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

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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)

20

RKKY INTERACTION IN BIASED BILAYER GRAPHENE

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Biased, doped

Parhizgar et al. Phys. Rev. B 87,165429 (2013)

22

Biased, undoped

Parhizgar et al. Phys. Rev. B 87,165429 (2013)

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Thanks For your Attention