Exact e – e (exchange) correlations of 2-D quantum dots in magnetic field: Size extensive<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si0048.gif" overflow="scroll"><mml:mrow><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>3</mml:mn><mml:mo>,</mml:mo><mml:mn>4</mml:mn><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:mo>′</mml:mo><mml:mi>n</mml:mi><mml:mo>′</mml:mo></mml:mrow></mml:math>-electron systems via multi-pole expansion

Aggarwal, Priyanka; Sharma, Shivalika; Singh, Sunny; Kaur, Harsimran; Hazra, Ram Kuntal

doi:10.1016/j.physe.2016.11.015

Cited by 14 publications

(9 citation statements)

References 46 publications

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“…Monopole and dipole factors have significant contribution to coulomb (exchange) correlations in comparison to quadrapole factor. Contribution of monopole factor to Coulomb (exchange) integral can roughly be formulated as (quantum number of all other coordinates are conserved) [17]:…”

Section: Resultsmentioning

confidence: 99%

“…Level spacing statistics and specific heat measurements (C v ) are also investigated in detail. It is evident that switching over of statistics between Poisson and Wigner distribution is very much prominent for N=2 in comparision to N=3, 4, 5, 6, K and consequently, C v shows maximum fluctuations for N=2 rather than the cases of higher carrier density [17]. Therefore, for the brevity and compactness of the paper we have refrained to discuss it.…”

Section: Resultsmentioning

confidence: 99%

“…Here, H i 0 represents the unperturbed hamiltonian of the ith particle and ¢ H represent coulomb interaction term among charge carriers. For N=2, the hamiltonion can be segregated into relative and center-of-mass coordinates [17]. But for N>2, the interaction term ( ¢ H ) replicates by a factor of N(N−1)/2.…”

Section: Theoretical Developmentmentioning

confidence: 99%

“…Moreover, surface integrals of both Dirichlet and Newman forms of Coulomb interaction in Green's function expansion exhibit sharp falls in the values for harmonic oscillator and reach multipole expansion of generic coordinates (r i ). Thus, each interaction term ( ¢ H ) is expanded via well known multi-pole expansion corroborating to [20]: Although, Schrödinger equations for both generic coordinates and relative/center-of-mass coordinates resemble to each other but their scaling factors differ [17]. Thus, it is very necessary to examine the nonrelativistic equation for generic coordinates.…”

Section: Theoretical Developmentmentioning

confidence: 99%

“…Other magnificent contributions in solving 2-D multi-electron systems have been improvised by Chakraborty et al, Hamaguchi et al and Taut [8][9][10][11][12][13][14][15][16]. Recently, our group proposed a modest alternate to many-body approximation methods for strong e-e and e-h correlations of 2-D quantum dots in magnetic field [17][18][19]. As many-body physics holds great importance, we have designed a prototype to solve exactly generalized N-e systems using multi-pole expansion (section 2) [20].…”

Section: Introductionmentioning

confidence: 99%

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Electronic spectra and chemical potential of 2-D multi-electron quantum dots in magnetic field: exact multi-pole expansion of coulomb correlation

et al. 2019

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Two-dimensional superlattices, TMDCs and graphene family exhibit strong coulomb correlations among e-e, e-h, electron-phonon and etc. As the number of electron N increases, confining gate voltage and transverse magnetic field are superseded by increasing coulomb interactions (N(N−1)/2 factors) that composes non-trivial Schrödinger equations. Representing such equations in Whittaker-M functions yields a modest alternate formalism, that accommodates integrals of coulomb (exchange) correlations in single-summed, finite and exact Lauricella functions via Chu-Vandermonde identity. For higher carrier density (N=3, 4, 5, 6, ..), the multipole expansion is incurred as exact and finitesummed coulomb, coulomb-type and dipole-type integrals. Although, fermionic exchange symmetry of many electron systems could be included in terms of various two-electron integrals, for the sake of brevity we have aimed to reproduce experimental results without spin. Signature of interplay among gate voltage, magnetic field, dielectric constant, mass and density of carriers is examined in electronic spectra, magnetization, chemical potential for the systems spanning over wide range of materials (He, BN, GaAs and etc.). Interestingly, chemical potential and addition energy as a function of magnetic field and number of carriers monitor the statistics between strongly degenerate to weakly degenerate composite fermions, coulomb blockade and shell structure of 2-D superlattices. At the most, quadrapole and octapole suffice the convergence.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Theoretical Developmentmentioning

confidence: 99%

Section: Theoretical Developmentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Electronic spectra and chemical potential of 2-D multi-electron quantum dots in magnetic field: exact multi-pole expansion of coulomb correlation

et al. 2019

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Many‐Body Multi‐Configurational Calculation Using Coulomb Green's Function

Kapil,

Sharma,

Aggarwal

et al. 2024

Electron Density

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Charged Black‐Hole‐Like Electronic Structure Driven by Geometric Potential of 2D Semiconductors

Shin,

Park,

Kong

et al. 2024

Advanced Materials

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One of the exotic expectations in the 2D curved spacetime is the geometric potential from the curvature of the 2D space, still possessing unsolved fundamental questions through Dirac quantization. The atomically thin 2D materials are promising for the realization of the geometric potential, but the geometric potential in 2D materials is not identified experimentally. Here, the curvature‐induced ring‐patterned bound states are observed in structurally deformed 2D semiconductors and formulated the modified geometric potential for the curvature effect, which demonstrates the ring‐shape bound states with angular momentum. The formulated modified geometric potential is analogous to the effective potential of a rotating charged black hole. Density functional theory and tight‐binding calculations are performed, which quantitatively agree well with the results of the modified geometric potential. The modified geometric potential is described by modified Gaussian and mean curvatures, corresponding to the curvature‐induced changes in spin‐orbit interaction and band gap, respectively. Even for complex structural deformation, the geometric potential solves the complexity, which aligns well with experimental results. The understanding of the modified geometric potential provides us with an intuitive clue for quantum transport and a key factor for new quantum applications such as valleytronics, spintronics, and straintronics in 2D semiconductors.

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Exact e – e (exchange) correlations of 2-D quantum dots in magnetic field: Size extensiveN=3,4,…,′n′-electron systems via multi-pole expansion

Cited by 14 publications

References 46 publications

Electronic spectra and chemical potential of 2-D multi-electron quantum dots in magnetic field: exact multi-pole expansion of coulomb correlation

Electronic spectra and chemical potential of 2-D multi-electron quantum dots in magnetic field: exact multi-pole expansion of coulomb correlation

Many‐Body Multi‐Configurational Calculation Using Coulomb Green's Function

Charged Black‐Hole‐Like Electronic Structure Driven by Geometric Potential of 2D Semiconductors

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