Luttinger Liquid Model Research Articles

Andreev-Like Reflections with Cold Atoms

We propose a setup in which Andreev-like reflections predicted for 1D transport systems could be observed time dependently using cold atoms in a 1D optical lattice. Using time-dependent density matrix renormalization group methods we analyze the wave packet dynamics as a density excitation propagates across a boundary in the interaction strength. These phenomena exhibit good correspondence with predictions from Luttinger liquid models and could be observed in current experiments in the context of the Bose-Hubbard model.

The one-dimensional Wigner crystal in carbon nanotubes

A dilute system of electrons interacting through long-range Coulomb forces has been predicted to form a periodic solid known as a Wigner crystal. To date, this state has been observed directly only in two-dimensional systems. Here, using low-temperature single-electron transport spectroscopy, we show that the hole gas in low-disorder semiconducting carbon nanotubes forms a one-dimensional Wigner crystal. In an axial magnetic field, we observe three distinct regimes of spin and isospin polarization as carrier density is varied. We explain these regimes in terms of a Wigner crystal picture based on a gapped Luttinger liquid model, with the carriers represented by spatially localized solitons. Our observations could enable greater control over the behaviour of the spatially separated system of carriers. Such control, combined with the inherently long coherence times of carriers in carbon nanotubes, could prove useful in the development of solid-state quantum computing. The one-dimensional case of the so-called ‘Wigner crystal’ phase of electrons—long predicted but previously only seen in two-dimensional electron systems—has finally been observed, in a carbon nanotube.

Deformed Wigner crystal in a one-dimensional quantum dot

The spatial Fourier spectrum of the electron density distribution in a finite 1D system and the distribution function of electrons over single-particle states are studied in detail to show that there are two universal features in their behavior, which characterize the electron ordering and the deformation of Wigner crystal by boundaries. The distribution function has a $\delta$-like singularity at the Fermi momentum $k_F$. The Fourier spectrum of the density has a step-like form at the wavevector $2k_F$, with the harmonics being absent or vanishing above this threshold. These features are found by calculations using exact diagonalization method. They are shown to be caused by Wigner ordering of electrons, affected by the boundaries. However the common Luttinger liquid model with open boundaries fails to capture these features, because it overestimates the deformation of the Wigner crystal. An improvement of the Luttinger liquid model is proposed which allows one to describe the above features correctly. It is based on the corrected form of the density operator conserving the particle number.

Electron transport in a disordered Luttinger liquid

We study the transport properties of interacting electrons in a disordered quantum wire within the framework of the Luttinger liquid model. We demonstrate that the notion of weak localization is applicable to the strongly correlated one-dimensional electron system. Two alternative approaches to the problem are developed, both combining fermionic and bosonic treatment of the underlying physics. We calculate the relevant dephasing rate, which for spinless electrons is governed by the interplay of electron-electron interaction and disorder, thus vanishing in the clean limit. Our approach provides a framework for a systematic study of mesoscopic effects in strongly correlated electron systems.

Ground state properties of the one-dimensional Coulomb gas using the lattice regularized diffusion Monte Carlo method

We study the ground state properties of a quasi one dimensional electron gas, interacting via an effective potential with a harmonic transversal confinement and long range Coulomb tail. The exact correlation energy has been calculated for a wide range of electron densities by using the lattice regularized diffusion Monte Carlo method, which is a recent development of the standard projection Monte Carlo technique. In this case it is particularly useful as it allows to sample the exact ground state of the system, even in the low density regime when the exchange between electrons is extremely small. For different values of the width parameter b (0.1 a*_0 <= b <= 4 a*_0), we give a simple parametrization of the correlation energy, which provides an accurate local density energy functional for quasi one dimensional systems. Moreover we show that static correlations are in qualitative agreement with those obtained for the Luttinger liquid model with long range interactions.

Ground-state properties of the one dimensional electron liquid

We present a theory of the pair distribution function g ( z ) and many-body effective electron–electron interaction for the one dimensional (1D) electron liquid. Our approach involves the solution of a zero-energy scattering Schrödinger equation for g ( z ) where we implemented the Fermi hypernetted-chain approximation including the elementary diagram corrections. We present numerical results for g ( z ) and the static structure factor S ( k ) and obtain good agreement with data from diffusion Monte Carlo studies of the 1D system. We calculate the correlation energy and charge excitation spectrum over an extensive range of electron density. Furthermore, we obtain the static correlations in good qualitative agreement with those calculated for the Luttinger liquid model with long-range interactions.

Luttinger-Liquid Behavior in Weakly Disordered Quantum Wires

We have measured the temperature dependence of the conductance in long V-groove quantum wires fabricated in GaAs/AlGaAs heterostructures. Our data are consistent with recent theories developed within the framework of the Luttinger-liquid model, in the limit of weakly disordered wires. We show that, for the relatively low level of disorder in our quantum wires, the value of the interaction parameter g congruent with 0.66, which is the expected value for GaAs. However, samples with a higher level of disorder show conductance with stronger temperature dependence, which does not allow their treatment in the framework of perturbation theory. Fitting such data with perturbation-theory models leads inevitably to wrong (lower) values of g.

