Topological Hunds rules and the electronic properties of a triple   lateral quantum dot molecule
  We analyze theoretically and experimentally the electronic structure and charging diagram of three coupled lateral quantum dots filled with electrons. Using the Hubbard model and real-space exact diagonalization techniques we show that the electronic properties of this artificial molecule can be understood using a set of topological Hunds rules. These rules relate the multi-electron energy levels to spin and the inter-dot tunneling $t$, and control charging energies. We map out the charging diagram for up to N=6 electrons and predict a spin-polarized phase for two holes. The theoretical charging diagram is compared with the measured charging diagram of the gated triple-dot device. 
Marek Korkusinski, Irene Puerto Gimenez, Pawel Hawrylak, Louis   Gaudreau, Sergei A. Studenikin, Andrew S. Sachrajda