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Exciton formation in graphene bilayer

Exciton formation in graphene bilayer

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Exciton formation in graphene bilayer

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  1. 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)

  2. Outline • Introduction • Main work • Summary and Conclusion • Assumptions and Comments • Excitonic Superfluidity

  3. Introduction • Exciton: Bound state of an electron and an hole in an insulator or semiconductor ; Coulomb-correlated electron-hole pair. • Exciton in bilayer systems(semiconductors): • Strong magnetic field • All electrons reside in the lowest Landau Level • Electron-hole pairs form because of Coulomb attraction J. P. Eisenstein and A. H. MacDonald, Nature London 432, 691 (2004)

  4. Introduction(cont.) • Why Graphene? 1. It is atomically two dimensional. 2. Perfect particle-hole symmetry • Lecture note 1 of phy570X; • 2. E. McCann, D.S.L. Abergel, and Vladimir I. Fal’ko,European Physical Journal-special topics 148, (2007)

  5. Main work • The possibility of an excitonic instability in the biased graphene bilayer in the framework of Hartree-Fock theory Bernal stacking

  6. Main work (cont.) :The bare kinetic energy within the monolayer

  7. Main work-nearest (U1)

  8. Main work-nearest (U1)(cont.)

  9. Main work-second nearest(U2)

  10. Main work-(U2)(cont.)

  11. 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.

  12. Assumptions and Comments • Band truncation (Low energy approximation) • short-range Coulomb interaction: up to second nearest neighbor • Same-spin electron-hole exciton • Interlayer distance? • Consider U1 and U2 separately • Using different “order parameters” in the calculations for U1 and U2 cases • Exciton formation and BEC

  13. 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 Suand A. H. MacDonald ,Nature Physics  4, 799 (2008)