Electrical properties of carbon nanofibers synthesized using carbon disulfide as precursor

Abstract Electrical characterization of carbon nanofibers synthesized by a thermal chemical vapor deposition technique using carbon disulfide as the source of carbon is reported. Electrical resistance of mats and thin films samples of carbon nanofibers has been measured in the range of temperatures of 100–430 K. The electrical behavior of the mats can be explained within the Luttinger liquid model, but thin films show an anomaly around 273 K that may be related to charge trapping enhanced by the presence of water molecules.

Tunneling of interacting one-dimensional electrons through a single scatterer: Luttinger liquid behavior in the Hartree–Fock model

We study tunneling of weakly interacting spinless electrons at zero temperature through a single δ barrier in one-dimensional wires and rings of finite lengths. Our numerical calculations are based on the self-consistent Hartree–Fock approximation, nevertheless, our results exhibit features known from correlated many-body models. In particular, the transmission in a wire of length L at the Fermi level is proportional to L - 2 α with the universal power α (depending on the electron–electron interaction only, not on the strength of the δ barrier). Similarly, the persistent current in a ring of the circumference L obeys the rule I ∝ L - 1 - α known from the Luttinger liquid and Hubbard models. We show that the transmission at the Fermi level in the wire is related to the persistent current in the ring at the magnetic flux h / 4 e .

Transport properties for a Luttinger liquid wire in the presence of a time-dependent impurity

We study theoretically the transport properties of an interacting quantum wire in the presence of a time-dependent point impurity. Using the Keldysh formalism within the framework of Luttinger liquid model, we calculate and analyze the dc contribution of the backscattered current and the shot noise of the system with arbitrary Luttinger interaction strength and impurity position. From some numerical examples, we find that the time-dependent point impurity in the wire can enhance the total current in the strongly interaction regime, and the total current enhancement is dependent on both the impurity potential frequency and the equivalent frequency in relation to the drain-source voltage $V$. The dc contribution of the backscattered current oscillates as a function of impurity frequency with the period depending on the Luttinger interaction strength. Furthermore, the oscillation of the dc contribution of the backscattered current is not a finite-length effect, which is different from that in the case of system with a static point impurity, and the oscillation characteristic is also connected with $V$. However, the final current-noise relation is similar to that in the case of a static point impurity.

Electronic Mach-Zehnder interferometer in the fractional quantum Hall effect

We compute the interference pattern of a Mach-Zehnder interferometer operating in the fractional quantum Hall effect. Our theoretical proposal is inspired by a remarkable experiment on edge states in the Integer Quantum Hall effect (IQHE). The Luttinger liquid model is solved via two independent methods: refermionization at nu=1/2 and the Bethe Ansatz solution available for Laughlin fractions. The current differs strongly from that of single electrons in the strong backscattering regime. The Fano factor is periodic in the flux, and it exhibits a sharp transition from sub-Poissonian (charge e/2) to Poissonian (charge e) in the neighborhood of destructive interferences.

Time-controlled charge injection in a quantum Hall fluid

We consider the injection of a controlled charge from a normal metal into an edge state of the fractional quantum Hall effect, with a time-dependent voltage $V(t)$. Using perturbative calculations in the tunneling limit, and a chiral Luttinger liquid model for the edge state, we show that the electronic correlations prevent the charge fluctuations to be divergent for a generic voltage pulse $V(t)$. This is in strong contrast with the case of charge injection in a normal metal, where this divergence is present. We show that explicit formul{ae} for the mean injected charge and its fluctuations can be obtained using an adiabatic approximation, and that non perturbative results can be obtained for injection in an edge state of the FQHE with filling factor $ nu=1/3$. Generalization to other correlated systems which can be described with the Luttinger liquid model, like metallic Carbon nanotube, is given.

Hartree-Fock Simulation of Persistent Current in Rings with Single Scatterer

Using the self-consistent Hartree–Fock approximation for spinless electrons at zero temperature, we calculate the persistent current of the interacting electron gas in a one-dimensional ring containing a single δ barrier. Our results agree with correlated models like the Luttinger liquid model and lattice model with nearest-neighbor interaction. The persistent current is a sine-like function of magnetic flux. It decays with the ring length (L) faster than L−1 and eventually like L−α−1, where α > 0 is universal.

Phonon-assisted tunnelling in interacting suspended single-wall carbon nanotubes

Transport in suspended metallic single-wall carbon nanotubes in the presence of strong electron–electron interaction is investigated. We consider a tube of finite length and discuss the effects of the coupling of the electrons to the deformation potential associated to the acoustic stretching and breathing modes. Treating the interacting electrons within the framework of the Luttinger liquid model, the low-energy spectrum of the coupled electron–phonon system is evaluated. The discreteness of the spectrum is reflected in the differential conductance which, as a function of the applied bias voltage, exhibits three distinct families of peaks. The height of the phonon-assisted peaks is very sensitive to the parameters. The phonon peaks are best observed when the system is close to the Wentzel–Bardeen singularity.

