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Biexciton-Exciton C ascades in Graphene Quantum Dots

Biexciton-Exciton C ascades in Graphene Quantum Dots. CAP 2014, Sudbury Isil Ozfidan. I.Ozfidan , M. Korkusinski,A.D.Guclu,J.McGuire and P.Hawrylak , PRB89,085310 (2014). Motivation.

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Biexciton-Exciton C ascades in Graphene Quantum Dots

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  1. Biexciton-ExcitonCascades in Graphene Quantum Dots CAP 2014, Sudbury IsilOzfidan I.Ozfidan, M. Korkusinski,A.D.Guclu,J.McGuire and P.Hawrylak, PRB89,085310 (2014).

  2. Motivation • Biexciton-Exciton Cascades in semiconductor quantum dots for entangled photon generation.-Benson et al, PRL 84, 2513 (2000). XX σ+ σ- Two paths for radiative recombination X2 X1 σ- σ+ GS

  3. Motivation • Biexciton-Exciton Cascades in semiconductor quantum dots for entangled photon generation. -Korkusinski et al, Phys. Rev. B 79, 035309 (2009). XX XX σ+ σ- H V Two paths for radiative recombination But in semiconductor qdots, due to anisotropy the X levels are not degenerate. X2 X2 X1 X1 σ- V σ+ H GS GS Post-growth tuning of excitonic splitting.

  4. Motivation XX σ+ σ- C168 X2 X1 σ- σ+ GS Biexciton-Exciton Cascades in graphene quantum dots for entangled photon generation.

  5. Outline Theory Introducing C168 Band-Edge Excitons and Biexcitons Auger Coupling Conclusion

  6. Theory pz Tight Binding + HartreeFock + CI sp2 Tight-binding Hamiltonian, τij is the tunelling element sp2 sp2 Mobile electrons occupy the spin-degenerate pz orbitals I.Ozfidan, M. Korkusinski,A.D.Guclu,J.McGuire and P.Hawrylak, PRB89,085310 (2014).

  7. Theory Tight Binding + HartreeFock + CI Electron-electron interactions Coulomb elements • : dielectric constant • Screening by sigma electrons and surrounding fluid is introduced • as the dielectric constant Slater pz orbitals

  8. Theory Tight Binding + HartreeFock + CI Exchange Direct Density Matrix Mean Field – HartreeFock Hamiltonian

  9. Theory Tight Binding + HartreeFock + CI Mean Field – HartreeFock Hamiltonian ci+→bi+ Tight-binding states →HartreeFock states Rotating the basis!

  10. Theory Tight Binding + HartreeFock + CI Rewrite the full Hamiltonian in the HF basis:

  11. Theory Tight Binding + HartreeFock + CI Configuration – Interaction Hamiltonian Corellated ground And excited states

  12. Outline Theory Introducing C168 Band-Edge Excitons and Biexcitons Auger Coupling Conclusion

  13. C3 Symmetry of C168 We can characterize the C168 eigenstates according to their rotational symmetry Atom j in section A; 3 identical segments. Create states by combining the same atom from each segment with a phase. and m is the angular momentum m={0,1,2} Then the Hamiltonian becomes block diagonal w.r.t. the phase; angular momentum, m.

  14. C3 Symmetry of C168 Since m=1 and m=2 states are conjugates of each other, we have degenerate m=1,2 subspaces. m=0 m=1 m=2

  15. C3 Symmetry of C168 m=0 m=1 m=2 m=2m=1 Degenerate band edge due to symmetry! m=1m=2

  16. C3 Symmetry of C168 m=0 m=1 m=2 m=2m=1 Looking at the dipole element between these eigenfunctions; Optical Selection rule! ∆m!=0 m=1m=2

  17. Outline Theory Introducing C168 Band-Edge Excitons and Biexcitons Auger Coupling Conclusion

  18. Band edge is robust Only C168?

  19. Band edge is robust Any GQD with C3 symmetry! Triangle

  20. Band edge is robust Any GQD with C3 symmetry! Hexagon

  21. Band edge is robust Any GQD with C3 symmetry! Star

  22. Band edge is robust Any GQD with C3 symmetry! The Superman

  23. Band Edge Excitons Δm=0 Excitons Dark Transitions X0A X0B σ+ Δm=1 Excitons X1 Dipole allowed Transitions Δm=-1 Excitons σ- X2 TOTAL = 8

  24. Band Edge ExcitonsΔm=±1 singlet triplet σ- σ+ σ- σ+

  25. Band Edge ExcitonsΔm=0 σ- σ+ σ- σ+ Only optically active BE-X Singlet ∆m=±1

  26. Band Edge-Biexcitons Δm=0Δm=1 Δm=-1 Δm=-2 Δm=2 Total=18

  27. Band Edge Biexcitons Too many to talk about!

  28. Band Edge-Biexcitons Only Interested in the Cascade ones emit to the bright excitons?

  29. Band Edge-Biexcitons Only Interested in the Cascade ones emit to the bright excitons? Δm=-2 Δm=2 Δm=0Δm=1 Δm=-1

  30. Band Edge BiexcitonsΔm=±2 σ- σ+

  31. Band Edge BiexcitonsΔm=0 σ+ σ-

  32. Band Edge BiexcitonsΔm=0 σ+ σ- GREAT CANDIDATE!

  33. Outline Theory Introducing C168 Band-Edge Excitons and Biexcitons Auger Coupling Conclusion

  34. CI-Space & Auger Coupling Smallest CI-Space to properly understand auger coupling of BE-XXs ?? Eg

  35. CI-Space & Auger Coupling Eg

  36. CI-Space & Auger Coupling Eg

  37. CI-Space & Auger Coupling Eg Eg

  38. CI-Space & Auger Coupling Eg Eg

  39. CI-Space & Auger Coupling Eg Eg Eg

  40. CI-Space & Auger Coupling Eg • GS+X+XX in this 15 valence (v), 23 conduction (c) • level – space we have: 172846 states Eg Eg

  41. CI-Space & Auger Coupling Eg • GS+X+XX in this 15 valence (v), 23 conduction (c) • level – space we have: 172846 states • Introduce cut-offs, check convergence. Eg Eg

  42. Evolution of the band-edge XXs 58.29meV XX binding energies 47.94meV

  43. Spectral Function of XX Turn on XX – X interactions: XX & X correlation

  44. Outline Theory Introducing C168 Band-Edge Excitons and Biexcitons Auger Coupling Conclusion

  45. XX-X cascade identified We’ve got a candidate!buthow stable is he? Conclusion EXX-EX=2.07eV σ+ σ- EX-GS=2.13eV σ- σ+

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