Gauge-invariant formulation of spin-current density-functional theory

Physical Review B - Condensed Matter and Materials Physics

Volumn 81, Issue 12, 2010, Pages

  Abedinpour, Saeed H ^a,b   Vignale, G ^a   Tokatly, I V ^c,d,e  

^a UNIVERSITY OF MISSOURI   (United States)

^b INSTITUTE FOR RESEARCH IN FUNDAMENTAL SCIENCES IPM   (Iran)

^c BASQUE FOUNDATION FOR SCIENCE   (Spain)

^d UNIVERSITY OF THE BASQUE COUNTRY UPV EHU   (Spain)

^e NATIONAL RESEARCH UNIVERSITY OF ELECTRONIC TECHNOLOGY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77955127894     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.81.125123     Document Type: Article

References (24)

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15. Here Greek indices go from 0 to 3, while Latin indices go from 1 to 3. Moreover we are distinguishing three and four vectors with bold characters and overhead arrows, respectively.
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17. The field strength is usually defined as a tensor: F μ ν α τ α = D μ A ν α τ α - D ν A μ α τ α. For our purpose it is simpler to work with the dual vector field B i α. Notice that B i α B i α = F i j α F i j α.
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21. Notice Eq. defines only the spin part of the xc vector potential, A x c, i a. The ordinary charge component A x c, i 0 is still given by the VR weak field approximation.
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23. We have added a α 2 / 2 term to the single particle part of the original Rashba Hamiltonian to make it gauge-invariant. Evidently this does not affect the exchange-correlation energy.
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