attract much attention with respect to possible applications as future transistor structures or for quantum cryptography. Here, surface acoustic wave mediated single charge transport through quantum dots (QDs) formed in a carbon nanotube (CNT) is presented. The CNT bridges metallic source and drain contacts on a piezoelectric host substrate, employing an acoustic alignment technique. The metal electrodes in contact with the nanotube provide tunnel barriers to the quasi one-dimensional electron system, hence forming a few QD in series due to the presence of defects within the CNT. The dynamic piezoelectric field associated with the surface wave leads to an acoustoelectric current through the system which turns out to be quantized like in a turnstile device.

Electron phase modulation in a suspended InAs∕AlGaSb nanomechanical beam

The magnetopiezoresistance in a quasi one-dimensional electron system incorporated into an InAs∕AlGaSb nanomechanical suspended beam was measured while the beam was at mechanical resonance. The magnetopiezoresistance showed reproducible highly periodic resistance oscillations which arise via strain induced electron phase modulation. The Fourier transform of the magnetopiezoresistance indicates that mechanical activation of the beam affects only a few electron trajectories and the electron interference in only a single electron loop gives rise to the resistance oscillations in the magnetopiezoresistance.

Finite-Temperature Charge-Ordering Transition and Fluctuation Effects in Quasi One-Dimensional Electron Systems at Quarter Filling

Finite-temperature charge-ordering phase transition in quasi one-dimensional (1D) molecular conductors is investigated theoretically, based on a quasi 1D extended Hubbard model at quarter filling with interchain Coulomb repulsion $V_\perp$. The interchain term is treated within mean-field approximation whereas the 1D fluctuations in the chains are fully taken into account by the bosonization theory. Three regions are found depending on how the charge ordered state appears at finite temperature when $V_\perp$ is introduced: (i) weak-coupling region where the system transforms from a metal to a charge ordered insulator with finite transition temperature at a finite critical value of $V_\perp$, (ii) an intermediate region where this transition occurs by infinitesimal $V_\perp$ due to the stability of inherent 1D fluctuation, and (iii) strong-coupling region where the charge ordered state is realized already in the purely 1D case, of which the transition temperature becomes finite with infinitesimal $V_\perp$. Analytical formula for the $V_\perp$ dependence of the transition temperature is derived for each region.

Magnetic field effects and renormalization of the long-range Coulomb interaction in carbon nanotubes

We develop two theoretical approaches for dealing with the low-energy effects of the repulsive interaction in one-dimensional electron systems. Renormalization Group methods allow us to study the low-energy behavior of the unscreened interaction between currents of well-defined chirality in a strictly one-dimensional electron system. A dimensional regularization approach is useful, when dealing with the low-energy effects of the long-range Coulomb interaction. This method allows us to avoid the infrared singularities arising from the long-range Coulomb interaction at D=1. We can also compare these approaches with the Luttinger model, to analyze the effects of the short-range term in the interaction. Thanks to these methods, we are able to discuss the effects of a strong magnetic field B in quasi one-dimensional electron systems, by focusing our attention on Carbon Nanotubes. Our results imply a variation with B in the value of the critical exponent α for the tunneling density of states, which is in fair agreement with that observed in a recent transport experiment involving carbon nanotubes. The dimensional regularization allows us to predict the disappearance of the Luttinger liquid, when the magnetic field increases, with the formation of a chiral liquid with α=0.

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.

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.

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.

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.

Unconventional spin density waves in quasi-one dimensional systems

We consider the possibility of formation of an unconventional spin density wave (SDW) 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 A(k) on the Fermi surface. 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. Among the transport properties the frequency dependent conductivity in directions perpendicular to the linear chain direction is evaluated for various gap functions, and found to reflect the maximum gap value.

SELF-MATCHING PROPERTY OF CORRELATED ELECTRONS: CHARGE–DENSITY WAVE ENHANCES SPIN ORDERING

The local minima of the free energy of a quasi one-dimensional electron system with short-range repulsion on a lattice were found which correspond with the symmetry allowed matching pairs of the precursor CDW and SDW modulation periods. Possible relation of the theory to the `staircase' instabilities in the doped nickelates with perovskite structure is discussed.

Ac conductance of a quantum wire with electron-electron interactions

The complex ac-response of a quasi-one dimensional electron system in the one-band approximation with an interaction potential of finite range is investigated. It is shown that linear response is exact for this model. The influence of the screening of the electric field is discussed. The complex absorptive conductance is analyzed in terms of resistive, capacitive and inductive behaviors.

Imaging of a suspended helium film with 2-D electrons by interferometry

A helium film suspended between elevations on a substrate forms an excellent surface for a two-dimensional electron gas. With the structure on the substrate a quasi one-dimensional electron system can be created. Experiments probing the electrical transport properties of this system have raised questions about the suspended helium film itself. We report measurements of the suspended film using interferometry. The profile is mapped out as a function of the bulk helium level beneath the substrate. By measuring the electron signal simultaneously the relation between the signal and the film profile can be obtained.

FAST ALGORITHM FOR COMPUTATIONAL STUDY OF DEEP LEVEL PHOTOLUMINESCENCE SPECTRA

An algorithm for fast calculation of theoretical deep level photoluminescence (PL) lineshapes is presented. The algorithm can be used for effective comparison with experimental spectra in cases of bulk photoluminescence. The method was expanded and for the cases of deep level photoluminescence in quasi-two and quasi-one dimensional electron systems in semiconductors.

VARIATIONAL CALCULATION FOR ELECTRON CORRELA-TIONS OF QUASI ONE-DIMENSIONAL SYSTEM

For the quasi one-dimensional electron systems with coulomb interaction, a new model is presented. The form of effective Coulomb potential is derived. Based on the correlated wave function theory, the many-body wave function is obtained on the basis of the collective oscillation behavior of the electron gas. The pair correlation functions and correlation energies of the different electron densities are obtained. The pair correlation functions obtained in this paper are positive definite and satisfy the normalization condition.