First principles calculations of monolayer compressibilities

We perform high quality, first principles calculations of the properties of Pb and Tl isolated monolayers. Among these, we consider the equilibrium lattice constant, the two dimensional compressibilities and the electronic density. Comparison is made with previous results obtained using more simplified models. The present results represent an improvement concerning the calculated compressibilities; these remaining still lower than the measured values. We speculate that the latter could be due to some corrugation of the monolayer, not considered in the present modeling.