The calculation of transport properties and density of states of disordered solids

MacKinnon, A.

doi:10.1007/bf01328846

Cited by 315 publications

(221 citation statements)

References 14 publications

Supporting

Mentioning

217

Contrasting

Order By: Relevance

“…Instead, we expand on well known recursive Green's function methods. 38,39 These methods are commonly applied to transport studies of finite or semi-infinite structures sandwiched between semi-infinite leads. Here, periodicity of the central region is at most along a single direction and the Hamiltonian can easily be written in block-diagonal form, which is the basis upon which the recursive Green's function formalism is built.…”

Section: Theory and Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Hofstadter butterflies and magnetically induced band-gap quenching in graphene antidot lattices

Pedersen

2013

Phys. Rev. B

View full text Add to dashboard Cite

We study graphene antidot lattices (GALs) in magnetic fields. Using a tight-binding model and a recursive Green's function technique that we extend to deal with periodic structures, we calculate Hofstadter butterflies of GALs. We compare the results to those obtained in a simpler gapped graphene model. A crucial difference emerges in the behavior of the lowest Landau level, which in a gapped graphene model is independent of magnetic field. In stark contrast to this picture, we find that in GALs the band gap can be completely closed by applying a magnetic field. While our numerical simulations can only be performed on structures much smaller than can be experimentally realized, we find that the critical magnetic field for which the gap closes can be directly related to the ratio between the cyclotron radius and the neck width of the GAL. In this way, we obtain a simple scaling law for extrapolation of our results to more realistically sized structures and find resulting quenching magnetic fields that should be well within reach of experiments.

show abstract

Section: Theory and Methodsmentioning

confidence: 99%

“…38,39 We include the results here for completeness. For the final step of the recursive algorithm we take into account periodicity of the structure via Eqs.…”

Section: Appendix: Recursive Methodsmentioning

confidence: 99%

Hofstadter butterflies and magnetically induced band-gap quenching in graphene antidot lattices

Pedersen

2013

Phys. Rev. B

View full text Add to dashboard Cite

show abstract

“…5 Numerical algorithm for the calculation of the conductance is described in Ref. [154,156] and in Ref. [157] for the case of critical quantum Hall regime.…”

Section: Two Dimensional Critical Regimesmentioning

confidence: 99%

Numerical analysis of the Anderson localization

Markoš¹

2006

Acta Physica Slovaca. Reviews and Tutorials

135

242

View full text Add to dashboard Cite

The aim of this paper is to demonstrate, by simple numerical simulations, the main transport properties of disordered electron systems. These systems undergo the metal insulator transition when either Fermi energy crosses the mobility edge or the strength of the disorder increases over critical value. We study how disorder affects the energy spectrum and spatial distribution of electronic eigenstates in the diffusive and insulating regime, as well as in the critical region of the metal-insulator transition. Then, we introduce the transfer matrix and conductance, and we discuss how the quantum character of the electron propagation influences the transport properties of disordered samples. In the weakly disordered systems, the weak localization and anti-localization as well as the universal conductance fluctuation are numerically simulated and discussed. The localization in the one dimensional system is described and interpreted as a purely quantum effect. Statistical properties of the conductance in the critical and localized regimes are demonstrated. Special attention is given to the numerical study of the transport properties of the critical regime and to the numerical verification of the single parameter scaling theory of localization. Numerical data for the critical exponent in the orthogonal models in dimension 2 < d ≤ 5 are compared with theoretical predictions. We argue that the discrepancy between the theory and numerical data is due to the absence of the self-averaging of transmission quantities. This complicates the analytical analysis of the disordered systems. Finally, theoretical methods of description of weakly disordered systems are explained and their possible generalization to the localized regime is discussed. Since we concentrate on the one-electron propagation at zero temperature, no effects of electronelectron interaction and incoherent scattering are discussed in the paper.

show abstract

“…The model ͑1͒ shows a MIT at the critical disorder w c Ӎ16.5. 13 The numerical calculation of the conductances uses a standard Green's function recursion technique 14 that yields the transmission matrix t of the sample. The latter is connected to the two-probe conductance of the sample by the Landauer-Büttiker formula…”

Section: Numerical Investigation At the Anderson Transitionmentioning

confidence: 99%

Boundary conditions, the critical conductance distribution, and one-parameter scaling

Braun¹,

Hofstetter

Montambaux

et al. 2001

Phys. Rev. B

View full text Add to dashboard Cite

We study the influence of boundary conditions transverse to the transport direction for disordered mesoscopic conductors both at the Anderson metal-insulator transition and in the metallic regime. We show that the boundary conditions strongly influence the conductance distribution exactly at the metal-insulator transition and we discuss implications for the standard picture of one-parameter scaling. We show in particular that the scaling function that describes the change of conductance with system size depends on the boundary conditions from the metallic regime up to the metal-insulator transition. An experiment is proposed that might test the correctness of the one-parameter scaling theory.

show abstract

The calculation of transport properties and density of states of disordered solids

Cited by 315 publications

References 14 publications

Hofstadter butterflies and magnetically induced band-gap quenching in graphene antidot lattices

Hofstadter butterflies and magnetically induced band-gap quenching in graphene antidot lattices

Numerical analysis of the Anderson localization

Boundary conditions, the critical conductance distribution, and one-parameter scaling

Contact Info

Product

Resources

About