Interaction effects in the thermodynamic properties of quantum-dots: a Hartree-Fock study.

We study electron-electron interaction effects in the thermodynamic properties of quantum-dot systems. Using a finite-temperature self-consistent Hartree-Fock method, [1,2,3] we obtain the direct and exchange contributions to the specific heat $C_{v}$ of square quantum dots of size $L$ with up to $N=20$ electrons. An exchange-induced phase transition [2] is observed at a finite transition temperature $T^*$. Our analysis shows that $T^*$ scales with $L^{-1}$ and is on the range of a few Kelvin for dots tens of nanometers across. The exchange contribution to $C_{v}$ dominates over the direct and kinetic contributions in the intermediate regime of interaction strength ($r_{s}\sim 1$), similarly to results obtained for the magnetic susceptibility [3]. Furthermore, the specific oscillates as function of an applied magnetic field and both oscillation amplitude and period are modified by the electron-electron interaction. Supported by FAPESP-Brazil. \newline [1] H. Tamura and M. Ueda, Phys. Rev. Lett. 79 1345 (1997). \newline [2] D.~J. Dean, M.~R. Strayer, and J.~C. Wells, Phys. Rev. B 64, 125305 (2001). \newline [3] L.~G.~G.~V. Dias da Silva, C. Lewenkopf, and Nelson Studart, Phys. Rev. B 69, 075311 (2004).