Parallel Computation for Electronic Waves in Quantum Corrals
Recent scanning tunneling microscopy (STM) studies on the (111) faces of noble metals have directly imaged electronic surface-confined states and dramatic standing-wave patterns have been observed 1,2]. We solve for the local density of electronic states in these “leaky” quantum corral confinement structures using a coherent elastic scattering theory. We seek solutions of the two-dimensional Schrödinger equation compatible with non-reflecting boundary conditions which asymptotically satisfy the Sommerfeld radiation condition [11,14]. The large matrices generated by the discretization of realistic quantum corral structures require the use of sparse matrix methods. In addition, a parallel finite element solution was undertaken using the message passing interface standard (MPI) and the Portable, Extensible, Toolkit for Scientific Computation (PETSc)  for an efficient computational solution on both distributed and shared memory architectures. Our calculations reveal excellent agreement with the reported experimental dl/dV STM data.