RKKY Interaction In Bilayer
Graphene
Fariborz Parhizgar
Mohammad Sherafati
Reza Asgari
Sashi Satpathy
INSTITUTE FOR RESEARCH IN
FUNDAMENTAL SCIENCES (IPM)
1
Outline
RKKY Interaction
Graphene & It’s bilayer
RKKY in 2D system
RKKY in un-biased bilayer graphene
RKKY in biased bilayer graphene
2
RKKY INTERACTION
3
Motivation
RKKY: Indirect Exchange interaction between two
magnetic impurities via host material electrons.
Adatom properties
Spintronic applications
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Motivation
Electron spin oscillation around
magnetic impurity
Ordering of impurities:
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RKKY Interaction (Formalism)
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rr
0( , , )G r r E
0( , , )G r r E
2
1 1 2 2( , )RKKY i ij j
ij
H I R R I
0 0
1 2 1 2 2 1ˆ ˆ( , ) Im[ [ ( , , ) ( , , )]
F
ij i jR R d Tr G R R G R R
, , ,i j x y z
GRAPHENE & IT’S BILAYER
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Graphene Structure
Pseudo spin (A,B)
Valley degeneracy
Tunable Fermi energy
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( ) FE k v k
*0
0
0
F q
F q
v qH
v q
Bilayer Graphene (BLG)
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*
4
* *
† 4 3
*
4
*
4 3
( ) ( )
( ) ( ) ( )( ) ( )
( ) ( )
( ) ( ) ( )
k
f k t f k
f k f k f kH k k
t f k f k
f k f k f k
Bilayer Graphene
BLG: Dispersion relation
Dispersion relation:
2Band effective model:
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2 22 2 2 2 2 2 2 4( ) / 4
2 4
t Vv p v p V t t
† 2
2
1 00 ( )1
0 12 2( ) 0low
VH
m
Bilayer Graphene: Band Structure
Klein Tunelling in BLG
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0 ( )
( ) 0
j
x y
j
x y
p ipH
p ip
Klein Tunneling in Bilayer Graphene
RKKY INTERACTION IN 2D SYSTEMS
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RKKY in 2DEG
1 2ˆ .RKKYH J S S
RKKY Interaction in Graphene
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Sherafati et. al. PRB, 83, 165425
RKKY in Graphene
2
1 (( ). )(2 )
( / )AA F
Cos K K RJ C Sin k R
R a
3
1 (( ). )
( / )AA
Cos K K RJ C
R a
Sherafati et. al. PRB, 84, 125416
RKKY Interaction in Graphene
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RKKY in spin polarized Graphene
Parhizgar et. al. PRB, 87, 125402
2
1 2 1 2 1 2[ ( ) ( ]RKKY x x x y y z z zH J S S S S J S S
RKKY Interaction in Graphene
Topological Insulators
2DEG + Rashba spin orbit
MoS2
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RKKY in Rashba spin orbit systems
Parhizgar et. al. PRB, 87, 125401
1 2 1 2 1 2ˆ . ( )RKKY z z
H I DM zH J S S J S S J S S
RKKY INTERACTION IN
UN-BIASED BILAYER
GRAPHENE
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Un-biased, undoped
Parhizgar et al. Phys. Rev. B 87,165429 (2013)
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ˆ ( , , )RKKY
FH I V R E
Un-biased, doped
Parhizgar et al. Phys. Rev. B 87,165429 (2013)
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1 11 1 2
( ) (2 )( ')Fk RB BB B F
CJ R Sin k R e C
R
Necessity of 4-band model
Parhizgar et al. Phys. Rev. B 87,165429 (2013)
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RKKY INTERACTION IN BIASED BILAYER GRAPHENE
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Biased, doped
Parhizgar et al. Phys. Rev. B 87,165429 (2013)
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Biased, undoped
Parhizgar et al. Phys. Rev. B 87,165429 (2013)
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Thanks For your Attention