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Biexciton-Exciton Cascades in Graphene Quantum DotsCAP 2014, SudburyIsil OzfidanI.Ozfidan, M. Korkusinski,A.D.Guclu,J.McGuire and P.Hawrylak, PRB89,085310 (2014).MotivationBiexciton-Exciton Cascades in semiconductor quantum dots for entangled photon generation.-Bensonetal,PRL84,2513(2000).

XXX1X2GS++--

Two paths for radiative recombination

MotivationBiexciton-Exciton Cascades in semiconductor quantum dots for entangled photon generation. -Korkusinskietal,Phys. Rev. B 79, 035309 (2009).

XXX1X2GSVHHVBut in semiconductor qdots, due to anisotropy the X levels are not degenerate.Post-growth tuning of excitonic splitting.XXX1X2GS++--

Two paths for radiative recombinationMotivationBiexciton-Exciton Cascades in graphene quantum dots for entangled photon generation.

C168XXX1X2GS++--OutlineTheoryIntroducing C168Band-Edge Excitons and BiexcitonsAuger CouplingConclusion

TheoryTight Binding + Hartree Fock + CITight-binding Hamiltonian, ij is the tunelling element

sp2pzsp2sp2

I.Ozfidan, M. Korkusinski,A.D.Guclu,J.McGuire and P.Hawrylak, PRB89,085310 (2014).Mobile electrons occupy the spin-degenerate pz orbitals: dielectric constantScreening by sigma electrons and surrounding fluid is introducedas the dielectric constant

TheoryTight Binding + Hartree Fock + CIElectron-electron interactions

Slater pz orbitalsCoulomb elementsTheoryTight Binding + Hartree Fock + CI

Mean Field Hartree Fock HamiltonianDensity MatrixDirectExchangeTheoryTight Binding + Hartree Fock + CI

Mean Field Hartree Fock Hamiltonianci+ bi+Tight-binding states Hartree Fock statesRotating the basis!TheoryTight Binding + Hartree Fock + CI

Rewrite the full Hamiltonian in the HF basis:TheoryTight Binding + Hartree Fock + CICorellated groundAnd excited statesConfiguration Interaction Hamiltonian

OutlineTheoryIntroducing C168Band-Edge Excitons and BiexcitonsAuger CouplingConclusionC3 Symmetry of C168

We can characterize the C168eigenstates according to their rotational symmetryThen the Hamiltonian becomes block diagonalw.r.t. the phase; angular momentum, m.

and m is the angular momentum m={0,1,2}3 identical segments. Create states by combining the same atom from each segment with a phase.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=2C3 Symmetry of C168

m=1 m=2m=2 m=1

m=0 m=1 m=2Degenerate band edgedue to symmetry!C3 Symmetry of C168

Optical Selection rule! m!=0m=1 m=2m=2 m=1

m=0 m=1 m=2Looking at the dipole element between these eigenfunctions;OutlineTheoryIntroducing C168Band-Edge Excitons and BiexcitonsAuger CouplingConclusionBand edge is robust

Only C168?

Band edge is robust

Any GQD withC3 symmetry!

TriangleBand edge is robust

Any GQD withC3 symmetry!

HexagonBand edge is robust

Any GQD withC3 symmetry!

StarBand edge is robust

Any GQD withC3 symmetry!

The Superman

Band Edge Excitonsm=0 Excitonsm=1 Excitonsm=-1 ExcitonsDipole allowed Transitions+-X1X2X0AX0BDark TransitionsTOTAL = 8

-Band Edge Excitons

m=1-++tripletsinglet

Band Edge Excitons

m=0+-Only optically active BE-XSinglet m=1-+m=-2 m=2m=0 m=1m=-1Band Edge-BiexcitonsTotal=18

Band Edge Biexcitons

Too many to talk about!

Band Edge-Biexcitons Only Interested in the Cascadeones emit to the bright excitons?m=-2 m=2m=0 m=1m=-1Band Edge-Biexcitons Only Interested in the Cascadeones emit to the bright excitons?

Band Edge Biexcitons

m=2+-

Band Edge Biexcitons

m=0-+

Band Edge Biexcitons

m=0GREAT CANDIDATE!

-+OutlineTheoryIntroducing C168Band-Edge Excitons and BiexcitonsAuger CouplingConclusion

CI-Space & Auger CouplingEgSmallest CI-Space to properly understand auger coupling of BE-XXs ??

EgCI-Space & Auger Coupling

EgCI-Space & Auger Coupling

EgEgCI-Space & Auger Coupling

EgEgCI-Space & Auger Coupling

EgEgEgCI-Space & Auger Coupling

EgEgEgGS+X+XX in this 15 valence (v), 23 conduction (c)level space we have: 172846 states

CI-Space & Auger Coupling

EgEgEgGS+X+XX in this 15 valence (v), 23 conduction (c)level space we have: 172846 states

Introduce cut-offs, check convergence.

CI-Space & Auger CouplingEvolution of the band-edge XXs

58.29meV47.94meVXX bindingenergies

Spectral Function of XXTurn on XX X interactions: XX & X correlationOutlineTheoryIntroducing C168Band-Edge Excitons and BiexcitonsAuger CouplingConclusionXX-X cascade identified

Weve got a candidate!

buthow stable is he?

-+-+EXX-EX=2.07eVEX-GS=2.13eVConclusion