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.本研究构建并在密度泛函理论（density functional theory, DFT）水平上优化了环形碳纳米管（toroidal carbon nanotubes, TCNTs）的分子结构。研究中采用高对称点群对环形碳纳米管的结构进行约束。本次研究涵盖两类环形碳纳米管：一类为仅由六边形构成的扶手椅型、手性型与锯齿型多六边形（polyhex）环形碳纳米管，另一类为含有五边形与七边形的环形碳纳米管。本文讨论了构建通用多六边形环形碳纳米管的方法。我们采用含规范不变性的磁感应电流（gauge-including magnetically induced currents, GIMIC）方法计算了磁感应电流密度，并通过积分穿过环形碳纳米管环平面的电流密度，得到了磁感应环电流的强度。通过对电流密度进行可视化处理，我们确定了电流密度的主要传输路径。计算结果显示，扶手椅型多六边形环形碳纳米管的抗磁环电流强度通常随其尺寸增大而提升，而锯齿型环形碳纳米管的抗磁环电流则普遍极弱。部分含五边形与七边形的环形碳纳米管可产生较强的抗磁环电流，其余同类结构则呈现顺磁环电流，且多数情况下其强度相对较弱。最后，本文针对外观相似但电流密度行为存在显著差异的环形碳纳米管，探讨了其行为差异的成因。