Exchange Splitting of Zero-Dimensional Exciton Levels

Abstract

A theory of nonanalytic (long-range) exchange interaction between an electron and a hole is developed for zero-dimensional excitons in semiconductor nanostructures. Two particular cases are considered in detail: (i) that of exciton confined in a spherical nanocrystal and (ii) a quantum-well exciton localized as a whole on an anisotropic island of well-width monolayer fluctuation.

Band-Edge Exciton in CdSe and Other II–VI and III–V Compound Semiconductor Nanocrystals − Revisited

“…Complete neglect of the long-range exchange interaction in refs and was justified by reference to the work of Takagahara, who, using the Wannier function approach, had argued that the long-range exchange interaction vanishes from the exciton fine structure identically in a spherical shape semiconductor NC with simple 2-fold degenerate conduction and valence bands. However, this conclusion disagreed with effective mass calculations of the exchange interaction in bound excitons in bulk semiconductors as well as with later calculations of the exchange interaction in semiconductor quantum dots conducted both within the effective mass approximation − and within the Wannier function approach, collectively indicating that the long-range exchange interaction does not vanish in spherical NCs.…”

“…Consequently, the position of these levels, which could be potentially seen in photoluminescence excitation (PLE) experiments, has never been properly described within the theory which neglected the long-range exchange interaction . It was previously demonstrated that the long-range exchange interaction is critical for description of these upper optically active levels. , In Figure B, we show that even neglecting the deviation of the NC shape from spherical, the full theory very well describes the PL Stokes shift and PLE experiments conducted by several experimental groups.…”

“…The long-range exchange interaction, η 1S 3/2 1S e LR , within the 1S 3/2 1S e exciton manifold can be written as: ,,, where ℏω LT is the bulk exciton longitudinal transverse splitting, which, in CdSe, is equal to 0.95 meV . The dimensionless functions ξ 1S 3/2 1S e (β) and Q 0 (1) (β) in eq are defined in the Supporting Information via the electron and hole radial wave functions, and κ = ϵ in /ϵ out is the ratio of internal, ϵ in , to external, ϵ out , high-frequency dielectric constants.…”

Spin coherence generation and detection in spherical nanocrystals

“…Therefore, the trion state is fourfold degenerate, and its states can be labeled as F z = ±3/2, ±1/2. In the spherical (isotropic) approximation F z is the component of the hole total angular momentum, which includes the orbital momentum of size-quantized state, L, and the angular momentum of the Bloch function, J [20][21][22][23]. The singlet trion wave function can be written as a product of two-electron function…”

Direct-Bandgap InAs Quantum-Dots Have Long-Range Electron−Hole Exchange whereas Indirect Gap Si Dots Have Short-Range Exchange

“…The LR e-h exchange interaction is an add-on to the theory and does not emerge from its structure. For example, Goupalov and Ivchenko introduced an additional term A LR = π 9 χ ℏ ω LT true( a B R true) 3 where χ is another structural parameter defined in ref , ℏω LT is the longitudinal-transverse splitting of the bulk exciton, and a B is the Bohr radius in the corresponding bulk semiconductor. While this model was determined to be consistent with earlier experimental observations , of Δ X ∼ R −3 in CdSe dots, recent experiments found Δ X ∼ R −2 .…”