Temperature Effects on Electron Correlations in Two Coupled Quantum Dots

The path-integral Monte Carlo simulation method is used to examine one and two electrons in a system of two coupled disc-like quantum dots (QD) in a zero magnetic field. With this approach we are able to evaluate the one-electron distributions and two-electron correlation functions, and finite temperature effects on both. Increase of temperature broadens the distributions as expected, the effect being smaller for correlated electrons than for single ones. The simulated one- and two-particle distributions of a single and two coupled quantum dots are also compared to those from other theoretical methods. For the one-particle distributions we find a good agreement with those from the DFT approach. The effect of the third dimension or the thickness of the almost two-dimensional disc-like QDs is small for the one-particle distributions, but it is clearly seen in the electron-electron correlation or the two-particle distribution function at low temperatures. The mutual Coulomb energy of the two electrons is found to be temperature-independent, and also, independent of the correlation effects on the dynamics. Computational capacity is found to become the limiting factor in simulations with increasing accuracy or increasing number of particles, and in case of fermions in particular. This and other aspects of PIMC and its capability for this type of calculations are also discussed.