### Speaker

Dr
Constantine Yannouleas
(School of Physics, Georgia Institute of Technology)

### Description

The physics of condensed-matter nanosystems exhibits
remarkable analogies with
atomic nuclei. Examples are: Plasmons corresponding to Giant
resonances [1],
electronic shells, de- formed shapes, and fission [2],
beta-type decay, strongly
correlated phenomena associated with symmetry breaking and
symmetry restoration
[3], etc. Most recently, analogies with relativistic
quantum-field theories (RQFT) and
high-energy particle physics are beeing explored in the
field of graphene nanostructures
[4].
The talk will review these analogies focusing in particular
on the following three aspects:
(1) The shell-correction method (SCM, commonly known as
Strutinsky’s averaging
method and introduced in the 1960’s in nuclear physics) was
formulated [5] in the
context of density functional theory (DFT).
Applications of the DFT-SCM (and of a semiempirical variant,
SE-SCM, closer to the
nuclear Strutinsky approach) to condensed-matter finite
systems will be discussed,
including the charging and fragmentation of metal clusters,
fullerenes, and metallic
nanowires [5]. The DFT-SCM offers an improvement compared to
the use of Thomas-
Fermi gradient expansions for the kinetic energy density
functional in the framework of
orbital-free DFT.
(2) A unified description of strongly correlated phenomena
in finite systems of repelling
particles [whether electrons in quantum dots (QDs) or
ultracold bosons in rotating
traps] has been achieved through a two-step method of
symmetry breaking at the
unrestricted Hartree- Fock (UHF) level and of subsequent
symmetry restoration via post
Hartree-Fock projection techniques [3]. The general
principles of the two-step method
can be traced to nuclear theory (Peierls and Yoccoz) and
quantum chemistry (L ̈owdin).
This method can describe a wide variety of novel strongly
correlated phenomena,
including:
(I) Chemical bonding and dissociation in quantum dot
molecules and in single elliptic
QDs, with potential technological applications to
solid-state quantum computing.
(II) Particle localization at the vertices of concentric
polygonal rings and formation of
rotating (and other less symmetric) Wigner molecules in
quantum dots and ultracold
rotating bosonic clouds [6].
(III) At high magnetic field (electrons) or rapid rotation
(neutral bosons), the method
yields analytic trial wave functions in the lowest Landau
level [7], which are an
alternative to the fractional-quantum-Hall-effect (FQHE)
composite-fermion and
Jastrow-Laughlin approaches.
(3) The physics of planar graphene nanorings with armchair
edge terminations shows
analo- gies with the physics described by the RQFT
Jackiw-Rebbi model and the related
Su-Schrieffer- Heeger model of polyacetylene [4]. This part
of the talk will describe the
emergence of exotic states and properties, like solitons,
charge fractionization, and
nontrivial topological insulators, in these graphene
nanosystems.
[1] C. Yannouleas, R.A. Broglia, M. Brack, and P.F.
Bortignon, Phys. Rev. Lett. 63, 255
(1989); [2] C. Yannouleas, U. Landman, and R.N. Barnett, in
Metal Clusters, edited by
W. Ekardt (John-Wiley, New York, 1999) Ch. 4, p. 145; [3] C.
Yannouleas and U.
Landman, Rep. Prog. Phys. 70, 2067 (2007), and references
therein; [4] I.
Romanovsky, C. Yannouleas, and U. Landman, Phys. Rev. B 87,
165431 (2013); Phys.
Rev. B 89, 035432 (2014). [5] C. Yannouleas and U. Landman,
Phys. Rev. B 48, 8376
(1993); Ch. 7 in ”Recent Advances in Orbital-Free Density
Functional Theory,” Y.A.
Wang and T.A. Wesolowski Eds. (Word Scientific, Singapore,
2013) p. 203
(arXiv:1004.3536); [6] C. Yannouleas and U. Landman, Phys.
Rev. Lett. 82, 5325
(1999); I. Romanovsky, C. Yannouleas, and U. Landman, Phys.
Rev. Lett. 97, 090401
(2006). [7] C. Yannouleas and U. Landman, Phys. Rev. A 81,
023609 (2010); Phys.
Rev. B 84, 165327 (2011).

### Primary author

Dr
Constantine Yannouleas
(School of Physics, Georgia Institute of Technology)