1
|
Modelling of Electron and Thermal Transport in Quasi-Fractal Carbon Nitride Nanoribbons. FRACTAL AND FRACTIONAL 2022. [DOI: 10.3390/fractalfract6020115] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Abstract
In this work, using calculations based on the density functional theory, molecular dynamics, non-equilibrium Green functions method, and Monte Carlo simulation, we study electronic and phonon transport in a device based on quasi-fractal carbon nitride nanoribbons with Sierpinski triangle blocks. Modifications of electronic and thermal conductance with increase in generation g of quasi-fractal segments are estimated. Introducing energetic disorder, we study hopping electron transport in the quasi-fractal nanoribbons by Monte Carlo simulation of a biased random walk with generalized Miller–Abrahams transfer rates. Calculated time dependencies of the mean square displacement bear evidence of transient anomalous diffusion. Variations of anomalous drift-diffusion parameters with localization radius, temperature, electric field intensity, and energy disorder level are estimated. The hopping in quasi-fractal nanoribbons can serve as an explicit physical implementation of the generalized comb model.
Collapse
|
2
|
Pessoa NL, Barbosa ALR, Vasconcelos GL, Macedo AMS. Multifractal magnetoconductance fluctuations in mesoscopic systems. Phys Rev E 2021; 104:054129. [PMID: 34942834 DOI: 10.1103/physreve.104.054129] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2021] [Accepted: 10/28/2021] [Indexed: 06/14/2023]
Abstract
We perform a multifractal detrended fluctuation analysis of the magnetoconductance data of two standard types of mesoscopic systems: a disordered nanowire and a ballistic chaotic billiard, with two different lattice structures. We observe in all cases that multifractality is generally present and that it becomes stronger in the quantum regime of conduction, i.e., when the number of open scattering channels is small. We argue that this behavior originates from correlations induced by the magnetic field, which can be characterized through the distribution of conductance increments in the corresponding "stochastic time series," with the magnetic field playing the role of a fictitious time. More specifically, we show that the distributions of conductance increments are well fitted by q Gaussians and that the value of the parameter q is a useful quantitative measure of multifractality in magnetoconductance fluctuations.
Collapse
Affiliation(s)
- N L Pessoa
- Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, Pernambuco, Brazil
- Centro de Apoio à Pesquisa, Universidade Federal Rural de Pernambuco, 52171-900 Recife, Pernambuco, Brazil
| | - A L R Barbosa
- Departamento de Física, Universidade Federal Rural de Pernambuco, 52171-900 Recife, Pernambuco, Brazil
| | - G L Vasconcelos
- Departamento de Física, Universidade Federal do Paraná, 81531-980 Curitiba, Paraná, Brazil
| | - A M S Macedo
- Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, Pernambuco, Brazil
| |
Collapse
|
3
|
Fractal Generalization of the Scher–Montroll Model for Anomalous Transit-Time Dispersion in Disordered Solids. MATHEMATICS 2020. [DOI: 10.3390/math8111991] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
The Scher–Montroll model successfully describes subdiffusive photocurrents in homogeneously disordered semiconductors. The present paper generalizes this model to the case of fractal spatial disorder (self-similar random distribution of localized states) under the conditions of the time-of-flight experiment. Within the fractal model, we calculate charge carrier densities and transient current for different cases, solving the corresponding fractional-order equations of dispersive transport. Photocurrent response after injection of non-equilibrium carriers by the short laser pulse is expressed via fractional stable distributions. For the simplest case of one-sided instantaneous jumps (tunneling) between neighboring localized states, the dispersive transport equation contains fractional Riemann–Liouville derivatives on time and longitudinal coordinate. We discuss the role of back-scattering, spatial correlations induced by quenching of disorder, and spatiotemporal non-locality produced by the fractal trap distribution and the finite velocity of motion between localized states. We derive expressions for the photocurrent and transit time that allow us to determine the fractal dimension of the distribution of traps and the dispersion parameter from the time-of-flight measurements.
Collapse
|
4
|
Tempered Fractional Equations for Quantum Transport in Mesoscopic One-Dimensional Systems with Fractal Disorder. FRACTAL AND FRACTIONAL 2019. [DOI: 10.3390/fractalfract3040047] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
New aspects of electron transport in quantum wires with Lévy-type disorder are described. We study the weak scattering and the incoherent sequential tunneling in one-dimensional quantum systems characterized by a tempered Lévy stable distribution of spacing between scatterers or tunneling barriers. The generalized Dorokhov–Mello–Pereyra–Kumar equation contains the tempered fractional derivative on wire length. The solution describes the evolution from the anomalous conductance distribution to the Dorokhov function for a long wire. For sequential tunneling, average values and relative fluctuations of conductance and resistance are calculated for different parameters of spatial distributions. A tempered Lévy stable distribution of spacing between barriers leads to a transition in conductance scaling.
