The tight-binding method is ideal for modeling small nanostructures. However, for modeling nanostructures with more than 25,000 atoms, the method is impractical on sequential computers due to long run times. Significant improvements in run time can be achieved through parallelization.

There are two parts to parallelizing this problem: creating the structure; and solving the Hamiltonian equation. The structure is created geometrically. We parallelize this by dividing the structure into layers. Communication is across layers. The starting point is a cubic structure that encompasses the desired nanostructure; the structure shape is created by pruning away the excess. We parallelize solving the Hamiltonian with PARPACK. The parallel implementation can handle arbitrary nanostructure shapes through an input file specification procedure.

We ran the code on the NIST NBS Cluster of 500Mhz Pentium III processors. Each processor has a Gigabyte of memory. For the structure consisting of three concentric spheres with diameters 3, 4, and 5 lattice units, the timing data closely matches the formula: T = 655.7 + 3116.0/N. T is execution time (in seconds), and N is the number of processors. The non-parallelizable computation time is 655.7 seconds; while the parallelizable portion of the computation uses 3116.0 seconds. Thus the portion of the code that was directly parallelizable with PARPACK is almost 83%.

Modeling Quantum Dots: The optics of self-assembled quantum dots, also known as artificial atoms, has been studied using our parallelization. Such systems contain up to a million atoms and can only be studied using the parallel implementation. We show how nanomechanical strain can be used to dynamically reengineer the optics of these quantum dots, giving a tool to manipulate mechanoexciton shape, fine-structure splitting and optical transitions, transfer carriers between dots and interact qubits for quantum processing. Most importantly, nanomechanical strain provides both phase and energy control to modify the inner workings of excitons. These are all capabilities needed to use QDs in nanophotonics, quantum information processing, and in optically active devices, such as optomechanical cavities and semiconductor nanotubes.