Binding energies and current density of heavy-hole trions of monolayer transition metal dichalcogenides: analytical perturbation treatment of Coulomb interaction with 2D H-like basis set

Kapil, Bharti; Sharma, Shivalika; Aggarwal, Priyanka; Hazra, Ram Kuntal

doi:10.1140/epjp/s13360-022-02970-7

Cited by 6 publications

(2 citation statements)

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“…and Kapil et al . improvised analytical treatments to Coulomb and exchange interactions for 3D and 2D He ‐isoelectronic series and heavy‐hole trions [36–39] . Kapil et al .…”

Section: Introductionmentioning

confidence: 99%

“…Sharma et al and Kapil et al improvised analytical treatments to Coulomb and exchange interactions for 3D and 2D Heisoelectronic series and heavy-hole trions. [36][37][38][39] Kapil et al recently emphasized on analytical multiconfiguration calculation for Period-II elements with hydrogenic spin orbitals as basis set. [40] In this paper, we have formulated analytical diagonal Coulomb integrals (Js) over hydrogenic orbitals employing Green function expansion.…”

Section: Introductionmentioning

confidence: 99%

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Lah Number Mediated Analytical Two‐center Two‐electron Integrals of Coulomb Green Function of H‐like Orbitals for ¹Σ States

Kapil,

Sharma,

Aggarwal

et al. 2023

ChemistrySelect

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Energetics of two‐center two‐electron (2c–2e) systems carry challenges in theoretical understanding of Schrödinger equation (SE) for well‐known divergence of Coulomb interactions and nuclear separation (R) in modified H‐like AOs, Slater type orbitals (STOs), Gaussian type orbitals (GTOs), B‐spline, Sturmian function and etc. employed to VBT and MOT. Certain elegant computational and analytical techniques were developed for STO, GTO and other square integrable basis set within Born‐Oppenheimer (BO) approximation. STOs and GTOs have an essential limitation of absence of radial nodes. Thus, analytical treatment has become an urge for H‐like AOs. We have considered the diatomic molecules only for the sake of simplicity. Employing Sheffer identity in associated Laguerre polynomial/Whittaker‐M function forms of H‐like AOs and transforming integrals into elliptic coordinates with two nuclei on two foci furnishes exact, analytical and simple Coulomb integrals (Js) in terms of R. Lah number originated from for nuclear coordinates only due to Sheffer identity shows that energetics of diatomic molecules can be anticipated as extremum function of R. Therefore, the optimization of potential energy surface (PES) of electrons as gradient of R may lead to σ‐bond formation. In this paper, we have developed diagonal Js for bound states of H2 molecule.

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“…and Kapil et al . improvised analytical treatments to Coulomb and exchange interactions for 3D and 2D He ‐isoelectronic series and heavy‐hole trions [36–39] . Kapil et al .…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Lah Number Mediated Analytical Two‐center Two‐electron Integrals of Coulomb Green Function of H‐like Orbitals for ¹Σ States

Kapil,

Sharma,

Aggarwal

et al. 2023

ChemistrySelect

Self Cite

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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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Binding energies and current density of heavy-hole trions of monolayer transition metal dichalcogenides: analytical perturbation treatment of Coulomb interaction with 2D H-like basis set

Cited by 6 publications

References 51 publications

Lah Number Mediated Analytical Two‐center Two‐electron Integrals of Coulomb Green Function of H‐like Orbitals for ¹Σ States

Lah Number Mediated Analytical Two‐center Two‐electron Integrals of Coulomb Green Function of H‐like Orbitals for ¹Σ States

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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Binding energies and current density of heavy-hole trions of monolayer transition metal dichalcogenides: analytical perturbation treatment of Coulomb interaction with 2D H-like basis set

Cited by 6 publications

References 51 publications

Lah Number Mediated Analytical Two‐center Two‐electron Integrals of Coulomb Green Function of H‐like Orbitals for 1Σ States

Lah Number Mediated Analytical Two‐center Two‐electron Integrals of Coulomb Green Function of H‐like Orbitals for 1Σ States

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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Lah Number Mediated Analytical Two‐center Two‐electron Integrals of Coulomb Green Function of H‐like Orbitals for ¹Σ States

Lah Number Mediated Analytical Two‐center Two‐electron Integrals of Coulomb Green Function of H‐like Orbitals for ¹Σ States