Transport signatures of few-atom carbon rings.

We study the electronic transport through an all-carbon quantum ring side-coupled to a quantum wire. We employ both first-principles calculations and a tight-binding approach; the latter allows for the derivation of analytical expressions for the conductance and density of states, which facilitates the interpretation of the transport characteristics. Two bond models are employed: either all the hoppings are equal (cumulenic ring) or they have alternating bonds (polyynic ring). Assuming cumulenic bonds, if the number of atoms in the carbon ring is a multiple of four, it produces an antiresonant peak in the conductance at the Fermi level. This effect disappears for the polyynic configuration, , when the hoppings in the carbon rings are alternating. Additionally, a gap opens at the Fermi energy in the polyynic rings, yielding distinct transport signatures for the two bond configurations. Comparison to first-principles calculations shows an excellent agreement on the changes of the conductance due to the carbon ring. We propose such transport measurements as a way to elucidate the character of the bonds in these novel carbon nanostructures.