Double-gap superconducting proximity effect in armchair carbon nanotubes

We theoretically explore the possibility of a superconducting proximity effect in single-walled metallic carbon nanotubes due to the presence of a superconducting substrate. An unconventional double-gap situation can arise in the two bands for nanotubes of large radius wherein the tunneling is (almost) symmetric in the two sublattices. In such a case, a proximity effect can take place in the symmetric band below a critical experimentally accessible Coulomb interaction strength in the nanotube. Furthermore, due to interactions in the nanotube, the appearance of a BCS gap in this band stabilizes superconductivity in the other band at lower temperatures. We also discuss the scenario of highly asymmetric tunneling and show that this case too supports double-gap superconductivity.

Figure 1

(Color online) A metallic armchair SWMNT, comprising an underlying graphene structure having sublattices $A$ and $B$, deposited on an $s$-wave paired BCS superconductor. The SWMNT is coupled to the substrate via electron-tunneling.

Figure 2

(Color online) Low-energy band structure of a SWMNT. Fermi points are labeled by $\nu =\pm$ and the sublattices $A$ and $B$ combine to build two bands with right (+) and left (−) movers. Here, $k$ represents the momentum associated with the $x$ direction and ${\mu }_N$ corresponds to the Fermi energy.