Exciton formation in graphene bilayer

PHYSICAL REVIEW B 78, 045401 (2008)

Raoul Dillenschneider, and Jung Hoon Han

Presented by Wan-Ju Li

02/25/2009

PHYSICAL REVIEW B 78, 121401(R) (2008)

Outline

• Introduction

• Main work

• Summary and Conclusion

• Assumptions and Comments

• Excitonic Superfluidity

Introduction

• Exciton: Bound state of an electron and an hole in an insulator or se

miconductor ; Coulomb-correlated electron-hole pair.

• Exciton in bilayer systems(semiconductors):

J. P. Eisenstein and A. H. MacDonald, Nature London 432, 691 (2004)

1. Strong magnetic field

2. All electrons reside in the lowest Landau Level

3. Electron-hole pairs form because of Coulomb attraction

Introduction(cont.)

• Why Graphene?1. It is atomically two dimensional.

2. Perfect particle-hole symmetry

1. Lecture note 1 of phy570X;

2. 2. E. McCann, D.S.L. Abergel, and Vladimir I. Fal’ko,European Physical Journal-special topics 148, (2007)

Main work

• The possibility of an excitonic instability in the biased graphene bilayer in the framework of Hartree-Fock theory

CVHH 0

Bernal stacking

Main work (cont.)

:The bare kinetic energy within the monolayerk

Main work-nearest (U1)

1~,5.3~

052.0

9.2~

0

0

1

t

V

t

Ut

t

eVt

T

k

C

5.8

1.0

9.2

0

1

t

Ut

V

eVt

T

Main work-nearest (U1)(cont.)

0T 1t

V

Main work-second nearest(U2)

1~,5.1~

052.0

9.2~

2

t

V

t

Ut

t

eVt

C

3

1

9.2

2

t

Ut

V

eVt

Main work-(U2)(cont.)

?T

1

052.0

9.2

t

Vt

t

eVt

Summary and Conclusion

• The short-ranged Coulomb interaction was introduced for both nearest U1 and second nearest U2 between the two layers.

• The critical strength is U1c / t ~3.5 for a bias V/t~1; U2c / t~1.5 at V/ t~1.

• Doping by applying the voltage difference between the bilayer can control the excitonic properties of the graphene bilayer.

• intercalation of nondoping and insulating atomic layers between the carbon layers could reduce significantly in such a way that the screened Coulomb interaction U obeys the condition U>Uc and excitons could form.

t

Assumptions and Comments

• Band truncation (Low energy approximation)• short-range Coulomb interaction: up to second n

earest neighbor• Same-spin electron-hole exciton• Interlayer distance? • Consider U1 and U2 separately • Using different “order parameters” in the calculat

ions for U1 and U2 cases• Exciton formation and BEC

Superfluidity

• Bose-Einstein Condensation of Excitons

• Room-temperature superfluidity in Graphene bilayer system

1. Hongki Min, Rafi Bistritzer, Jung-Jung Su, and A. H. MacDonald, Physical Review B 78, 121401(R) (2008); 2. J. P. Eisenstein and A. H. MacDonald, Nature 432, 691 (2004); 3. Jung-Jung Su and A. H. MacDonald ,Nature Physics  4, 799 (2008)