Linear conductance of an interacting carbon nanotube ring

Linear transport through a single-walled carbon nanotube ring, pierced by a magnetic field and capacitively coupled to a gate voltage source, is investigated starting from a model of interacting $p_z$ electrons. Rings of armchair type are considered. The dc conductance, calculated in the limit of weak tunneling between the ring and the leads, displays a periodic resonance pattern determined by the interplay between Coulomb interactions and quantum interference phenomena. Coulomb blockade effects are manifested in the absence of resonances for any applied flux in some gate voltage regions; the periodicity as a function of the applied flux can be smaller or larger than a flux quantum depending on the nanotube band mismatch.

Figure 1

Top view of a SWNT ring contacted to extended left and right leads and threaded by a magnetic flux $\varphi$. The ring is also capacitively coupled to a gate voltage $V_g$ plane situated beneath the ring (not shown).

Figure 2

Low-energy spectrum of a noninteracting SWNT ring threaded by a magnetic flux $\varphi$. The underlying graphene structure is reflected in the two Fermi points at $\pm K_0$. Notice the misalignment $\tilde{\varphi }{\epsilon }_0$, with $\tilde{\varphi }=\frac{\varphi }{{\varphi }_0}+\delta$, of the energy levels between the left $\left(L\right)$ and right $\left(R\right)$ branches due to the intrinsic mismatch $\delta$ and the applied flux $\varphi$. The flux quantum is denoted ${\varphi }_0$.

Figure 3

Ground-state resonances for a ring with two fermionic species $b=R,L$: Along the lines the energies are degenerate and transport there is maximal. Continuous lines correspond to the interaction parameter $\tilde{W}=2$ and dotted lines correspond to the noninteracting case, $\tilde{W}=1$.

Figure 4

(Color online) Ground-state energies $E\left(k_{{\mu }_g},N,J\right)$ for $k_{\varphi }=0$ and interaction parameter $\tilde{W}=2$. Notice that the parabolas corresponding to an odd electron number are doubly degenerate.

Figure 5

Conductance resonances of the carbon nanotube ring as a function of $k_{{\mu }_g}$ and $k_{\varphi }$. The interaction is chosen to be $\tilde{W}=2$. The lines with different slopes correspond to an excess of electrons propagating in opposite directions (counterclockwise and clockwise). Dashed lines are for the noninteracting case.