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 dl/dV STM data.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jan 01, 1998
- Source ID
- 10.1155/1998/15645
Entities
People
- Henry K. Harbury
- Wolfgang Porod
Organizations
- Air Force Office of Scientific Research
- University of Notre Dame