Title: Quantum Mechanics and Many-Body Correlation in a Complex Environment

Speaker: Mike Stopa, Center for Nanoscale Systems, Harvard University

Date/Time: Tuesday, February 24, 2009, 10:00 – 11:00 am

Location: CSRI Building/Room 90 (Sandia-NM)

Brief Abstract: Analysis of many nanoscale systems requires the computation of the electronic structure of a subsystem embedded in a complex environment with which the subsystem interacts either electrostatically, electrodynamically or via particle exchange. One classical case of this problem is the treatment of solvation, wherein a molecule’s electronic structure depends on the fluctuating electric fields generated by a dielectric medium such as water. Modern examples relating to fabricated nanoscale systems include quantum dots interacting with metallic gates and leads, molecules exchanging electrons with neighboring nanoparticles in surface enhanced Raman spectroscopy (SERS) and excitonic transfer in photovoltaic materials coupled to metal surfaces with plasmon resonances.

In this talk, I will use calculations on electronic structure of lateral, semiconductor quantum dots to illustrate the principal issues, which include the following.

• The electron-electron interaction in the subsystem is screened by the environment in a complex fashion.
• The expression for the total free energy of the system (in the ground state), when the number of electrons on the dot-subsystem N is fixed, must include the work done by the power supplies to the leads and gates.
• When many-body correlation effects are considered (for the N-fixed case) the fact that electrons do not interact with themselves but do interact with their image charges must be incorporated into the formalism.
• For subsystems that exchange electrons with the environment, a grand canonical approach to the energy of the system (using multiple “redox” states) needs to be employed.
• Computationally efficient methods of calculating matrix elements (e.g. Coulomb matrix elements) employing numerical solutions to Poisson’s equation can make configuration interaction calculations more computationally feasible for a given system size.

While we have explored these issues in a piecemeal fashion over the last few years, I will try to provide some unifying perspective of the various phenomena from the point of view of computational methods for open physical systems.

CSRI POC: Rick Muller, (505) 284-3669