Signature of the Aharonov-Bohm phase in field emission of carbon nanotubes under magnetic fields

The field emission behavior of single-wall carbon nanotubes (SWNTs) is studied in the presence of a magnetic field parallel to the nanotube axis by using a combination of tunneling theory with tight-binding approximation. We find that the SWNT field emission properties are strongly affected through change of their energy band structures due to application of magnetic field. This effect has a direct application to distinguishing metallic and semiconducting SWNTs, i.e., by simply measuring either of the current density versus magnetic flux $\varphi$ or the emitted electron energy distribution versus magnetic flux. More important, the separation in the plots of $d{j}_L∕d\varphi$ versus $\varphi$ of SWNTs of different chirality is clearly shown. Using this characteristic the chirality of individual SWNT samples may be identified so that previously reported chirality and quantum-size effects may be characterized in a magnetic field-added field emission experiment without use of high cost and complicated method such as high-resolution transmission microscopy technique. Further, we also find that for a given electric field, a universal current density may be obtained for all SWNTs at the magnetic flux of 0.215 of the fundamental magnetic flux. The chiral and quantum-size effects in SWNT field emission can also be diminished at this magnetic flux. These properties strongly suggest that the Aharonov-Bohm phase may be observed experimentally.

Figure 1

(a) The characteristic of the emission current density versus the magnetic flux $(j_L-\varphi ∕{\varphi }_0)$ for the applied field $F=7\mathrm{V}∕\mathrm{nm}$. The armchair (8,8), zigzag (18,0), and chiral (12,6) SWNTs are metal and the zigzag (19,0) and chiral (12,5) SWNTs are semiconducting. (b) The energy band gaps of the five SWNTs as a function of the magnetic flux $(Eg-\varphi ∕{\varphi }_0)$ (see Refs. 10, 13).

Figure 2

The field electron energy distributions of two typical SWNTs in three magnetic fluxes.

Figure 3

The derivative of the current density to the magnetic flux versus the magnetic flux for two groups of metallic and semiconducting SWNTs.

Figure 4

The current density versus the radius of CNTs at different magnetic fluxes $\varphi ∕{\varphi }_0$ for metallic armchair tubes (a), metallic chiral tubes with a chiral angle of 15° (b), semiconducting zigzag tubes (c), and semiconducting chiral tubes with a chiral angle of 15° (d).

Figure 5

The current density versus the radius of CNTs at two magnetic fluxes $\varphi ∕{\varphi }_0=0$ and 0.215. Inset shows the relative error of the current density versus the magnetic field $\varphi ∕{\varphi }_0$ for all tubes, metallic tubes and semiconducting tubes, respectively.