Linear combination of bulk bands method for large-scale electronic structure calculations on strained nanostructures

A "strained linear combination of bulk bands" method is introduced for calculating the single-particle electronic states of strained, million-atom nanostructure systems, within an empirical pseudopotential Hamiltonian. This method expands the wave functions of a nanostructure (superlattice, wire, and dot) as linear combinations of bulk Bloch states of the constituent materials, over band indices n and wave vectors k. This allows one to use physical intuition in selecting the n and k that are most relevant for a given problem. This constitutes a useful approximation over the "direct diagonalization" approach where the basis is complete (individual plane waves) but unintuitive. It also constitutes a dramatic improvement upon the k.p approach, where the continuum model Hamiltonian is used, losing the atomistic details of the system. For a pyramidal InAs quantum dot embedded in GaAs, we find electronic eigenenergies that are within 20 meV of the exact direct diagonalization calculation, while the speed of the current method is 100-1000 times faster. The sublinear scaling of the current method with the size of the system enables one to calculate the atomistic electronic states of a million-atom system on a personal computer in about 10 h. Sufficient detail is provided in the formalism, so that the method can be promptly implemented.