The structure and photoluminescence (PL) characteristics of AlGaAs quantum wires self-formed by metallorganic vapor-phase epitaxy in inverted tetrahedral pyramids are reported. Capillarity-driven Ga−Al segregation yields vertical quantum wires (VQWRs) at the center of the pyramid, connected to more-weakly segregated vertical quantum wells (VQWs) formed along their wedges. The segregation is evidenced in transmission electron microscope images and in the PL spectra of these structures. Transitions between quantum-confined electron and hole states in the VQWR are identified in the micro-PL spectra with energies in good agreement with model calculations. The temperature dependence of the micro-PL spectra clearly reveals efficient carrier capture into the VQWR from the VQWs, particularly at an intermediate temperature range (∼100 K) where carrier mobility is enhanced. These wires offer new possibilities for tailoring the confinement potential in one-dimensional systems.

We present a general theory for semiconductor polarons in the framework of the Fröhlich interaction between electrons and phonons. The latter is investigated using non-commuting phonon creation/annihilation operators associated with a natural set of non-orthogonal modes. This setting proves effective for mathematical simplification and physical interpretation and reveals a nested coupling structure of the Fröhlich interaction. The theory is non-perturbative and well adapted for strong electron-phonon coupling, such as found in quantum dot (QD) structures. For those particular structures we introduce a minimal model that allows the computation and qualitative prediction of the spectrum and geometry of polarons. The model uses a generic non-orthogonal polaron basis, baptized "the natural basis". Accidental and symmetry-related electronic degeneracies are studied in detail and are shown to generate unentangled zero-shift polarons, which we consistently eliminate. As a practical example, these developments are applied to realistic pyramidal GaAs QDs. The energy spectrum and the 3D-geometry of polarons are computed and analyzed, and prove that realistic pyramidal QDs clearly fall in the regime of strong coupling. Further investigation reveals an unexpected substructure of "weakly coupled strong coupling regimes", a concept originating from overlap considerations. Using Bennett's entanglement measure, we finally propose a heuristic quantification of the coupling strength in QDs.

A general formalism for the maximal symmetrization and reduction of fields ͑MSRFs͒ is proposed and applied to wave functions in solid-state nanostructures. Its primary target is to provide an essential tool for the study and analysis of the electronic and optical properties of semiconductor quantum heterostructures with relatively high point-group symmetry and studied with the k · p formalism. Nevertheless the approach is valid in a much larger framework than k · p theory; it is applicable to arbitrary systems of coupled partial differential equations ͑e.g., strain equations or Maxwell equations͒. This general MSRF formalism makes extensive use of group theory at all levels of analysis. For spinless problems ͑scalar equations͒, one can use a systematic spatial domain reduction ͑SDR͒ technique which allows, for every irreducible representation, to reduce the set of equations on a minimal domain with automatic incorporation of the boundary conditions at the border, which are shown to be nontrivial in general. For a vectorial or spinorial set of functions, the SDR technique must be completed by the use of an optimal basis in vectorial or spinorial space ͑in a crystal we call it the optimal Bloch function basis͒. The full MSR formalism thus consists of three steps: ͑1͒ explicitly separate spatial ͑or Fourier space͒ and vectorial ͑spinorial͒ part of the operators and eigenstates, ͑2͒ choose, according to the symmetry and well defined prescriptions ͑e.g., specific transformation properties͒, optimal fully symmetrized basis for both spatial and vector ͑or spin͒ space, and ͑3͒ finally apply the SDR to every individual scalar ultimate component function. We show that with such a formalism the coupling between different vectorial ͑spinorial͒ components by symmetry operations becomes minimized and every ultimately reduced envelope function acquires a welldefined specific symmetry. The advantages are numerous: sharper insights on the symmetry properties of every eigenstate, minimal coupling schemes ͑analytically and computationally exploitable at the component function level͒, and minimal computing domains. The formalism can be applied also as a postprocessing operation, offering all subsequent analytical and computational advantages of symmetrization. The specific case of a quantum wire with C 3v point group symmetry is used as a concrete illustration of the application of MSRF.

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