Stability and image-potential-induced screening of electron vibrational excitations in a three-layer structure

Meissner, G.; Namaizawa, Hiroshi; Voss, Matthew G.

doi:10.1103/physrevb.13.1370

Cited by 91 publications

(19 citation statements)

References 21 publications

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“…In the absence of the kinetic energy term, i.e., in the classical limit, a two-dimensional electron system forms a triangular Wigner crystal. 14,15 In this limit, the N-electron system has N!-fold degenerate ground states, and one of them is denoted by ͉X I ͘. 16 We can assume that the ith electron, whose coordinate is denoted by r i , is localized at the ith lattice site R i in the state ͉X I ͘,…”

Section: Formulationmentioning

confidence: 99%

Multiple-spin exchange in a two-dimensional Wigner crystal

Katano

Hirashima

2000

Phys. Rev. B

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Multiple-spin exchange constants in a two-dimensional Wigner crystal are calculated with a WKB approximation. Contributions of the Gaussian fluctuations around classical exchange paths are accurately calculated. In the dilute limit, the three-spin exchange interaction is found to be dominant in agreement with the previous study. Over a wide range of the electron density, however, n-spin exchange interactions with nу4 are found to be of considerable magnitude, which makes the ground phase diagram nontrivial. Recent experimental findings by Okamoto and Kawaji ͓Phys. Rev. B 57, 9097 ͑1998͔͒ are also discussed in the light of the present results.

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Section: Formulationmentioning

confidence: 99%

Multiple-spin exchange in a two-dimensional Wigner crystal

Katano

Hirashima

2000

Phys. Rev. B

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“…For electron-electron or electron and positive background interaction, we use screened Coulomb potential. For Si MOSFETs, the image charge in the metal substrate induces the screening and the interaction in the momentum space can be written as [8] V (k) = 1 ε…”

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confidence: 99%

Droplet state in an interacting two-dimensional electron system

Shi

He²,

Xie³

1999

Phys. Rev. B

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It is well known that the dielectric constant of two-dimensional (2D) electron system goes negative at low electron densities. A consequence of the negative dielectric constant could be the formation of the droplet state. The droplet state is a two-phase coexistence region of high density liquid and low density "gas". In this paper, we carry out energetic calculations to study the stability of the droplet ground state. The possible relevance of the droplet state to recently observed 2D metal-insulator transition is also discussed. PACS numbers: 71.30.+h, 73.40.Hm The recent discovery of two-dimensional (2D) metalinsulator transition (MIT) by Kravchenko et al. [1] has challenged the scaling theory of localization [2,3] in which a 2D MIT is forbidden. A noticeable character of the electron system in these experiments is that r s , the parameter measures the strength of the Coulomb interaction, is fairly large. We suspect that the electron system may be unstable against phase separation at these large values of r s . We demonstrated in our previous paper [4] that this assumption alone is sufficient to provide a theoretical description that is consistent with all the known experiments. For a two-dimensional (2D) electron system, there believed to be two phases: a high density Fermi gas phase and a low density insulating Wigner crystal phase. The dielectric constant of the liquid phase becomes negative when r s ≃ 2 [5], which indicates that the liquid phase is unstable. At lower densities, the Wigner crystal phase appears around r s ≃ 37 in the absence of disorder [6]. This critical value of r s appears to be reduced to around r s ≃ 10 with disorders [7]. In the intermediate values of r s , we believe that there is a liquid phase which we think is responsible for the observed MIT.In this paper, we propose that a droplet state of the electron system resulted from the phase separation of the electrons into this new liquid phase and a low density "gas" phase. Here we call the low density phase "gas" purely for the reason that its density is low. In fact, in the presence of impurities, the "gas" phase is disordered Wigner crystal. To investigate our proposal, we have studied the energetics of such a droplet state. We find that both electron-electron interaction and potential fluctuations are crucial for the formation of the droplet state.An obvious condition for the droplet state is that the electron gas is unstable. To investigate what possibilities of the instability leads to, we study a simple but physically motivated model. Let us consider electrons in the disc of radius b with positive background. Imagine that the electron system is shrunk to a new radius a < b while the positive background remains intact. Clearly the charging energy due to the separation of the electrons from the positive background increases the energy of the system. However there can also be energy gained (decreasing total energy): since for a uniform electron gas the ground state energy E g is at its minimum when r s ≃ 2 [5], for r s > 2 the...

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“…The energy (per particle) of the triangular electron lattice on a neutralizing positive background with the charge density +|e|n s is slightly lower than that of the square one, [36,37] …”

Section: Introductionmentioning

confidence: 94%

“…First of all, there exists a solution of the classical many-electron problem [35][36][37]. If electrons are considered as classical point particles, they form, due to the Coulomb repulsion, a regular Wigner-crystal lattice [27] of a triangular,…”

Section: Introductionmentioning

confidence: 99%

A new approach to the ground state of quantum Hall systems. Basic principles

Mikhaǐlov

2001

Physica B: Condensed Matter

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I present a new approach to the many-body ground state of quantum-Hall systems. The method describes the behavior of a two-dimensional electron system at all Landau-level filling factors ν, continuously as a function of magnetic field, and enables one to analytically calculate any physical value, characterizing the system, at all ν. New proposed trial many-body wave functions have a clear physical meaning and a very large variational freedom, which opens up wide possibilities to search for the ground state of the system at all magnetic fields.

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Stability and image-potential-induced screening of electron vibrational excitations in a three-layer structure

Cited by 91 publications

References 21 publications

Multiple-spin exchange in a two-dimensional Wigner crystal

Multiple-spin exchange in a two-dimensional Wigner crystal

Droplet state in an interacting two-dimensional electron system

A new approach to the ground state of quantum Hall systems. Basic principles

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