Collapse
|
5
|
Kotimäki V, Räsänen E, Hennig H, Heller EJ. Fractal dynamics in chaotic quantum transport. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:022913. [PMID: 24032907 DOI: 10.1103/physreve.88.022913] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2013] [Indexed: 06/02/2023]
Abstract
Despite several experiments on chaotic quantum transport in two-dimensional systems such as semiconductor quantum dots, corresponding quantum simulations within a real-space model have been out of reach so far. Here we carry out quantum transport calculations in real space and real time for a two-dimensional stadium cavity that shows chaotic dynamics. By applying a large set of magnetic fields we obtain a complete picture of magnetoconductance that indicates fractal scaling. In the calculations of the fractality we use detrended fluctuation analysis-a widely used method in time-series analysis-and show its usefulness in the interpretation of the conductance curves. Comparison with a standard method to extract the fractal dimension leads to consistent results that in turn qualitatively agree with the previous experimental data.
Collapse
Affiliation(s)
- V Kotimäki
- Nanoscience Center, Department of Physics, University of Jyväskylä, FI-40014 Jyväskylä, Finland
| | | | | | | |
Collapse
|
6
|
Onat B, Konuk M, Durukanoğlu S, Dereli G. Energetics and atomic relaxations of Cu nanowires: the effect of local strain and cross-sectional area. NANOTECHNOLOGY 2009; 20:075707. [PMID: 19417435 DOI: 10.1088/0957-4484/20/7/075707] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
We have calculated the activation energies for several single atom and vacancy diffusion processes on Cu nanowires with the axial orientation of [Formula: see text], using the nudged elastic band technique based on the interaction potential obtained from the embedded atom method. It is shown that the dimer-initiated local strain and its relief at the transition state have a significant effect on the characteristics of self-surface diffusion mechanisms on nanowires. Contrary to the case for cylindrical multishell-type Cu nanowires, the vacancy formation energy for rectangular nanowires is maximum in the core region and is nearly zero at the corner of the nanowire. In addition, the activation energy barriers for the vacancy diffusion processes taking place in the core region are found to be higher than those occurring near the corner of the nanowire. Our calculations further show that the vacancy diffusion processes taking place near the corner of the wire are dictated by the lower coordination of the surrounding atoms. From the structural investigation of nanowires, we have also established that multilayer relaxations for rectangular nanowires with smaller cross-sectional area cannot be defined.
Collapse
Affiliation(s)
- Berk Onat
- Informatics Institute, Istanbul Technical University, Maslak, Istanbul, Turkey
| | | | | | | |
Collapse
|
7
|
Fujita T, Okada H, Koyama K, Watanabe K, Maekawa S, Chen MW. Unusually small electrical resistance of three-dimensional nanoporous gold in external magnetic fields. PHYSICAL REVIEW LETTERS 2008; 101:166601. [PMID: 18999696 DOI: 10.1103/physrevlett.101.166601] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2007] [Revised: 06/27/2008] [Indexed: 05/27/2023]
Abstract
We report the electric conductivity of three-dimensional (3D) nanoporous gold at low temperatures and in strong magnetic fields. It was found that topologically disordered 3D nanoporosity leads to extremely low magnetoresistance and anomalous temperature dependence as the characteristic length of nanoporous gold is tuned to be approximately 14 nm. This study underscores the importance of 3D topology of a nanostructure on electronic transport properties and has implications in manipulating electron transport by tailoring 3D nanostructures.
Collapse
Affiliation(s)
- T Fujita
- WPI Advanced Institute for Materials Research, Tohoku University, Sendai, Japan
| | | | | | | | | | | |
Collapse
|
8
|
Hennig H, Fleischmann R, Hufnagel L, Geisel T. Fractal conductance fluctuations of classical origin. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:015202. [PMID: 17677525 DOI: 10.1103/physreve.76.015202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2006] [Indexed: 05/16/2023]
Abstract
In mesoscopic systems, conductance fluctuations are a sensitive probe of electron dynamics and chaotic phenomena. We show that the conductance of a purely classical chaotic system, with either fully chaotic or mixed phase space, generically exhibits fractal conductance fluctuations unrelated to quantum interference. This might explain the unexpected dependence of the fractal dimension of the conductance curves on the (quantum) phase breaking length observed in experiments on semiconductor quantum dots.
