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Volumn 78, Issue 11, 2008, Pages

Optical spectra of doubly charged quantum dot molecules in electric and magnetic fields

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EID: 52949085831     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.78.115316     Document Type: Article
Times cited : (58)

References (64)
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    • Note that this change in sign applies to the term t. An additional sign change for the off-diagonal matrix elements responsible for tunneling occurs when we move from the X- and e2- Hamiltonians to the X2- Hamiltonian as a result of antisymmetrization of the three-particle wave functions.
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    • Interactions with other charges confined in the dots can introduce an additional small change in the tunneling rate between different excitonic species (which have different numbers of spectator charges) (Ref.). We have neglected these Coulomb corrections to the tunneling rate, which are generally negligible unless the tunnel barrier is quite thin. Note also that the tunneling matrix element now appears as -t rather than t, as it does in Eq. 1. This sign change is a result of the proper antisymmetrization of the basis states as defined in the Appendix 0. Because of the antisymmetrization, tunneling matrix elements in the Hamiltonians for the X2- and X2+ states pick up an additional minus sign relative to the e2- and h2+ state Hamiltonians. The sign of the tunneling matrix element does not change the calculation of energy levels at zero magnetic field, but it does determine the energy ordering of the symmetric and antisymmetric combinations of the basis states.
    • Interactions with other charges confined in the dots can introduce an additional small change in the tunneling rate between different excitonic species (which have different numbers of spectator charges) (Ref.). We have neglected these Coulomb corrections to the tunneling rate, which are generally negligible unless the tunnel barrier is quite thin. Note also that the tunneling matrix element now appears as -t rather than t, as it does in Eq. 1. This sign change is a result of the proper antisymmetrization of the basis states as defined in the Appendix 0. Because of the antisymmetrization, tunneling matrix elements in the Hamiltonians for the X2- and X2+ states pick up an additional minus sign relative to the e2- and h2+ state Hamiltonians. The sign of the tunneling matrix element does not change the calculation of energy levels at zero magnetic field, but it does determine the energy ordering of the symmetric and antisymmetric combinations of the basis states.
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    • Note that in the limit of infinite tunneling rate, which is equivalent to the merger of the two dots, this kinetic exchange splitting becomes the Pauli exclusion principle: The singlet state becomes the only allowed and energetically stable state.
    • Note that in the limit of infinite tunneling rate, which is equivalent to the merger of the two dots, this kinetic exchange splitting becomes the Pauli exclusion principle: The singlet state becomes the only allowed and energetically stable state.
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    • Light-hole states have been neglected.
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    • In principle an optical transition to the T0 triplet could also occur for the higher-energy electron-hole exchange-split state. However, the T0 triplet transition can be expected to be weak because at the resonance the ↑ electron is tunneling and cannot recombine with the hole (up double arrow sign). As a result, the overlap integral with the T0 triplet (where the ↑ electron is not tunneling) is substantially smaller than the overlap integral with the singlet (where the ↑ is tunneling).
    • In principle an optical transition to the T0 triplet could also occur for the higher-energy electron-hole exchange-split state. However, the T0 triplet transition can be expected to be weak because at the resonance the ↑ electron is tunneling and cannot recombine with the hole (up double arrow sign). As a result, the overlap integral with the T0 triplet (where the ↑ electron is not tunneling) is substantially smaller than the overlap integral with the singlet (where the ↑ is tunneling).
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    • Independent values of the electron and hole g factors are determined at electric fields far from any anticrossing region in order to eliminate the impact of resonant changes in the g factor.
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