Absorption of Electromagnetic Waves by Plasma Oscillations in an Infinite Two-Dimensional Electron Gas in a Magnetic Field

Rodionov, D. A.; Zagorodnev, I. V.

doi:10.1134/s0021364019020139

Cited by 7 publications

(4 citation statements)

References 16 publications

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“…A two-dimensional Wigner crystal has recently been observed experimentally by Smolenski and co-workers . Two-dimensional crystal lattices made up of electrons have also been obtained experimentally on the surface of liquid helium, in magnetic fields − and in Moiré superlattices. − Such systems are often also termed Wigner crystals in the literature. Wigner crystals have also been observed in one dimension. − The properties of Wigner crystals have been studied extensively in condensed-matter physics and have important implications for understanding the behavior of electrons in low-dimensional systems.…”

Section: Introductionmentioning

confidence: 98%

Solution to the Thomson Problem for Clifford Tori with an Application to Wigner Crystals

Alrakik,

Escobar Azor,

Brumas

et al. 2023

J. Chem. Theory Comput.

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In its original version, the Thomson problem consists of the search for the minimum-energy configuration of a set of point-like electrons that are confined to the surface of a two-dimensional sphere ( 2 ) that repel each other according to Coulomb's law, in which the distance is the Euclidean distance in the embedding space of the sphere, i.e., 3 . In this work, we consider the analogous problem where the electrons are confined to an n-dimensional flat Clifford torus n with n = 1, 2, 3. Since the torus n can be embedded in the complex manifold n , we define the distance in the Coulomb law as the Euclidean distance in n , in analogy to what is done for the Thomson problem on the sphere. The Thomson problem on a Clifford torus is of interest because supercells with the topology of a Clifford torus can be used to describe periodic systems such as Wigner crystals. In this work, we numerically solve the Thomson problem on a square Clifford torus. To illustrate the usefulness of our approach, we apply it to Wigner crystals. We demonstrate that the equilibrium configurations we obtain for large numbers of electrons are consistent with the predicted structures of Wigner crystals. Finally, in the one-dimensional case, we analytically obtain the energy spectrum and the phonon dispersion law.

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Section: Introductionmentioning

confidence: 98%

Solution to the Thomson Problem for Clifford Tori with an Application to Wigner Crystals

Alrakik,

Escobar Azor,

Brumas

et al. 2023

J. Chem. Theory Comput.

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“…However, they did not determine the lattice structure. Two-dimensional crystal lattices consisting of electrons have also been obtained in other experiments, mainly by using magnetic fields or Moiré superlattices. − In the literature, these systems are also frequently called Wigner crystals. Closely related to the Wigner fragments studied here are Wigner molecules, in which the electrons are typically confined by an external potential which breaks the translational invariance of the electron gas. − Wigner molecules have also been observed experimentally. − …”

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confidence: 99%

The Emergence of the Hexagonal Lattice in Two-Dimensional Wigner Fragments

Escobar Azor,

Alrakik,

de Bentzmann

et al. 2024

J. Phys. Chem. Lett.

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At very low density, the electrons in a uniform electron gas spontaneously break symmetry and form a crystalline lattice called a Wigner crystal. But which type of crystal will the electrons form? We report a numerical study of the density profiles of fragments of Wigner crystals from first principles. To simulate Wigner fragments, we use Clifford periodic boundary conditions and a renormalized distance in the Coulomb potential. Moreover, we show that high-spin restricted open-shell Hartree−Fock theory becomes exact in the low-density limit. We are thus able to accurately capture the localization in two-dimensional Wigner fragments with many electrons. No assumptions about the positions where the electrons will localize are made. The density profiles we obtain emerge naturally when we minimize the total energy of the system. We clearly observe the emergence of the hexagonal crystal structure, which has been predicted to be the ground-state structure of the two-dimensional Wigner crystal.

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“…This suppression allows the interaction energy to play a more dominant role, consequently intensifying the correlation effect. This is a reminiscent of the magnetic-field-induced Wigner crystal, wherein a B⊥ field turns electrons into more localized cyclotron orbits and Coulomb repulsion organizes them into lattice subsequently [40]. This is in sharp contrast with magic angle twisted bilayer graphene, wherein the electrons are already highly localized at correlated states (Fig.…”

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confidence: 99%

Correlated insulators in twisted bilayer graphene

2021

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Electrons residing in flat-band system can play a vital role in triggering spectacular phenomenology due to relatively large interactions and spontaneous breaking of different degeneracies. In this work we demonstrate chirally twisted triple bilayer graphene, a new moiré structure formed by three pieces of helically stacked Bernal bilayer graphene, as a highly tunable flat-band system. In addition to the correlated insulators showing at integer moiré fillings, commonly attributed to interaction induced symmetry broken isospin flavors in graphene, we observe abundant insulating states at half-integer moiré fillings, suggesting a longer-range interaction and the formation of charge density wave insulators which spontaneously break the moiré translation symmetry. With weak out-of-plane magnetic field applied, as observed half-integer filling states are enhanced and more quarter-integer filling states appear, pointing towards further quadrupling moiré unit cells. The insulating states at fractional fillings combined with Hartree-Fock calculations demonstrate the observation of a new type of correlated charge density wave insulators in graphene and points to a new accessible twist manner engineering correlated moiré electronics.

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Absorption of Electromagnetic Waves by Plasma Oscillations in an Infinite Two-Dimensional Electron Gas in a Magnetic Field

Cited by 7 publications

References 16 publications

Solution to the Thomson Problem for Clifford Tori with an Application to Wigner Crystals

Solution to the Thomson Problem for Clifford Tori with an Application to Wigner Crystals

The Emergence of the Hexagonal Lattice in Two-Dimensional Wigner Fragments

Correlated insulators in twisted bilayer graphene

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