Screening of the electron-electron interaction by gate electrodes in semiconductor quantum dots

The effect of conducting electrodes on the Coulomb electron-electron interaction in a quantum dot in an applied magnetic field is studied. General expressions for the electrostatic energy and Hamiltonian of a gated nanostructure are derived and it is shown that the interaction between the electrons inside the nanostructure is screened by induced charges on the gate electrodes. The importance of this effect is demonstrated with the aid of numerical calculations of the quantum states of electrons in a quantum dot between the plates of a parallel plate capacitor. For typical experimental dot-plate separations, the screening is found to have a measurable effect on physical properties of the dot such as the electrochemical potential. This has important implications for the interpretation of current experiments on quantum dot charging and electron transport through quantum dots. In particular, transitions of the total angular momentum and spin of the ground state, which are believed to affect physical properties of the dot, are shifted to higher magnetic fields.