Multi-electron anisotropic quantum dots/TMDCs/CNT families under magnetic field: analytical treatment to first Brillouin zone by Fermi liquid model

Abstract

Acute Coulomb interaction of the two-dimensional systems has drawn special attention due to its unusual logarithmic Green function expansion. As the number of electrons (N) increases, Pauli Exclusion principle emerges inevitably with rapidly growing electronic correlations. Quantum dot, Transition metal dichalcogenides (TMDC) and Carbon nanotube (CNT) families of 2-D anisotropic mesoscopic systems are rich habitats of electrons. Schrödinger equations of such electrons in electrical confinement and transverse magnetic field can be recast in self-adjoint Whittaker-M functions facilitating each Coulomb interaction to terminable, exact and single summed Lauricella function via Chu-Vandermonde identity. For $N=3,4,5,6,\dots 20$, multipoles of Green function expansion also succumb to terminable, single-summed, analytical integrals by inserting discretised closure relations. Thus, multi-configuration Slater determinantal states are employed for strong correlation of Fermi liquid model of first Brillouin zone (FBZ) within giga-units of reciprocal lattices (mesoscopic scale). Chemical potential, addition energies of WS${}_2$, GaAs and model systems of dielectric constant $=1.0$ have set benchmark at low and high confinement potentials, as a function of magnetic field and density of electrons. Because of sharp falls in surface integrals of both Newman and Dirichlet forms of Green function, Coulomb interaction takes to (or leads to) multipole expansion of generic coordinates. Formation of composite-fermions may be anticipated. At the most, octupole is sufficient for the convergence.

GRAPHICAL ABSTRACT

KEYWORDS:

• Fermi liquid model
• multi-configuration slater determinant
• quantum dots/TMDC
• strong Coulomb interaction
• Lauricella Functions

Acknowledgments

We express our sincere thanks to Professor Shankar Prasad Bhattacharyya for his inspiration and support in pursuing many-body physics. We also thank Ms. Bharti Kapil for helping us in constructing plots and fruitful suggestions. Financial support from DST-SERB (2013-2016), UGC, DU-DST, R&D council (Delhi University) and CSIR (Research Associate scheme) are highly acknowledged.

Disclosure statement

No potential conflict of interest was reported by the author(s).

ORCID

Ram Kuntal Hazra http://orcid.org/0000-0003-0787-431X

Additional information

Funding

Financial support from DST-SERB (2013-2016), UGC, DU-DST, R&D council (Delhi University) and CSIR (Research Associate scheme) are highly acknowledged.