Abstract
We study the two-electron eigenspectrum of a carbon-nanotube double quantum dot with spin-orbit coupling. Exact calculation are combined with a simple model to provide an intuitive and accurate description of single-particle and interaction effects. For symmetric dots and weak magnetic fields, the two-electron ground state is antisymmetric in the spin-valley degree of freedom and is not a pure spin-singlet state. When double occupation of one dot is favored by increasing the detuning between the dots, the Coulomb interaction causes strong correlation effects realized by higher orbital-level mixing. Changes in the double-dot configuration affect the relative strength of the electron-electron interactions and can lead to different ground state transitions. In particular, they can favor a ferromagnetic ground state both in spin and valley degrees of freedom. The strong suppression of the energy gap can cause the disappearance of the Pauli blockade in transport experiments and thereby can also limit the stability of spin-qubits in quantum information proposals. Our analysis is generalized to an array of coupled dots which is expected to exhibit rich many-body behavior.
Highlights
Experiments on few-electron double quantum dots allow the measurement and manipulation of the spin degree of freedom of the confined electrons.[1]
The spin and valley degrees of freedom could lead to a SU共4兲 symmetry at zero magnetic field instead of the standard SU共2兲
II, we introduce the microscopic model for the double dot and analyze the noninteracting predictions taking into account a magnetic field parallel to the nanotube axis, spin-orbit couplings and detuning between the dots
Summary
Experiments on few-electron double quantum dots allow the measurement and manipulation of the spin degree of freedom of the confined electrons.[1]. Since 12C has no nuclear spin, carbon-based nanostructures are expected to reduce hyperfine-induced decoherence as compared with GaAs.[12]. Carbon-based materials exhibit richer physics than GaAs semiconducting materials because of the additional valley degree of freedom.[13,14,15] In principle, the spin and valley degrees of freedom could lead to a SU共4兲 symmetry at zero magnetic field instead of the standard SU共2兲 symmetry in conventional semiconductors 共see, e.g., Ref. 16 and references therein兲. It has been recently demonstrated[17] that the enhancement of the spin-orbit splitting in small-radius nanotubes breaks the fourfold degeneracy of the single-electron ground state into a twofold degeneracy
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