Optical absorption in quantum dots: Coupling to longitudinal optical phonons treated exactly

Abstract

Optical transitions in a semiconductor quantum dot are theoretically investigated, with emphasis on the coupling to longitudinal optical phonons, and including excitonic effects. When limiting to a finite number of m electron and n hole levels in the dot, the model can be solved exactly within numerical accuracy. Crucial for this to work is the absence of dispersion of the phonons. A suitable orthogonalization procedure leaves only m(m + 1)/2 + n(n + 1)/2 − 2 phonon modes to be coupled to the electronic system. We calculate the linear optical polarization following a delta pulse excitation, and by a subsequent Fourier transformation the resulting optical absorption. This strict result is compared with a frequently used approximation modeling the absorption as a convolution between spectral functions of electron and hole, which tends to overestimate the effect of the phonon coupling. Numerical results are given for two electron and three hole states in a quantum dot made from the polar material CdSe. Parameter values are chosen such that a quantum dot with a resonant sublevel distance can be compared with a nonresonant one.

Linear spectrum of a quantum dot coupled to a nanocavity

“…As examples we quote the broad sidebands originating by the coupling to longitudinal acoustic phonons beyond perturbation theory, 2,3,5,[15][16][17] or the similar effect due to optical phonons. 18,19 In addition to these homogeneous modifications of the bare QD spectrum, other significant spectral changes can arise when the QD is multiply excited, due to transitions between continuum states in the wetting layer above the QD confining barrier. This effect occurs already at moderate excitation and leads to a sizeable enhancement of off-resonance light emission.…”

Nonorthogonal theory of polarons and application to pyramidal quantum dots

“…Within the approximation of monochromatic LO-modes for the Fröhlich interaction, electrons only couple to a finite number of lattice modes as analytically explained through an algebraic decomposition introduced by Stauber et al 22 Their procedure constructs an orthonormalized basis of relevant lattice modes from the finite set of phonon creation/annihilation operators naturally appearing in the Fröhlich Hamiltonian. This leads to a numerically solvable model of QDPs 23 , which can be viewed as an extension of the work by Ferreira et al 24 In this work, the polaron problem is tackled from a different viewpoint: the full electron-phonon Hamiltonian is reformulated in terms of non-orthogonal modes, which naturally span all coupled and uncoupled crystal vibrations. The non-orthogonal structure is preserved from the beginning to the end and exhibits undisputable advantages for computation and physical understanding.…”

Second-Order Resonant Polaron in a Self-Assembled Quantum Dot

“…Such resonant polarons are an object of current interest, both from the point of view of their properties in various QD systems as well as of the formal methods that can be used to describe them [2][3][4]. The spectrum of a resonant polaron can easily be described for a single-phonon (first order) resonance [5].…”