We study the free-electron gas in an Apollonian network within the
tight-binding framework. The scale-free and small-world character of the
underlying lattice is known to result in a quite structured energy
spectrum with deltalike singularities, gaps, and minibands. After an
exact numerical diagonalization of the corresponding adjacency matrix of
the network with a finite number of generations, we employ a scaling
analysis of the moments of the density of states to characterize its
multifractality and report the associated singularity spectrum. The
fractal nature of the energy spectrum is also shown to be reflected in
the thermodynamic behavior by logarithmic modulations on the temperature
dependence of the specific heat. The absence of chiral symmetry of the
Apollonian network leads to distinct thermodynamic behaviors due to
electrons and holes thermal excitations.
%0 Journal Article
%1 WOS:000262976900010
%A de Oliveira, I N
%A de Moura, F A B F
%A Lyra, M L
%A Jr., J S Andrade
%A Albuquerque, E L
%C ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA
%D 2009
%I AMER PHYSICAL SOC
%J PHYSICAL REVIEW E
%K calculations} density electronic fractals; gas; heat; of properties; specific states; thermodynamic tight-binding {electron
%N 1, 2
%R 10.1103/PhysRevE.79.016104
%T Free-electron gas in the Apollonian network: Multifractal energy
spectrum and its thermodynamic fingerprints
%V 79
%X We study the free-electron gas in an Apollonian network within the
tight-binding framework. The scale-free and small-world character of the
underlying lattice is known to result in a quite structured energy
spectrum with deltalike singularities, gaps, and minibands. After an
exact numerical diagonalization of the corresponding adjacency matrix of
the network with a finite number of generations, we employ a scaling
analysis of the moments of the density of states to characterize its
multifractality and report the associated singularity spectrum. The
fractal nature of the energy spectrum is also shown to be reflected in
the thermodynamic behavior by logarithmic modulations on the temperature
dependence of the specific heat. The absence of chiral symmetry of the
Apollonian network leads to distinct thermodynamic behaviors due to
electrons and holes thermal excitations.
@article{WOS:000262976900010,
abstract = {We study the free-electron gas in an Apollonian network within the
tight-binding framework. The scale-free and small-world character of the
underlying lattice is known to result in a quite structured energy
spectrum with deltalike singularities, gaps, and minibands. After an
exact numerical diagonalization of the corresponding adjacency matrix of
the network with a finite number of generations, we employ a scaling
analysis of the moments of the density of states to characterize its
multifractality and report the associated singularity spectrum. The
fractal nature of the energy spectrum is also shown to be reflected in
the thermodynamic behavior by logarithmic modulations on the temperature
dependence of the specific heat. The absence of chiral symmetry of the
Apollonian network leads to distinct thermodynamic behaviors due to
electrons and holes thermal excitations.},
added-at = {2022-05-23T20:00:14.000+0200},
address = {ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA},
author = {de Oliveira, I N and de Moura, F A B F and Lyra, M L and Jr., J S Andrade and Albuquerque, E L},
biburl = {https://www.bibsonomy.org/bibtex/2202284fd2794765282faf4160a14600b/ppgfis_ufc_br},
doi = {10.1103/PhysRevE.79.016104},
interhash = {37aab627716e155060adcd438859399b},
intrahash = {202284fd2794765282faf4160a14600b},
issn = {1539-3755},
journal = {PHYSICAL REVIEW E},
keywords = {calculations} density electronic fractals; gas; heat; of properties; specific states; thermodynamic tight-binding {electron},
number = {1, 2},
publisher = {AMER PHYSICAL SOC},
pubstate = {published},
timestamp = {2022-05-23T20:00:14.000+0200},
title = {Free-electron gas in the Apollonian network: Multifractal energy
spectrum and its thermodynamic fingerprints},
tppubtype = {article},
volume = 79,
year = 2009
}