  Possibility of flat-band ferromagnetism in quantum dot arrays is
theoretically discussed. By using a quantum dot as a building block, quantum
dot superlattices are possible. We consider dot arrays on Lieb and kagome
lattices known to exhibit flat band ferromagnetism. By performing an exact
diagonalization of the Hubbard Hamiltonian, we calculate the energy difference
between the ferromagnetic ground state and the paramagnetic excited state, and
discuss the stability of the ferromagnetism against the second nearest neighbor
transfer. We calculate the dot-size dependence of the energy difference in a
dot model and estimate the transition temperature of the
ferromagnetic-paramagnetic transition which is found to be accessible within
the present fabrication technology. We point out advantages of semiconductor
ferromagnets and suggest other interesting possibilities of electronic
properties in quantum dot superlattices.
