A Short Review on One Dimensional Wigner Crystallization

The simplest possible structural transition that an electronic system can undergo is Wigner crystallization. The aim of this short review is to discuss the main aspects of three recent experimets on the one dimensional Wigner molecule, starting from scratch. To achieve this task, the Luttinger liquid theory of weakly and strongly interacting fermions will be shortly addressed, together with the basic properties of carbon nanotubes that are require. Then, the most relevant properties of Wigner molecules will be addressed, and finally the experiments will be described.

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A Short Review of One-Dimensional Wigner Crystallization

Crystals ◽

10.3390/cryst11010020 ◽

2020 ◽

Vol 11 (1) ◽

pp. 20

Author(s):

Niccolo Traverso Ziani ◽

Fabio Cavaliere ◽

Karina Guerrero Becerra ◽

Maura Sassetti

Keyword(s):

Carbon Nanotubes ◽

Electron Density ◽

Structural Transition ◽

Luttinger Liquid ◽

Electronic System ◽

Short Review ◽

One Dimensional ◽

Wigner Crystallization ◽

Liquid Theory ◽

The One

The simplest possible structural transition that an electronic system can undergo is Wigner crystallization. The aim of this short review is to discuss the main aspects of three recent experimets on the one-dimensional Wigner molecule, starting from scratch. To achieve this task, the Luttinger liquid theory of weakly and strongly interacting fermions is briefly addressed, together with the basic properties of carbon nanotubes that are required. Then, the most relevant properties of Wigner molecules are addressed, and finally the experiments are described. The main physical points that are addressed are the suppression of the energy scales related to the spin and isospin sectors of the Hamiltonian, and the peculiar structure that the electron density acquires in the Wigner molecule regime.

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Fermi-Liquid Features of the One-Dimensional Luttinger Liquid

International Journal of Modern Physics B ◽

10.1142/s0217979298002817 ◽

1998 ◽

Vol 12 (32) ◽

pp. 3465-3473 ◽

Cited By ~ 7

Author(s):

Yupeng Wang

Keyword(s):

Fermi Liquid ◽

Luttinger Liquid ◽

Finite Size ◽

Electron Systems ◽

Dynamical Correlation ◽

One Dimensional ◽

Conformal Field ◽

Liquid Theory ◽

The One ◽

Finite Size Corrections

We show that the one-dimensional (1D) electron systems can also be described by Landau's phenomenological Ferimi-liquid theory. Most of the known results derived from the Luttinger-liquid theory can be retrieved from the one-dimensional Fermi-liquid theory. Exact correspondence between the Landau parameters and Haldane parameters is established. The exponents of the dynamical correlation functions and the impurity problem are also discussed based on the finite size corrections of elementary excitations with the predictions of the conformal field theory, which provides a bridge between the one-dimensional Fermi-liquid and the Luttinger liquid.

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ON THE THEORY OF THE ONE-DIMENSIONAL LUTTINGER LIQUID

Modern Physics Letters B ◽

10.1142/s021798499300062x ◽

1993 ◽

Vol 07 (09) ◽

pp. 641-653 ◽

Cited By ~ 1

Author(s):

DJORDJE MINIC

Keyword(s):

Field Theory ◽

Conformal Field Theory ◽

Luttinger Liquid ◽

Point Of View ◽

One Dimensional ◽

Basic Properties ◽

Conformal Field ◽

The One

Basic properties of the one-dimensional Luttinger liquid are studied from the point of view of an effective conformal field theory.

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Gate-tunable plasmons in mixed-dimensional van der Waals heterostructures

Nature Communications ◽

10.1038/s41467-021-25269-0 ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Sheng Wang ◽

SeokJae Yoo ◽

Sihan Zhao ◽

Wenyu Zhao ◽

Salman Kahn ◽

...

Keyword(s):

Carbon Nanotubes ◽

Carrier Density ◽

Electromagnetic Interaction ◽

Luttinger Liquid ◽

Fundamental Physics ◽

Metallic Structures ◽

One Dimensional ◽

Figures Of Merit ◽

Electrostatic Gating ◽

Plasmon Dispersion

AbstractSurface plasmons, collective electromagnetic excitations coupled to conduction electron oscillations, enable the manipulation of light–matter interactions at the nanoscale. Plasmon dispersion of metallic structures depends sensitively on their dimensionality and has been intensively studied for fundamental physics as well as applied technologies. Here, we report possible evidence for gate-tunable hybrid plasmons from the dimensionally mixed coupling between one-dimensional (1D) carbon nanotubes and two-dimensional (2D) graphene. In contrast to the carrier density-independent 1D Luttinger liquid plasmons in bare metallic carbon nanotubes, plasmon wavelengths in the 1D-2D heterostructure are modulated by 75% via electrostatic gating while retaining the high figures of merit of 1D plasmons. We propose a theoretical model to describe the electromagnetic interaction between plasmons in nanotubes and graphene, suggesting plasmon hybridization as a possible origin for the observed large plasmon modulation. The mixed-dimensional plasmonic heterostructures may enable diverse designs of tunable plasmonic nanodevices.

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Some Results on Multigranulation Neutrosophic Rough Sets on a Single Domain

Symmetry ◽

10.3390/sym10090417 ◽

2018 ◽

Vol 10 (9) ◽

pp. 417 ◽

Cited By ~ 1

Author(s):

Hu Zhao ◽

Hong-Ying Zhang

Keyword(s):

Algebraic Structure ◽

Rough Sets ◽

Lattice Structure ◽

Single Domain ◽

One Dimensional ◽

Basic Properties ◽

Approximation Operators ◽

Rough Approximation ◽

The One ◽

Comprehensive Study

As a generalization of single value neutrosophic rough sets, the concept of multi-granulation neutrosophic rough sets was proposed by Bo et al., and some basic properties of the pessimistic (optimistic) multigranulation neutrosophic rough approximation operators were studied. However, they did not do a comprehensive study on the algebraic structure of the pessimistic (optimistic) multigranulation neutrosophic rough approximation operators. In the present paper, we will provide the lattice structure of the pessimistic multigranulation neutrosophic rough approximation operators. In particular, in the one-dimensional case, for special neutrosophic relations, the completely lattice isomorphic relationship between upper neutrosophic rough approximation operators and lower neutrosophic rough approximation operators is proved.

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Application of the Landau-Luttinger Liquid Formulation to the Study of the Magnetic Properties of the 1-D Hubbard Model

International Journal of Modern Physics B ◽

10.1142/s021797929100002x ◽

1991 ◽

Vol 05 (01n02) ◽

pp. 3-30 ◽

Cited By ~ 3

Author(s):

J. Carmelo ◽

P. Horsch ◽

P.A. Bares ◽

A.A. Ovchinnikov

Keyword(s):

Magnetic Field ◽

Magnetic Properties ◽

Low Temperature ◽

Hubbard Model ◽

Luttinger Liquid ◽

Liquid Formulation ◽

One Dimensional ◽

Spin Excitations ◽

Arbitrary Strength ◽

The One

The Landau-Luttinger liquid formulation is used to investigate the physics of the one-dimensional Hubbard model in a magnetic field of arbitrary strength H. The low lying charge and spin excitations are studied. A novel branch of sound wave-like spin excitations arises for H>0. The low temperature thermodynamics is considered in some detail.

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