Collapse
Affiliation(s)
- H Hennig
- Max Planck Institute for Dynamics and Self-Organization, 37073 Göttingen, Germany
| | | | | | | |
Collapse
|
9
|
|
10
|
Guarneri I, Terraneo M. Fractal fluctuations in quantum integrable scattering. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:015203. [PMID: 11800724 DOI: 10.1103/physreve.65.015203] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2001] [Indexed: 05/23/2023]
Abstract
We theoretically and numerically demonstrate that completely integrable scattering processes may exhibit fractal transmission fluctuations, due to typical spectral properties of integrable systems. Similar properties also occur with scattering processes in the presence of strong dynamical localization, thus explaining recent numerical observations of fractality in the latter class of systems.
Collapse
Affiliation(s)
- Italo Guarneri
- International Center for the Study of Dynamical Systems, Università degli Studi dell'Insubria, Via Valleggio 11, 22100 Como, Italy
| | | |
Collapse
|
11
|
Benenti G, Casati G, Guarneri I, Terraneo M. Quantum fractal fluctuations. PHYSICAL REVIEW LETTERS 2001; 87:014101. [PMID: 11461467 DOI: 10.1103/physrevlett.87.014101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2000] [Indexed: 05/23/2023]
Abstract
We numerically analyze quantum survival probability fluctuations in an open, classically chaotic system. In a quasiclassical regime and in the presence of classical mixed phase space, such fluctuations are believed to exhibit a fractal pattern, on the grounds of semiclassical arguments. In contrast, we work in a classical regime of complete chaoticity and in a deep quantum regime of strong localization. We provide evidence that fluctuations are still fractal, due to the slow, purely quantum algebraic decay in time produced by dynamical localization. Such findings considerably enlarge the scope of the existing theory.
Collapse
Affiliation(s)
- G Benenti
- International Center for the Study of Dynamical Systems, Università degli Studi dell'Insubria, Via Valleggio 11, 22100 Como, Italy
| | | | | | | |
Collapse
|
12
|
Ketzmerick R, Hufnagel L, Steinbach F, Weiss M. New class of eigenstates in generic hamiltonian systems. PHYSICAL REVIEW LETTERS 2000; 85:1214-1217. [PMID: 10991515 DOI: 10.1103/physrevlett.85.1214] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2000] [Revised: 04/28/2000] [Indexed: 05/23/2023]
Abstract
In mixed systems, besides regular and chaotic states, there are states supported by the chaotic region mainly living in the vicinity of the hierarchy of regular islands. We show that the fraction of these hierarchical states scales as Planck's over 2pi(alpha) and we relate the exponent alpha = 1-1/gamma to the decay of the classical staying probability P(t) approximately t(-gamma). This is numerically confirmed for the kicked rotor by studying the influence of hierarchical states on eigenfunction and level statistics.
Collapse
Affiliation(s)
- R Ketzmerick
- Max-Planck-Institut fur Stromungsforschung and Institut fur Nichtlineare Dynamik der Universitat Gottingen, Bunsenstrasse 10, 37073 Gottingen, Germany
| | | | | | | |
Collapse
|
13
|
Huckestein B, Ketzmerick R, Lewenkopf CH. Quantum transport through ballistic cavities: soft vs hard quantum chaos. PHYSICAL REVIEW LETTERS 2000; 84:5504-5507. [PMID: 10990980 DOI: 10.1103/physrevlett.84.5504] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/1999] [Indexed: 05/23/2023]
Abstract
We study transport through a two-dimensional billiard attached to two infinite leads by numerically calculating the Landauer conductance and the Wigner time delay. In the generic case of a mixed phase space we find a power-law distribution of resonance widths and a power-law dependence of conductance increments apparently reflecting the classical dwell time exponent, in striking difference to the case of a fully chaotic phase space. Surprisingly, these power laws appear on energy scales below the mean level spacing, in contrast to semiclassical expectations.
Collapse
Affiliation(s)
- B Huckestein
- Institut fur Theoretische Physik, Universitat zu Koln, D-50937 Koln, Germany
| | | | | |
Collapse
|
14
|
Casati G, Guarneri I, Maspero G. Fractal survival probability fluctuations. PHYSICAL REVIEW LETTERS 2000; 84:63-66. [PMID: 11015835 DOI: 10.1103/physrevlett.84.63] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/28/1999] [Indexed: 05/23/2023]
Abstract
We study fluctuations of survival probability in an open quantum system classically described by a map with a mixed phase space. Our results provide the first numerical support to theoretical predictions that such fluctuations have a fractal structure, quantitatively related to the algebraic decay of the classical survival probability.
Collapse
Affiliation(s)
- G Casati
- International Center for the Study of Dynamical Systems, Via Lucini 3, 22100 Como, Italy and Istituto Nazionale di Fisica della Materia, Unita di Milano, Via Celoria 16, 20133 Milano, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Milan
| | | | | |
Collapse
|
15
|
|