Electron tunneling energies of a quantum dot in a magnetic field

Abstract

Theoretical analysis of the experimental energy data for an electron tunneling into a single electron state and to two interacting electrons state confined by a finite Gaussian potential in a two-dimensional quantum dot subjected to a uniform magnetic field perpendicular to the plane of the dot is presented. While a previously published analytic solution for the magnetic field at which the 2-electron ground state transitions from the spin-singlet to the spin-triplet state agreed well with the data, the calculated energy for an electron tunneling into the two-electron state at higher magnetic fields diverged from the experimental data. The discrepancy was attributed to the magnetic field dependent Fermi energy of the n + electrode of the tunnel capacitor in the experiment. It is shown that the one electron and the two-electron experimental data agree remarkably well with the theory when we use a mechanism in which as if the added electron tunnels from a fixed energy state and the confining potential is a finite Gaussian potential in contrast to the generally used infinite harmonic confining potential. That the tunneling of an electron into the quantum dot from a fixed intermediate state assumed in the analysis is equivalent to the true tunneling picture where a mechanism known as “Coulomb blockade” that regulates the tunneling of one electron at a time into the quantum dot and thus the measured electron tunneling energies are independent of the magnetic field dependent Fermi energy of the n + electrode is discussed. • First time theoretical analysis of experimental electron tunneling energy data of a quantum dot is presented. • Both 1-e and 2-e experimental data fit extremely well with the theoretical results obtained by using only two fit parameters for the Gaussian confining potential. • In addition to the electron tunneling data, the singlet-to-triplet 2-e state transition magnetic field value agrees remarkably well with the theory. • The effect of the finite confining potential compared to the infinite harmonic potential is clearly demonstrated by a significantly better fit with the experimental data. • Our theoretical analysis of the experimental data confirms the mechanism of Coulomb blockade for electron tunneling into a quantum dot.