Biexciton binding energy in fractional dimensional semiconductors

Abstract

Biexcitons in fractional dimensional spaces are studied using variational quantum Monte Carlo. We investigate the biexciton binding energy as a function of the electron-hole mass fraction $\ensuremath{\sigma}$ as well as study the dimensional dependence of biexcitons for $\ensuremath{\sigma}=0$ and $\ensuremath{\sigma}=1$. As our first application of this model we treat the H${}_{2}$ molecule in two and three dimensions. Next we investigate biexcitons in carbon nanotubes within the fractional dimensional model. To this end we find a relation between the nanotube radius and the effective dimension. The results of both applications are compared with results obtained using different models and we find a reasonable agreement. Within the fractional dimensional model we find that the biexciton binding energy in carbon nanotubes accurately scales as ${E}_{B}(r,\ensuremath{\varepsilon})=1280\phantom{\rule{0.28em}{0ex}}\mathrm{meV}\phantom{\rule{0.16em}{0ex}}\AA{}/(r\ensuremath{\varepsilon})$, as a function of radius $r$ and the dielectric screening $\ensuremath{\varepsilon}$.