Anderson localization in two-dimensional graphene with short-range disorder: One-parameter scaling and finite-size effects

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dc.contributor Aalto-yliopisto fi
dc.contributor Aalto University en
dc.contributor.author Fan, Z.
dc.contributor.author Uppstu, A.
dc.contributor.author Harju, A.
dc.date.accessioned 2018-08-08T10:00:42Z
dc.date.available 2018-08-08T10:00:42Z
dc.date.issued 2014
dc.identifier.citation Fan , Z , Uppstu , A & Harju , A 2014 , ' Anderson localization in two-dimensional graphene with short-range disorder: One-parameter scaling and finite-size effects ' PHYSICAL REVIEW B , vol 89 , no. 24 , 245422 , pp. 1-14 . DOI: 10.1103/PhysRevB.89.245422 en
dc.identifier.issn 1098-0121
dc.identifier.issn 1550-235X
dc.identifier.other PURE UUID: 4457071e-4ce2-4e33-ba6c-4ec72d545498
dc.identifier.other PURE ITEMURL: https://research.aalto.fi/en/publications/anderson-localization-in-twodimensional-graphene-with-shortrange-disorder-oneparameter-scaling-and-finitesize-effects(4457071e-4ce2-4e33-ba6c-4ec72d545498).html
dc.identifier.other PURE LINK: http://journals.aps.org/prb/abstract/10.1103/PhysRevB.89.245422
dc.identifier.other PURE FILEURL: https://research.aalto.fi/files/26800935/PhysRevB.89.245422.pdf
dc.identifier.uri https://aaltodoc.aalto.fi/handle/123456789/33059
dc.description.abstract We study Anderson localization in graphene with short-range disorder using the real-space Kubo-Greenwood method implemented on graphics processing units. Two models of short-range disorder, namely, the Anderson on-site disorder model and the vacancy defect model, are considered. For graphene with Anderson disorder, localization lengths of quasi-one-dimensional systems with various disorder strengths, edge symmetries, and boundary conditions are calculated using the real-space Kubo-Greenwood formalism, showing excellent agreement with independent transfer matrix calculations and superior computational efficiency. Using these data, we demonstrate the applicability of the one-parameter scaling theory of localization length and propose an analytical expression for the scaling function, which provides a reliable method of computing the two-dimensional localization length. This method is found to be consistent with another widely used method which relates the two-dimensional localization length to the elastic mean free path and the semiclassical conductivity. Abnormal behavior at the charge neutrality point is identified and interpreted to be caused by finite-size effects when the system width is comparable to or smaller than the elastic mean free path. We also demonstrate the finite-size effect when calculating the two-dimensional conductivity in the localized regime and show that a renormalization group β function consistent with the one-parameter scaling theory can be extracted numerically. For graphene with vacancy disorder, we show that the proposed scaling function of localization length also applies. Last, we discuss some ambiguities in calculating the semiclassical conductivity around the charge neutrality point due to the presence of resonant states. en
dc.format.extent 1-14
dc.format.mimetype application/pdf
dc.language.iso en en
dc.relation.ispartofseries PHYSICAL REVIEW B en
dc.relation.ispartofseries Volume 89, issue 24 en
dc.rights openAccess en
dc.subject.other 114 Physical sciences en
dc.subject.other 221 Nanotechnology en
dc.subject.other 214 Mechanical engineering en
dc.subject.other 218 Environmental engineering en
dc.title Anderson localization in two-dimensional graphene with short-range disorder: One-parameter scaling and finite-size effects en
dc.type A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä fi
dc.description.version Peer reviewed en
dc.contributor.department Department of Applied Physics en
dc.subject.keyword graphene
dc.subject.keyword localization
dc.subject.keyword transport
dc.subject.keyword 114 Physical sciences
dc.subject.keyword 221 Nanotechnology
dc.subject.keyword 214 Mechanical engineering
dc.subject.keyword 218 Environmental engineering
dc.identifier.urn URN:NBN:fi:aalto-201808084459
dc.identifier.doi 10.1103/PhysRevB.89.245422
dc.type.version publishedVersion


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