Signatures of Wigner molecule formation in interacting Dirac fermion quantum dots

Paananen, Tomi; Egger, Reinhold; Siedentop, Heinz

doi:10.1103/PHYSREVB.83.085409

Title: Signatures of Wigner molecule formation in interacting Dirac fermion quantum dots

Full Record
Other Related Research

Abstract

We study N interacting massless Dirac fermions confined in a two-dimensional quantum dot. Physical realizations of this problem include a graphene monolayer and the surface state of a strong topological insulator. We consider both a magnetic confinement and an infinite mass confinement. The ground-state energy is computed as a function of the effective interaction parameter {alpha} from the Hartree-Fock approximation and, alternatively, by employing the Mueller exchange functional. For N=2, we compare those approximations to exact diagonalization results. The Hartree-Fock energies are highly accurate for the most relevant interaction range {alpha} < or approx. 2, but the Mueller functional leads to an unphysical instability when {alpha} > or approx. 0.756. Up to 20 particles were studied using Hartree-Fock calculations. Wigner molecule formation was observed for strong but realistic interactions, accompanied by a rich peak structure in the addition energy spectrum.

Authors:

Paananen, Tomi; Egger, Reinhold ^[1]; Siedentop, Heinz ^[2]

Institut fuer Theoretische Physik, Heinrich-Heine-Universitaet, D-40225 Duesseldorf (Germany)
Mathematisches Institut, Ludwigs-Maximilians-Universitaet Muenchen, D-80333 Muenchen (Germany)

Publication Date:: Tue Feb 15 00:00:00 EST 2011

OSTI Identifier:: 21538132

Resource Type:: Journal Article

Journal Name:: Physical Review. B, Condensed Matter and Materials Physics

Additional Journal Information:: Journal Volume: 83; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevB.83.085409; (c) 2011 American Institute of Physics; Journal ID: ISSN 1098-0121

Country of Publication:: United States

Language:: English

Subject:: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 77 NANOSCIENCE AND NANOTECHNOLOGY; CARBON; COMPARATIVE EVALUATIONS; ENERGY SPECTRA; FERMIONS; HARTREE-FOCK METHOD; HONEYCOMB STRUCTURES; INSTABILITY; INTERACTION RANGE; INTERACTIONS; LAYERS; MAGNETIC CONFINEMENT; MASS; MOLECULES; QUANTUM DOTS; SURFACES; TOPOLOGY; TWO-DIMENSIONAL CALCULATIONS; APPROXIMATIONS; CALCULATION METHODS; CONFINEMENT; DISTANCE; ELEMENTS; EVALUATION; MATHEMATICS; MECHANICAL STRUCTURES; NANOSTRUCTURES; NONMETALS; PLASMA CONFINEMENT; SPECTRA

Citation Formats


                    Paananen, Tomi, Egger, Reinhold, and Siedentop, Heinz. Signatures of Wigner molecule formation in interacting Dirac fermion quantum dots.  United States: N. p., 2011. 
        Web.  doi:10.1103/PHYSREVB.83.085409.

Copy to clipboard


                    Paananen, Tomi, Egger, Reinhold, & Siedentop, Heinz. Signatures of Wigner molecule formation in interacting Dirac fermion quantum dots.  United States.  https://doi.org/10.1103/PHYSREVB.83.085409

Copy to clipboard


                    Paananen, Tomi, Egger, Reinhold, and Siedentop, Heinz. 2011.  
        "Signatures of Wigner molecule formation in interacting Dirac fermion quantum dots".  United States.  https://doi.org/10.1103/PHYSREVB.83.085409.

Copy to clipboard


                    
@article{osti_21538132,

  title        = {Signatures of Wigner molecule formation in interacting Dirac fermion quantum dots},

  author       = {Paananen, Tomi and Egger, Reinhold and Siedentop, Heinz},

  abstractNote = {We study N interacting massless Dirac fermions confined in a two-dimensional quantum dot. Physical realizations of this problem include a graphene monolayer and the surface state of a strong topological insulator. We consider both a magnetic confinement and an infinite mass confinement. The ground-state energy is computed as a function of the effective interaction parameter {alpha} from the Hartree-Fock approximation and, alternatively, by employing the Mueller exchange functional. For N=2, we compare those approximations to exact diagonalization results. The Hartree-Fock energies are highly accurate for the most relevant interaction range {alpha} < or approx. 2, but the Mueller functional leads to an unphysical instability when {alpha} > or approx. 0.756. Up to 20 particles were studied using Hartree-Fock calculations. Wigner molecule formation was observed for strong but realistic interactions, accompanied by a rich peak structure in the addition energy spectrum.},

  doi          = {10.1103/PHYSREVB.83.085409},

  url          = {https://www.osti.gov/biblio/21538132},
  journal      = {Physical Review. B, Condensed Matter and Materials Physics},

  issn         = {1098-0121},

  number       = 8,

  volume       = 83,

  place        = {United States},

  year         = {Tue Feb 15 00:00:00 EST 2011},

  month        = {Tue Feb 15 00:00:00 EST 2011}

}

Copy to clipboard

Journal Article:

https://doi.org/10.1103/PHYSREVB.83.085409

Other availability

Find in Google Scholar

Search WorldCat to find libraries that may hold this journal

Save / Share:

