Unfolding spinor wave functions and expectation values of general operators: Introducing the unfolding-density operator
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
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.
Condensed Matter Physics
IdentifiersURN: urn:nbn:se:liu:diva-114465DOI: 10.1103/PhysRevB.91.041116ISI: 000348477200002OAI: oai:DiVA.org:liu-114465DiVA: 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 18.104.22.1685) 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.2015-02-202015-02-202015-05-11