Quantum Dots

Quantum dots are semiconductor nanostructures on the order of a few nm in size, consisting of one material embedded in a material with a larger band gap. This results in single (or a few) electrons and/or holes being confined to the dot.  

Spin related phenomena in nanostructures

One of the leading approaches to constructing a quantum computer is to use electrons confined to semiconductor quantum dots. The manipulation and measurement of such confined carriers will be affected and limited by the properties of quantum dots. An understanding of the dynamics of and interactions between electrons in quantum dots is needed to develop a quantum computer, and can only be addressed through detailed numerical computations. 
The spin of an electron in a quantum dot is effected by electron-phonon interactions, static magnetic fields, polarized light, and intense laser pulses. For dots with more than one electron or hole, Coulomb interactions  (especially exchange), give rise to fine structure in the spectrum of electronic states. 

Nanowhiskers

A promising new type of quantum dot with better uniformity is the nanowhisker. Since the composition may be varied as the whisker is grown, confinement may be obtained in the direction along the whisker in addition to the transverse direction, leading to 3D confinement. Such structures are under intense experimental investigation, and theoretical results currently lag behind.  
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Material Combinatorics

Semiconductor heterostructures are made from a wide range of different materials.  However, because of lattice mismatch, different combinations are strained differently, resulting in very different electronic structure.  For example, the commonly used diagram of conduction and valence band energies vs lattice constant for different semiconductor materials is modified if the material in question is coherently strained to a substrate with a different lattice constant.  

Mats-Erik Pistol and I have been systematically exploring the electronic structure obtained from lattice mismatched heterostructures [Physical Review B, 78, 115319 (2008), Physical Review B 72, 205311 (2005)]. Such calculations produce a large amount of data, which is often difficult to convey using figures in a paper. To supplement our papers, we have made the results available in electronic form here.