A Short Review of One-Dimensional Wigner Crystallization

Niccolo Ziani,Fabio Cavaliere,Karina Becerra,Maura Sassetti

doi:10.3390/cryst11010020

Niccolo Ziani, Fabio Cavaliere + Show 2 more

Open Access

https://doi.org/10.3390/cryst11010020

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Journal: Crystals	Publication Date: Dec 29, 2020
Citations: 10	License type: CC BY 4.0

Affiliation: University of Genoa, Italian Institute of Technology

Abstract

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.

Highlights

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
As we shall see, when equipped with the bosonization technique, the Luttinger liquid model can become an extremely powerful model to analytically tackle the study of Wigner molecules in 1D
In order to understand the physics of the one-dimensional Wigner molecule, one can start by inspecting a simple, abstract, yet far reaching model: 2N interacting spinful electrons, confined on a segment of length L by an infinite potential

Summary

Introduction

Wigner for electrons is the jellium, one of the most general and fundamental ones in condensed matter [2], in which the effects of the interacting electron liquid and the neutralizing background provided by the lattice ion charges are taken into account [3]. Of a Wigner crystal formed in a low-density 2D sheet of electrons floating atop the flat surface of liquid He. For a detailed review of this key topic, see e.g., Refs. As we shall see, when equipped with the bosonization technique, the Luttinger liquid model can become an extremely powerful model to analytically tackle the study of Wigner molecules in 1D This aspect, in a certain sense, sets the d = 1 case apart from higher dimensionality where computationally demanding numerical methods are unavoidable.

The Ground State Density

Standard Bosonization

Bosonization in the Strong Interaction Limit

Indicators of the Wigner Molecule

Carbon Nanotubes

Experiments

Perspectives