2.1 Review on Density Functional Theory (DFT) . . . . . . . . . . . . . 6 2.1.1 Hohenberg and Kohn Theorems . . . . . . . . . . . . . . . . . 8 2.1.2 The Kohn-Sham Equations . . . . . . . . . . . . . . . . . . . 9 2.1.3 Exchange and Correlation Functionals . . . . . . . . . . . . . 12 2.1.4 The Hellmann-Feynman Theorem . . . . . . . . . . . . . . . . 14 2.2 Nudge Elastic Band (NEB) Calculations . . . . . . . . . . . . . . . . 15 2.3 Spin-Polarized Density Functional Theory Calculations
3.2 Honeycomb lattice structure in graphene (a) and first Brillouin zone (1BZ) of the honeycomb lattice (b). a) The vectors a1 and a2 are the lattice unit vectors in graphene and γ1 is the nearest-neighbor hopping parameter. b) The vectors b1 and b2 are the reciprocal lattice vectors. The points Γ, K(K0) and M are the center of 1BZ, the Dirac points and the middle of the 1BZ edges, respectively. . . . . . . . . . . . . 22
3.3 Graphene band-structure: Linear dispersion relation near Dirac points lead to 6-identical cones called Dirac-cones. . . . . . . . . . . . . . . . 24
3.4 Defects induced magnetic moments: The spin density projection (in µB/a.u.2 from around the (a) hydrogen chemisorption defect (∆) and (b) vacancy [7] (left figure).The spin-resolved DOS first principle calculation [8] (right figures) for the (a) single hydrogen passivation (b) vacancy; dashed curve shows the reference graphene DOC, the red curve is for the majority and the blue curve for the minority. In the right figures, the splitting between the quasi-localized (QL) state peaks (for hydrogen adsorption) and dangling-bond (DB) states (for vacancy) shows the exchange splitting [8]. Figures are reprinted with permission from Ref. [8] and Ref. [7] . . . . . . . . . . . . . . . . . . 28
3.5 Different type of dimer position (two adatoms) on graphene: (a) Metha, (b) ortho and (c) para . . . . . . . . . . . . . . . . . . . . . . 29
SPINTRONICS IN HALF-PASSIVATED GRAPHENE
A Dissertation
by
SHAYAN HEMMATIYAN
Submitted to the Office of Graduate and Professional Studies of Texas A&M University in partial fulfillment of the requirements for the degree of
SHAYAN HEMMATIYAN
https://arxiv.org/pdf/1612.06846v1.pdf
Latest and Greatest ! WOW
3.2 Honeycomb lattice structure in graphene (a) and first Brillouin zone (1BZ) of the honeycomb lattice (b). a) The vectors a1 and a2 are the lattice unit vectors in graphene and γ1 is the nearest-neighbor hopping parameter. b) The vectors b1 and b2 are the reciprocal lattice vectors. The points Γ, K(K0) and M are the center of 1BZ, the Dirac points and the middle of the 1BZ edges, respectively. . . . . . . . . . . . . 22
3.3 Graphene band-structure: Linear dispersion relation near Dirac points lead to 6-identical cones called Dirac-cones. . . . . . . . . . . . . . . . 24
3.4 Defects induced magnetic moments: The spin density projection (in µB/a.u.2 from around the (a) hydrogen chemisorption defect (∆) and (b) vacancy [7] (left figure).The spin-resolved DOS first principle calculation [8] (right figures) for the (a) single hydrogen passivation (b) vacancy; dashed curve shows the reference graphene DOC, the red curve is for the majority and the blue curve for the minority. In the right figures, the splitting between the quasi-localized (QL) state peaks (for hydrogen adsorption) and dangling-bond (DB) states (for vacancy) shows the exchange splitting [8]. Figures are reprinted with permission from Ref. [8] and Ref. [7] . . . . . . . . . . . . . . . . . . 28
3.5 Different type of dimer position (two adatoms) on graphene: (a) Metha, (b) ortho and (c) para . . . . . . . . . . . . . . . . . . . . . . 29
SPINTRONICS IN HALF-PASSIVATED GRAPHENE
A Dissertation
by
SHAYAN HEMMATIYAN
Submitted to the Office of Graduate and Professional Studies of Texas A&M University in partial fulfillment of the requirements for the degree of
SHAYAN HEMMATIYAN
https://arxiv.org/pdf/1612.06846v1.pdf
Latest and Greatest ! WOW
