Parallel computation for electronic waves in quantum corrals

Abstract

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) [5] for an efficient computational solution on both distributed and shared memory architectures. Our calculations reveal excellent agreement with the reported experimental dI/dV STM data.