2020
DOI: 10.1103/physrevb.101.235142
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Spin-orbit coupling in periodic systems with broken time-reversal symmetry: Formal and computational aspects

Abstract: We discuss the treatment of spin-orbit coupling (SOC) in time reversal symmetry broken periodic systems for relativistic electronic structure calculations of materials within the generalized noncollinear Kohn-Sham density functional theory (GKS-DFT). We treat SOC self-consistently and express the GKS orbitals in a two-component spinor basis. Crucially, we present a methodology (and its corresponding implementation) for the simultaneous self-consistent treatment of SOC and exact non-local Fock exchange operator… Show more

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Cited by 36 publications
(31 citation statements)
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“…The origin of gap opening in the Dirac cones are due to hybridization of the electronic wave function between the top and bottom surfaces with the same quantum numbers [71]. In our case, the hybridization causes the time reversal symmetry breaking under SOC [72] and the Dirac cones behave massive states [73,74]. Similarly, linear gapped Dirac cone (i) and distorted gapped Dirac cone (j) are found near the Fermi level (above and below) in region K-Γ (FIG.…”
Section: Electronic and Magnetic Properties Without Vacancy Defectmentioning
confidence: 71%
See 1 more Smart Citation
“…The origin of gap opening in the Dirac cones are due to hybridization of the electronic wave function between the top and bottom surfaces with the same quantum numbers [71]. In our case, the hybridization causes the time reversal symmetry breaking under SOC [72] and the Dirac cones behave massive states [73,74]. Similarly, linear gapped Dirac cone (i) and distorted gapped Dirac cone (j) are found near the Fermi level (above and below) in region K-Γ (FIG.…”
Section: Electronic and Magnetic Properties Without Vacancy Defectmentioning
confidence: 71%
“…6B). The gap opening results from the time reversal symmetry breaking [72] and hybridization [71] of the opposite spin states (FIG. 6B).…”
Section: Electronic and Magnetic Properties Without Vacancy Defectmentioning
confidence: 99%
“…31,35 The origin of gap opening in the Dirac cones are due to hybridization of the electronic wave function between the top and bottom surfaces with the same quantum numbers. 53 In our case, the hybridization causes the time reversal symmetry breaking under SOC 54 and the Dirac cones behave massive states 55,56 . Similarly, linear gapped Dirac cone (i) and distorted gapped Dirac cone (j) are found near the Fermi level (above and below) in region K-Γ (Figure 4Q).…”
Section: Electronic and Magnetic Properties Without Vacancy Defectmentioning
confidence: 73%
“…Spin-orbitcoupling effects (SOC) on the band structures of pure and doped hafnia using richer basis sets [21,22,23,24]. for all atoms have been considered by applying a newly developed scheme in CRYSTAL based on two-component spin-current density functional theory [25,26]. In brief For Y and Hf we used a fully relativistic effective core potential (ECP) including both the scalarrelativistic AREP and the spin-orbit SOREP parts, developed by Peterson et al [27] and Figgen et al [28].…”
Section: Resultsmentioning
confidence: 99%