Hartree–Fock energy of a finite two-dimensional electron gas system in a jellium background

2022

J. Phys.: Conf. Ser.

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We consider a two-dimensional electron gas in the thermodynamic (bulk) limit. It is assumed that the system consists of fully spin-polarized (spinless) electrons with anisotropic mass. We study the variation of the shape of the expected elliptical Fermi surface as a function of the density of the system in presence of such form of internal anisotropy. To this effect, we calculate the energy of the system as well as the optimum ellipticity of the Fermi surface for two possible liquid states. One corresponds to the standard system with circular Fermi surface while the second one represents a liquid anisotropic phase with a tunable elliptical deformation of the Fermi surface that includes the state that minimizes the kinetic energy. The results obtained shed light on several possible scenarios that may arise in such a system. The competition between opposing tendencies of the kinetic energy and potential energy may lead to the stabilization of liquid phases where the optimal elliptical deformation of the Fermi surface is non-obvious and depends on the density as well as an array of other factors related to the specific values of various parameters that characterize the system.

Section: Theory and Modelmentioning

confidence: 99%

Variation of the elliptical Fermi surface for a two-dimensional electron gas with anisotropic mass

2022

J. Phys.: Conf. Ser.

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“…Low-dimensional systems in which electrons are restricted to move in less than three spatial dimensions have always attracted great interest as a result of novel theoretical phenomena and potential for technological applications in the field of electronic devices and materials. In particular, a two-dimensional electron gas (2DEG) system where electrons interact with a standard Coulomb interaction potential is one of the most widely studied problems in theoretical condensed matter physics 1 , 2 . Unexpected behavior occurs when a 2DEG system is subject to a strong perpendicular magnetic field.…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional finite quantum Hall clusters of electrons with anisotropic features

2022

Sci Rep

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Low-dimensional nano and two-dimensional materials are of great interest to many disciplines and may have a lot of applications in fields such as electronics, optoelectronics, and photonics. One can create quantum Hall phases by applying a strong magnetic field perpendicular to a two-dimensional electron system. One characterizes the nature of the system by looking at magneto-transport data. There have been a few quantum phases seen in past experiments on GaAs/AlGaAs heterostructures that manifest anisotropic magnetoresistance, typically, in high Landau levels. In this work, we model the source of anisotropy as originating from an internal anisotropic interaction between electrons. We use this framework to study the possible anisotropic behavior of finite clusters of electrons at filling factor 1/6 of the lowest Landau level.

“…For instance, calculation of the resulting Coulomb integrals corresponding to the self-energy of a uniformly charged square or cube turns out to be a highly non-trivial task. These type of integrals are often found in physics and chemistry theoretical models [16][17][18][19], and are computationally costly. Their numerical evaluation encounters two main drawbacks.…”

Section: Introductionmentioning

confidence: 99%

Coulomb self-energy integral of a uniformly charged d-cube: A physically-based method for approximating multiple integrals

Batle

Journal of Electrostatics

Naseri

et al. 2017

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We report a concise expression for the electrostatic Coulomb self-energy of a uniformly charged cube with arbitrary dimensionality. The result, conveniently expressed in integral form, shows the unique behavior of the system as dimensionality increases. We use the case study of a uniformly charged square and cube to illustrate the effectiveness of the method employed. The resulting integral expression of the Coulomb self-energy of a multi-dimensional cube can be calculated numerically at very high accuracy. Numerically exact values of Coulomb self-energy obtained this way provide an excellent tool to gauge the validity of various computational techniques including a straightforward discretization method employed in this work. The proposed method relates the self-energy multi-variable integral to energy contributions coming from a finite discrete system of point charges with the understanding that the number of point charges gradually increases towards the continuum limit. We achieve very good accuracy by using an expression with only two terms where the second term increases considerably the accuracy of computation of continuum integrals and represents a systematic first-order correction to the finite energy of the discrete system. The applied numerical method turns out to be very reliable as shown by the results obtained for cubic domains with dimensionality varying from two to five. The method can be easily generalized to other types of domains with arbitrary geometry.