Two-electrons in a quantum dot: Tunnelling rate under a magnetic field

This paper analyses a model of a pair of electrons collected by means of harmonic confinement V(x,y) and subjected to a magnetic field B=Bzˆ perpendicular to the quantum dot layer. Under these circumstances there exists a coupling between B and the harmonic potential which is going to alter both the effective length of the electronic functions and the tunnelling rates. The main conclusion of this paper is that, by using a finite potential barrier, a treatable expression of tunnelling rate is likely to be obtained. Likewise, another outcome is that, by increasing the magnetic fields, the harmonic confinement equalises the electronic effective widths, that is, both the x-width and the y-thickness tend to the same asymptotic value. Last but not least, one concludes that the magnetic field can be used to control the tunnelling rate.