Electron transport, interaction and spin in graphene and - DiVA
RKKY Interaction In Graphene systems
Transcript of RKKY Interaction In Graphene systems
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
4
Motivation
Electron spin oscillation around
magnetic impurity
Ordering of impurities:
5
RKKY Interaction (Formalism)
6
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
7
Graphene Structure
Pseudo spin (A,B)
Valley degeneracy
Tunable Fermi energy
8
( ) FE k v k
*0
0
0
F q
F q
v qH
v q
Bilayer Graphene (BLG)
9
*
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:
10
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
11
0 ( )
( ) 0
j
x y
j
x y
p ipH
p ip
Klein Tunneling in Bilayer Graphene
RKKY INTERACTION IN 2D SYSTEMS
12
13
RKKY in 2DEG
1 2ˆ .RKKYH J S S
RKKY Interaction in Graphene
14
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
15
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
16
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
17
Un-biased, undoped
Parhizgar et al. Phys. Rev. B 87,165429 (2013)
18
ˆ ( , , )RKKY
FH I V R E
Un-biased, doped
Parhizgar et al. Phys. Rev. B 87,165429 (2013)
19
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)
20
RKKY INTERACTION IN BIASED BILAYER GRAPHENE
21
Biased, doped
Parhizgar et al. Phys. Rev. B 87,165429 (2013)
22
Biased, undoped
Parhizgar et al. Phys. Rev. B 87,165429 (2013)
23
24
Thanks For your Attention