Magnetically Induced Current Densities in Toroidal Carbon Nanotubes

Molecular structures
of toroidal carbon nanotubes (TCNTs) have
been constructed and optimized at the density functional theory (DFT)
level. The TCNT structures have been constrained by using point groups
with high symmetry. TCNTs consisting of only hexagons (polyhex) with
armchair, chiral, and zigzag structures as well as TCNTs with pentagons
and heptagons have been studied. The employed method for constructing
general polyhex TCNTs is discussed. Magnetically induced current densities
have been calculated using the gauge-including magnetically induced
currents (GIMIC) method. The strength of the magnetically induced
ring currents has been obtained by integrating the current density
passing a plane cutting the ring of the TCNT. The main pathways of
the current density have been identified by visualizing the current
density. The calculations show that the strength of the diatropic
ring current of polyhex TCNTs with an armchair structure generally
increases with the size of the TCNT, whereas TCNTs with a zigzag structure
sustain very weak diatropic ring currents. Some of the TCNTs with
pentagons and heptagons sustain a strong diatropic ring current, whereas
other TCNT structures with pentagons and heptagons sustain paratropic
ring currents that are, in most cases, relatively weak. We discuss
the reasons for the different behaviors of the current density of
the seemingly similar TCNTs.