On optimizing JacobiDavidson method for calculating eigenvalues in low dimensional structures using eight band kp model
The paper presents two ways of improving the JacobiDavidson method for calculating the eigenvalues and eigenvectors described by eight-band kp model for quantum dots and other low dimensional structures. First, the method is extended by the application of time reversal symmetry operator. This extension allows efficient calculations of the twofold degeneracy present in the multiband kp model and other interior eigenvalues. Second, the preconditioner for the indefinite matrix which comes from the discretization of the eight band kp Hamiltonian is presented. The construction of this preconditioner is based on physical considerations about energy band structure in the kp model. On the basis of two real examples, it is shown that the preconditioner can significantly shorten the time needed to calculate the interior eigenvalues, despite the fact that the memory usage of the preconditioner and Hamiltionian is comparable. Finally, some technical details for implementing the eight band kp Hamiltonian and the eigensolver are provided.
jacobidavidson method low dimensional structures eight band kp model preconditioning electronic structure