Parallel Computation for Electronic Waves in Quantum Corrals

Recent scanning tunneling microscopy (STM) studies on the (111) faces of noble metals havedirectly imaged electronic surface-confined states and dramatic standing-wave patterns havebeen observed 1,2]. We solve for the local density of electronic states in these “leaky” quantumcorral confinement structures using a coherent elastic scattering theory. We seek solutionsof the two-dimensional Schrödinger equation compatible with non-reflecting boundaryconditions which asymptotically satisfy the Sommerfeld radiation condition [11,14]. Thelarge matrices generated by the discretization of realistic quantum corral structures require theuse of sparse matrix methods. In addition, a parallel finite element solution was undertakenusing the message passing interface standard (MPI) and the Portable, Extensible, Toolkit forScientific Computation (PETSc) [5] for an efficient computational solution on both distributedand shared memory architectures. Our calculations reveal excellent agreement with thereported experimental dl/dV STM data