Abstract
Theory of exciton fine structure in semiconductor quantum dots and its dependence on quantum-dot anisotropy and external lateral electric field is presented. The effective exciton Hamiltonian including long-range electron-hole exchange interaction is derived within the $k\ensuremath{\cdot}p$ effective-mass approximation. The exchange matrix elements of the Hamiltonian are expressed explicitly in terms of electron and hole envelope functions. The matrix element responsible for the ``bright'' exciton splitting is identified and analyzed. An excitonic fine structure for a model quantum dot with quasi-two-dimensional anisotropic harmonic oscillator confining potential is analyzed as a function of the shape anisotropy, size, and applied lateral electric field.
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