Electronic structures of finite double-walled carbon nanotubes in a magnetic field

The discrete electronic states of finite double-walled armchair carbon nanotubes are obtained in a magnetic field by using the Peierls tight-binding model. State energy, wavefunction, energy gap, and density of states are investigated in detail. Electronic properties strongly depend on the intertube atomic interactions, magnitude and direction of the magnetic field, boundary structure, length, and Zeeman splitting. The intertube atomic interactions result in an asymmetric energy spectrum about the Fermi level, a drastic change in energy gap, and obvious energy shifts. The magnetic field could lead to state crossing, alter the hybridization of the inner and outer tight-binding functions, destroy state degeneracy, increase more low-energy states, and induce complete energy-gap modulations (CEGMs). The different atomic positions along the tube axis make the C(5) system differ from the D(5h) or S(5) systems. According to the lengths N(l) = 3i, 3i + 1, and 3i + 2 (i an integer), there exist three types of magnetic-flux-dependent state energies. The Zeeman effect causes CEGMs to happen at weaker magnetic fields. The main features of quantized electronic states are directly reflected in the density of states. The predicted magneto-electronic properties could be examined by the transport and optical measurements.