Two-electronn−pdouble quantum dots in carbon nanotubes

Abstract

We consider electron states in $n\text{\ensuremath{-}}p$ double quantum dots defined in a semiconducting carbon nanotube (CNT) by an external potential. We describe formation of extended single-electron orbitals originating from the conduction and valence bands confined in a minimum and a maximum of the external potential, respectively. We solve the problem of a confined electron pair using an exact diagonalization method within the tight-binding approach, which allows for a straightforward treatment of the conduction- and valence-band states, keeping an exact account for the intervalley scattering mediated by the atomic defects and the electron-electron interaction. The exchange interaction, which in the unipolar double dots is nearly independent of the axial magnetic field ($B$) and forms singletlike and tripletlike states, in the $n\text{\ensuremath{-}}p$ system appears only for selected states and narrow intervals of $B$. In particular, the ground-state energy level of a $n\text{\ensuremath{-}}p$ double dot is not split by the exchange interaction and remains fourfold degenerate at zero magnetic field also for a strong tunnel coupling between the dots.