Molecular aspects of electron correlation in quantum dots

Abstract

The theory of electron correlation in semiconductor quantum dots isreviewed with emphasis on the physics of dots in strong magneticfields. A brief survey of dot fabrication and experimental resultsis given, the quantum mechanics of small numbers of interactingelectrons in a dot is discussed and the special values of angularmomentum quantum number that the ground state is allowed to have, ormagic numbers, are introduced. These numbers are selected becauseof the symmetry properties of the ground state and the symmetry isparticularly evident in the limit of strong magnetic field if thesystem is examined in a moving reference frame. Physically, thesystem in this limit can be pictured as an electron molecule thatrotates and vibrates in the dot, and this is the quantum dotanalogue of a Wigner crystal. This is illustrated with a detailedtreatment of a two-electron dot which can be studied withoutresorting to any special concepts of molecular physics. Next, themolecular physics concepts, such as the Eckart reference frame,needed to deal with rotational-vibrational motion of larger numbersof electrons are introduced. The physics of dots with more than twoelectrons is then described, including the evolution of magicnumbers with electron number and the implications of symmetry.Finally, the extension of these ideas to larger systems and coupleddots is briefly discussed. Quantum dots in strong magnetic fieldsprovide a unique opportunity to realize what could be calledelectron molecular physics, and some possible ways of probing thesystem experimentally are also proposed.