Non-Fermi-Liquid Behavior in Quasi-One-DimensionalLi0.9Mo6O17

We present temperature dependent scanning tunneling spectroscopy data of the quasi-one-dimensional conductor Li0.9Mo6O17. The differential tunneling current in our low-temperature spectra shows a power-law behavior around the Fermi energy, which is expected for a clean Luttinger liquid. The power-law exponent is found to be 0.6. Spectra for a temperature range of 5 to 55 K can be fitted fairly well with a model for tunneling into a Luttinger liquid at the appropriate temperature. A fit with a model based on a zero bias anomaly is significantly worse compared to the Luttinger liquid model. No signature of a phase transition at T = 24 K is observed in our temperature dependent data.

Dephasing and Weak Localization in Disordered Luttinger Liquid

We study the transport properties of interacting electrons in a disordered quantum wire within the framework of the Luttinger liquid model. The conductivity at finite temperature is nonzero only because of inelastic electron-electron scattering. We demonstrate that the notion of weak localization is applicable to the strongly correlated one-dimensional electron system. We calculate the relevant dephasing rate, which for spinless electrons is governed by the interplay of electron-electron interaction and disorder, thus vanishing in the clean limit.

Transport properties of single-channel quantum wires with an impurity: Influence of finite length and temperature on average current and noise

The inhomogeneous Tomonaga Luttinger liquid model describing an interacting quantum wire adiabatically coupled to non-interacting leads is analyzed in the presence of a weak impurity within the wire. Due to strong electronic correlations in the wire, the effects of impurity backscattering, finite bias, finite temperature, and finite length lead to characteristic non-monotonic parameter dependencies of the average current. We discuss oscillations of the non-linear current voltage characteristics that arise due to reflections of plasmon modes at the impurity and quasi Andreev reflections at the contacts, and show how these oscillations are washed out by decoherence at finite temperature. Furthermore, the finite frequency current noise is investigated in detail. We find that the effective charge extracted in the shot noise regime in the weak backscattering limit decisively depends on the noise frequency $\omega$ relative to $v_F/gL$, where $v_F$ is the Fermi velocity, $g$ the Tomonaga Luttinger interaction parameter, and $L$ the length of the wire. The interplay of finite bias, finite temperature, and finite length yields rich structure in the noise spectrum which crucially depends on the electron-electron interaction. In particular, the excess noise, defined as the change of the noise due to the applied voltage, can become negative and is non-vanishing even for noise frequencies larger than the applied voltage, which are signatures of correlation effects.

Effect of interactions on the noise of chiral Luttinger liquid systems

We analyze the current noise, generated at a quantum point contact in fractional quantum Hall edge state devices, using the chiral Luttinger liquid model with an impurity and the associated exact field theoretic solution. We demonstrate that an experimentally relevant regime of parameters exists where the noise coincides with the partition noise of independent Laughlin quasiparticles. However, outside of this regime, this independent particle picture breaks down and the inclusion of interaction effects is essential to understand the shot noise.

Theory of resonant Raman scattering in one-dimensional electronic systems

A theory of resonant Raman scattering spectroscopy of one dimensional electronic systems is developed on the assumptions that (i) the excitations of the one dimensional electronic system are described by the Luttinger Liquid model, (ii) Raman processes involve virtual excitations from a filled valence band to an empty state of the one dimensional electronic system and (iii) excitonic interactions between the valence and conduction bands may be neglected. Closed form analytic expressions are obtained for the Raman scattering cross sections, and are evaluated analytically and numerically for scattering in the polarized channel, revealing a "double-peak" structure with the lower peak involving multispinon excitations with total spin S=0 and the higher peak being the conventional plasmon. A key feature of our results is a nontrivial power law dependence, involving the Luttinger Liquid exponents, of the dependence of the Raman cross sections on the difference of the laser frequency from resonance. We find that near resonance the calculated ratio of intensity in the lower energy feature to the intensity in the higher energy feature saturates at a value of the order of unity (times a factor of the ratio of the velocities of the two modes). We explicate the differences between the 'Luttinger liquid' and 'Fermi liquid' calculations of RRS spectra and argue that excitonic effects, neglected in all treatments so far, are essential for explaining the intensity ratios observed in quantum wires. We also discuss other Luttinger liquid features which may be observed in future RRS experiments.

Collective modes and Raman scattering in one dimensional electron systems

In this paper, we review recent development in the theory of resonant inelastic light (Raman) scattering in one-dimensional electron systems. The particular systems we have in mind are electron doped GaAs based semiconductor quantum wire nanostructures, although the theory can be easily modified to apply to other one-dimensional systems. We compare the traditional conduction-band-based non-resonant theories with the full resonant theories including the effects of interband transitions. We find that resonance is essential in explaining the experimental data in which the single particle excitations have finite spectral weights comparable to the collective charge density excitations. Using several different theoretical models (Fermi liquid model, Luttinger liquid model, and Hubbard model) and reasonable approximations, we further demonstrate that the ubiquitously observed strong single particle excitations in the experimental Raman spectra cannot be explained by the spinless multi-spinon excitations in the Luttinger liquid description. The observability of distinct Luttinger liquid features in the Raman scattering spectroscopy is critically discussed.