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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)

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Outline Introduction Main work Summary and Conclusion Assumptions and Comments Excitonic Superfluidity

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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): 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

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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. Falko,European Physical Journal-special topics 148, (2007)

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

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

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Main work-nearest (U1)

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Main work-nearest (U1)(cont.)

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Main work-second nearest(U2)

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Main work-(U2)(cont.)

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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.

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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

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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)

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