Variational quantum Monte Carlo for solid surfaces: Application to GaAs (110)

Even today the proper theoretical treatment of solid surfaces as interacting inhomogeneous quantum systems remains a formidable task. While Quantum Monte Carlo calculations for solids are state of the art by now, the application to solid surfaces is a rather new area of current research.

Here we present some highlights of our results. Full details can be found in a recent publication.
We apply the variational quantum Monte Carlo method to the (110) surface of galliumarsenide. The variational parameters in the many-body trial wave function are minimized according to Ritz' rule the lower the energy the better the wave function. Some of these parameters influence the localization of the electrons to the whole surface system: Due to the repulsive electron-electron interaction the electrons want to drift into the vacuum, thereby lowering the total energy. But simultaneously the attractive electron-ion interaction decreases, leading to an increasing total energy. These two competing effects will lead to an optimal equilibrium distribution of the electron density with the lowest energy.
Typical energy landscapes for the GaAs(110) surface in the ideal(red) resp. Duke(green) model are shown in the following two pictures. Despite statistical noise a minimum is clearly resolvable. The x- and y- coordinates of the point of lowest energy give the optimal many-body wave function.

energy landscape of ideal GaAs(110)

energy landscape of GaAs(110) in the 
Duke model

Even more detailed information about the behavior of the electrons at the surface can be gained. E. g. the angle of the so called dangling bond orbital is unknown a priori. In the final picture the dependence of the total energy from this variational parameter for GaAs(110) in the Duke model is shown. Despite huge statistical noise in the QMC data an optimal value of 26 degree can be determined with the help of a statistical fit.

energy versus dangling bond angle for GaAs(110) 
in the Duke model

See also:
QIRM Package available for download.

CAU Kiel