Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userTransport in a one-dimensional Luttinger liquid
66
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In this paper we review recent theoretical results for transport in a one-dimensional (1d) Luttinger liquid. For simplicity, we ignore electron spin, and focus exclusively on the case of a single-mode. Moreover, we consider only the effects of a single (or perhaps several) spatially localized impurities. Even with these restrictions, the predicted behavior is very rich, and strikingly different than for a 1d non-interacting electron gas. The method of bosonization is reviewed, with an emphasis on physical motivation, rather than mathematical rigor. Transport through a single impurity is reviewed from several different perspectives, as a pinned strongly interacting ``Wigner crystal and in the limit of weak interactions. The existence of fractionally charged quasiparticles is also revealed. Inter-edge tunnelling in the quantum Hall effect, and charge fluctuations in a quantum dot under the conditions of Coulomb blockade are considered as examples of the developed techniques.
rate research
Read More
We study theoretically the transport through a single impurity in a one-channel Luttinger liquid coupled to a dissipative (ohmic) bath . For non-zero dissipation $eta$ the weak link is always a relevant perturbation which suppresses transport strongly. At zero temperature the current voltage relation of the link is $Isim exp(-E_0/eV)$ where $E_0simeta/kappa$ and $kappa$ denotes the compressibility. At non-zero temperature $T$ the linear conductance is proportional to $exp(-sqrt{{cal C}E_0/k_BT})$. The decay of Friedel oscillation saturates for distance larger than $L_{eta}sim 1/eta $ from the impurity.
The Luttinger liquid (LL) model of one-dimensional (1D) electronic systems provides a powerful tool for understanding strongly correlated physics including phenomena such as spin-charge separation. Substantial theoretical efforts have attempted to extend the LL phenomenology to two dimensions (2D), especially in models of closely packed perfect arrays of 1D quantum wires, each being described as a LL. For instance, such coupled-wire models have been successfully used to construct 2D anisotropic non-Fermi liquids, various quantum Hall states, topological phases, and quantum spin liquids. Despite these exciting theoretical developments, an experimental demonstration of high-quality arrays of 1D LLs suitable for realizing these models remains absent. Here we report the experimental realization of 2D arrays of 1D LLs with crystalline quality in a moire superlattice made of twisted bilayer tungsten ditelluride (tWTe$_{2}$). Originating from the anisotropic lattice of the monolayer, the moire pattern of tWTe$_{2}$ hosts identical, parallel 1D electronic channels, separated by a fixed nanoscale distance, which is tunable by the twist angle between layers. At a twist angle of ~ 5 degrees, we find that hole-doped tWTe$_{2}$ exhibits exceptionally large transport anisotropy with a resistance ratio of ~ 1000 between two orthogonal in-plane directions, suggesting the formation of 1D channels. The conductance measurement reveals a power-law scaling behavior, consistent with the formation of a 2D anisotropic phase that resembles an array of LLs. Our results open the door for realizing a variety of 2D correlated and topological quantum phases based on coupled-wire models and LL physics.
Ballistic transport of helical edge modes in two-dimensional topological insulators is protected by time-reversal symmetry. Recently it was pointed out [1] that coupling of non-interacting helical electrons to an array of randomly anisotropic Kondo impurities can lead to a spontaneous breaking of the symmetry and, thus, can remove this protection. We have analyzed effects of the interaction between the electrons using a combination of the functional and the Abelian bosonization approaches. The suppression of the ballistic transport turns out to be robust in a broad range of the interaction strength. We have evaluated the renormalization of the localization length and have found that, for strong interaction, it is substantial. We have identified various regimes of the dc transport and discussed its temperature and sample size dependencies in each of the regimes.
The ground-state properties of one-dimensional 3He are studied using quantum Monte Carlo methods. The equation of state is calculated in a wide range of physically relevant densities and is well reproduced by a power-series fit. The Luttinger liquid theory is found to describe the long-range properties of the correlation function. The density dependence of the Luttinger parameter is explicitly found and interestingly it shows a non-monotonic behavior. Depending on the density, the static structure factor can be a smooth function of the momentum or might contain a peak of a finite or infinite height. Although no phase transitions are present in the system, we identify a number of physically different regimes, including an ideal Fermi gas, a Bose-gas, a super-Tonks-Girardeau regime, and a quasi-crystal.
We study transport through a quantum dot side-coupled to two parallel Luttinger liquid leads in the presence of a Coulombic dot-lead interaction. This geometry enables an exact treatment of the inter-lead Coulomb interactions. We find that for dots symmetrically disposed between the two leads the correlation of charge fluctuations between the two leads can lead to an enhancement of the current at the Coulomb-blockade edge and even to a negative differential conductance. Moving the dot off center or separating the wires further converts the enhancement to a suppression.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
