Molecular aspects of electron correlation in quantum dots

The theory of electron correlation in semiconductor quantum dots is reviewe d with emphasis on the physics of dots in strong magnetic fields. A brief s urvey of dot fabrication and experimental results is given, the quantum mec hanics of small numbers of interacting electrons in a dot is discussed and the special values of angular momentum quantum number that the ground state is allowed to have, or magic numbers, are introduced. These numbers are se lected because of the symmetry properties of the ground state and the symme try is particularly evident in the limit of strong magnetic field if the sy stem is examined in a moving reference frame. Physically, the system in thi s limit can be pictured as an electron molecule that rotates and vibrates i n the dot, and this is the quantum dot analogue of a Wigner crystal. This i s illustrated with a detailed treatment of a two-electron dot which can be studied without resorting to any special concepts of molecular physics. Nex t, the molecular physics concepts, such as the Eckart reference frame, need ed to deal with rotational-vibrational motion of larger numbers of electron s are introduced. The physics of dots with more than two electrons is then described, including the evolution of magic numbers with electron number an d the implications of symmetry. Finally, the extension of these ideas to la rger systems and coupled dots is briefly discussed. Quantum dots in strong magnetic fields provide a unique opportunity to realize what could be calle d electron molecular physics, and some possible ways of probing the system experimentally are also proposed.