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Unfolding spinor wave functions and expectation values of general operators: Introducing the unfolding-density operator
Linköping University, Department of Physics, Chemistry and Biology, Theoretical Chemistry. Linköping University, The Institute of Technology.
DIPC, San Sebastian 20018, Basque Country, Spain; Tomsk State Univ, Tomsk 634050, Russia; St Petersburg State Univ, St Petersburg 198504, Russia .
Linköping University, Department of Physics, Chemistry and Biology, Theoretical Chemistry. Linköping University, The Institute of Technology.
Linköping University, Department of Physics, Chemistry and Biology, Theoretical Chemistry. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-1345-0006
2015 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 91, 041116(R)-041120(R) p.Article in journal (Refereed) Published
Abstract [en]

We show that the spectral weights W mK ⃗ (k ⃗ ) used for the unfolding of two-component spinor eigenstates ∣ ∣ ψ SC mK ⃗ ⟩=|α⟩|ψ SC mK ⃗ ,α⟩+|β⟩|ψ SC mK ⃗ ,β⟩ can be decomposed as the sum of the partial spectral weights W μ mK ⃗ (k ⃗ ) calculated for each component μ=α,β independently, effortlessly turning a possibly complicated problem involving two coupled quantities into two independent problems of easy solution. Furthermore, we define the unfolding-density operator ρ ˆ K ⃗ (k ⃗ ;ɛ) , which unfolds the primitive cell expectation values φ pc (k ⃗ ;ɛ) of any arbitrary operator φ ˆ according to φ pc (k ⃗ ;ɛ)=Tr(ρ ˆ K ⃗ (k ⃗ ;ɛ)φ ˆ ) . As a proof of concept, we apply the method to obtain the unfolded band structures, as well as the expectation values of the Pauli spin matrices, for prototypical physical systems described by two-component spinor eigenfunctions.

Place, publisher, year, edition, pages
2015. Vol. 91, 041116(R)-041120(R) p.
National Category
Condensed Matter Physics
URN: urn:nbn:se:liu:diva-114465DOI: 10.1103/PhysRevB.91.041116ISI: 000348477200002OAI: diva2:789925

P. V. C. M, S. S., and J.B. acknowledge the Swedish Research Council (VR) for funding. S. S. T. acknowledges funding from the University of Basque Country UPV/EHU (GIC07-IT-756-13), the Departamento de Educacion del Gobierno Vasco and the Spanish Ministerio de Ciencia e Innovacion (FIS2010-19609-C02-01), the Tomsk State University Competitiveness Improvement Program, the Saint Petersburg State University (project and the Spanish Ministry of Economy and Competitiveness MINECO (FIS2013-48286-C2-1-P). Computer resources were allocated by the National Supercomputer Centre, Sweden, through SNAC and the MATTER consortium, as well as in the SKIF-Cyberia and CRYSTAL supercomputers at Tomsk State University.

Available from: 2015-02-20 Created: 2015-02-20 Last updated: 2015-05-11
In thesis
1. Electronic properties of complex interfaces and nanostructures
Open this publication in new window or tab >>Electronic properties of complex interfaces and nanostructures
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis investigates the structural and electronic properties of graphene, polyaromatic hydrocarbon (PAH) molecules, and other carbon-based materials, when interacting with metallic surfaces, as well as under the influence of different types of perturbations. Density functional theory, incorporating van der Waals interactions, has been employed.

PAH molecules can, with gradual accuracy, be considered as approximations to an infinite graphene layer. A method to estimate the contributions to the binding energies and net charge transfers from different types of carbon atoms and CH groups in graphene- and PAH-metal systems has been generalized. In this extended method, the number and the nature of the functional groups is determined using a first-principles approach, rather than intuitively or through empirical considerations. Relationships between charge transfers, interface dipole moments and work functions in such systems are explored.

Although the electronic structure of physisorbed graphene keeps most of the features of freestanding graphene, the use of large supercells in calculations makes it difficult to resolve the changes introduced in the band structures of such materials. In this thesis, this was the initial motivation for the development of a method to perform the Brillouin zone unfolding of band structures. This method, as initially developed, is shown to be of general use for any periodic structure, and is even further generalized – through the introduction of the unfolding density operator – to tackle the unfolding of the eigenvalues of any arbitrary operator, with  both scalar as well as spinor eigenstates.

A combined experimental and theoretical investigation of the self-assembly of a binary mixture of 4,9-diaminoperylene-quinone-3,10-diimine (DPDI) and 3,4,9,10-perylene-tetracarboxylic acid dianhydride (PTCDA) molecules on Ag(111) is presented. The DFT calculations performed here allow for the investigation of the interplay between molecule-molecule and molecule-surface interactions in the network.

Besides the main results mentioned above, this thesis also incorporates a study of silicon-metal nanostructures, as well as an investigation of the use of hybrid graphene-graphane structures as prototypes for atomically precise design in nanoelectronics.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2015. 80 p.
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1668
National Category
Physical Sciences Condensed Matter Physics Atom and Molecular Physics and Optics
urn:nbn:se:liu:diva-117848 (URN)10.3384/diss.diva-117848 (DOI)978-91-7519-066-2 (print) (ISBN)
Public defence
2015-06-05, Nobel, Hus B, Campus Valla, Linköping, 09:00 (English)
Available from: 2015-05-11 Created: 2015-05-11 Last updated: 2015-05-12Bibliographically approved

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