Two-electron singlet states in semiconductor quantum dots with Gaussian confinement: a single-parameter variational calculation

Boyacıoğlu, Bahadır; Sağlam, M.; Chatterjee, Ashok

doi:10.1088/0953-8984/19/45/456217

Cited by 33 publications

(18 citation statements)

References 63 publications

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“…We would like to mention in passing that the Gaussian potential has been solved approximately for a single-particle problem by several authors. [11][12][13][14][15][16][17][18] There have been several investigations in the past few years on the heat capacity and entropy of quantum dots and other related low-dimensional systems in the presence of a magnetic field. [19][20][21][22][23][24][25][26][27] However, most of these investigations have used either a square well model (SQM) or a parabolic potential model (PPM) for the confining potential.…”

Section: Introductionmentioning

confidence: 99%

Heat capacity and entropy of a GaAs quantum dot with Gaussian confinement

Boyacıoğlu¹,

Chatterjee²

2012

Journal of Applied Physics

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The heat capacity and entropy effects in a GaAs quantum dot with Gaussian confinement are calculated in the presence of a magnetic field and its interaction with the electron spin using the canonical ensemble approach. It is shown that the heat capacity shows a Schottky-like anomaly at a low temperature, while it approaches a saturation value 2k B as the temperature increases. As a function of the magnetic field, the heat capacity shows a maximum and then reduces to zero. Also the width of the maximum becomes wider with temperature. It is also shown that the heat capacity remains constant up to a certain value of the confinement length beyond which it displays a monotonic increase. However as a function of the confinement strength, though the heat capacity initially shows a significant drop, it remains constant thereafter. At low temperatures like T ¼ 10 and 20 K, the entropy is found to decrease with increasing magnetic field, but at higher temperatures, it remains almost independent of the magnetic field. At high temperatures, entropy shows a monotonic increase with temperature, but at a sufficiently low temperature as the magnetic field decreases, the entropy is found to develop a shoulder which becomes more and more pronounced with decreasing magnetic field. V C 2012 American Institute of Physics.

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Section: Introductionmentioning

confidence: 99%

Heat capacity and entropy of a GaAs quantum dot with Gaussian confinement

Boyacıoğlu¹,

Chatterjee²

2012

Journal of Applied Physics

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“…In this situation, the parabolic approximation gives probably poor results. It can also be seen from Table 2 That is not the case for the Gaussian potential, i.e., the higher the pair of states considered lie, the worse the approximation becomes, as already noted by other authors [15,17]. The basis sets optimized for these one-electron calculations will now be used for few-electrons systems.…”

Section: One-electron Quantum Dotsmentioning

confidence: 73%

Few-electron semiconductor quantum dots with Gaussian confinement

Gómez¹,

Romero²

2009

Open Physics

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Abstract:We have performed Hartree-Fock calculations of the electronic structure of N ≤ 10 electrons in a quantum dot modeled with a confining Gaussian potential well. We discuss the conditions for the stability of N bound electrons in the system. We show that the most relevant parameter determining the number of bound electrons is V 0 R 2 . Such a feature arises from widely valid scaling properties of the confining potential. Gaussian Quantum dots having N = 2, 5, and 8 electrons are particularly stable in agreement with the Hund rule. The shell structure becomes less and less noticeable as the well radius increases. 73.21.-b; 73.22-f PACS (2008):

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“…Their results were presented graphically, very informative to inspect but not easy to make quantitative comparisons with. The ground state of the two-electron spherical quantum dot was also investigated by Boyacioglu et al [14] using a simple variational wave function with a Jastrow correlation factor. Results for all three states considered in the present paper (as well as for some P states) were presented (graphically) by Sajeev and Moiseyev [15].…”

Section: Introductionmentioning

confidence: 99%

Excited states of the Gaussian two-electron quantum dot

Sen

Montgomery

et al. 2021

Eur. Phys. J. D

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We consider the 1s2s 1,3 S states of the two-electron three-dimensional quantum dot with a Gaussian one-body potential, −V0 exp(−λr 2 ). For a single electron, a simple scaling relation allows the reduction into a one-parameter problem in terms of V 0 λ . However, for the two-electron system, the interelectronic repulsion term, 1 r 12 , frustrates this simple scaling transformation, so we face a genuine two-parameter system. We pay particular attention to the location and nature of the critical well-depths, at which the binding energy of the second electron vanishes. Several observations are noteworthy: For all λ, the triplet critical well-depth is lower than that in the singly excited singlet state. Hence, there exists a finite range of well-depths for which the triplet is bound and the singlet is not, a feature that can possibly be applied in some device. Above its critical well-depth, the triplet state energy is always lower than that of the singly excited singlet. Both well-depths are considerably higher than the critical well-depth in the ground state. The expectation value of the interelectronic repulsion is always lower in the triplet, like the harmonic quantum dot but unlike He-like atoms, the two-particle Debye (Yukawa) atom, or the confined He atom. In the infinite well-depth (V0) limit, keeping the well-width 1 λ constant, the energies and other expectation values of the bound states of the two-electron Gaussian quantum dot approach those of a non-interacting harmonic two-electron system.

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Two-electron singlet states in semiconductor quantum dots with Gaussian confinement: a single-parameter variational calculation

Cited by 33 publications

References 63 publications

Heat capacity and entropy of a GaAs quantum dot with Gaussian confinement

Heat capacity and entropy of a GaAs quantum dot with Gaussian confinement

Few-electron semiconductor quantum dots with Gaussian confinement

Excited states of the Gaussian two-electron quantum dot

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