Export Metadata

Save to My Library

Similar records in OSTI.GOV collections:

Finite-size version of the excitonic instability in graphene quantum dots

Journal Article Paananen, Tomi; Egger, Reinhold - Physical Review. B, Condensed Matter and Materials Physics

By a combination of Hartree-Fock simulations, exact diagonalization, and perturbative calculations, we investigate the ground-state properties of disorder-free circular quantum dots formed in a graphene monolayer. Taking the reference chemical potential at the Dirac point, we study N{<=}15 interacting particles, where the fine structure constant {alpha} parametrizes the Coulomb interaction. We explore three different models: (i) Sucher's positive projection (''no-pair'') approach, (ii) a more general Hamiltonian conserving both N and the number of additional electron-hole pairs, and (iii) the full quantum electrodynamics problem, where only N is conserved. We find that electron-hole pair production is important for {alpha} > ormore »« less
https://doi.org/10.1103/PHYSREVB.84.155456
Imaging electrostatically confined Dirac fermions in graphene quantum dots

Journal Article Lee, Juwon; Wong, Dillon; Velasco Jr, Jairo; ... - Nature Physics

Electrostatic confinement of charge carriers in graphene is governed by Klein tunnelling, a relativistic quantum process in which particle-hole transmutation leads to unusual anisotropic transmission at p-n junction boundaries. Reflection and transmission at these boundaries affect the quantum interference of electronic waves, enabling the formation of novel quasi-bound states. Here we report the use of scanning tunnelling microscopy to map the electronic structure of Dirac fermions confined in quantum dots defined by circular graphene p-n junctions. The quantum dots were fabricated using a technique involving local manipulation of defect charge within the insulating substrate beneath a graphene monolayer. Inside suchmore »« less
Cited by 141
https://doi.org/10.1038/nphys3805

Full Text Available
Universal signatures of Dirac fermions in entanglement and charge fluctuations

Journal Article Crépel, Valentin; Hackenbroich, Anna; Regnault, Nicolas; ... - Physical Review. B

We study the entanglement entropy (EE) and charge fluctuations in models where the low-energy physics is governed by massless Dirac fermions. We focus on the response to flux insertion which, for the EE, is widely assumed to be universal, i.e., independent of the microscopic details. We provide an analytical derivation of the EE and charge fluctuations for the seminal example of graphene, using the dimensional reduction of its tight-binding model to the one-dimensional Su-Schrieffer-Heeger model. Our asymptotic expression for the EE matches the conformal field theory prediction. We show that the charge variance has the same asymptotic behavior, up tomore »« less
https://doi.org/10.1103/physrevb.103.235108

Full Text Available
Strong-Weak Duality via Jordan-Wigner Transformation: Using Fermionic Methods for Strongly Correlated su(2) Spin Systems

Journal Article Henderson, Thomas; Chen, Guo; Scuseria, Gustavo - Journal of Chemical Physics

The Jordan-Wigner transformation establishes a duality between $su(2)$ and fermionic algebras. We present qualitative arguments and numerical evidence that when mapping spins to fermions, the transformation makes strong correlation weaker, as demonstrated by the Hartree-Fock approximation to the transformed Hamiltonian. This result can be rationalized in terms of rank reduction of spin shift terms when transformed to fermions. Conversely, the mapping of fermions to qubits makes strong correlation stronger, complicating its solution when one uses qubit-based correlators. The presence of string operators poses challenges to the implementation of quantum chemistry methods on classical computers, but these can be dealt withmore »« less
https://doi.org/10.1063/5.0125124

Full Text Available
Wigner energy, odd-even mass staggering and the time-odd mean-fields

Journal Article Satula, Wojciech - AIP Conference Proceedings

Various properties of single-particle Hartree-Fock ground-state solutions in N{approx}Z nuclei are investigated. The emphasis is on a role of single-particle mean-field in odd-even mass staggering. It is shown that, unlike in traditional scenario originating from the Fermi gas or macroscopic models, the symmetry energy contribution to odd-even mass staggering is nearly cancelled by the contribution coming from the average level density. It allows to construct indicators probing both pairing as well as mean-field components to the odd-even mass staggering. The impact of the single-particle Hartree-Fock field on Wigner energy and residual pn interaction in odd-odd nuclei is also discussed. (c)more » 1999 American Institute of Physics.« less
https://doi.org/10.1063/1.59544

Similar Records