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13: (5,5) Carbon Nanotube — Transport properties

  • Outline: Obtain the bandstructure, quantum conductance and density of states of a metallic (5,5) carbon nanotube

  • Directory: tutorials/tutorial13/ Files can be downloaded from here

  • Input Files

    • cnt55.scf The pwscf input file for ground state calculation

    • cnt55.nscf The pwscf input file to obtain Bloch states for the conduction states

    • cnt55.pw2wan Input file for pw2wannier90

    • cnt55.win The wannier90 input file

In order to form localised WF that describe both the occupied and unoccupied \(\pi\) and \(\pi^{\ast}\) manifolds, we use the disentanglement procedure to extract a smooth manifold of states that has dimension equal to 2.5 times the number of carbon atoms per unit cell 1. The positions of the energy windows are shown in this plot.

Image title
Bandstructure of (5,5) carbon nanotube showing the position of the outer and inner energy windows.

The part of the wannier90 input file that controls the transport part of the calculation looks like:

Input file
transport = true
transport_mode = bulk
one_dim_axis = z
dist_cutoff = 5.5
fermi_energy = -1.06
tran_win_min = -6.5
tran_win_max = 6.5
tran_energy_step = 0.01
dist_cutoff_mode = one_dim
translation_centre_frac = 0.0 0.0 0.0

Descriptions of these and other keywords related to the calculation of transport properties can be found in the User Guide.

  1. Run pwscf and wannier90.\ Inspect the output file cnt55.wout. The minimisation of the spread occurs in a two-step procedure. First, we minimise \(\Omega_{\rm I}\). Then, we minimise \(\Omega_{\rm O}+\Omega_{{\rm OD}}\).

  2. Note that the initial \(p_{z}\) projections on the carbon atoms are oriented in the radial direction with respect to the nanotube axis.

  3. The interpolated bandstructure is written to cnt55_band.agr (since bands_plot_format = xmgr in the input file).

  4. The quantum conductance and density of states are written to the files cnt55_qc.dat and cnt55_dos.dat, respectively. Note that this part of the calculation may take some time. You can follow its progress by monitoring the output to these files. Use a package such as gnuplot or xmgrace in order to visualise the data. You should get something that looks like this.

    Image title
    Wannier interpolated bandstructure, quantum conductance and density of states of (5,5) carbon nanotube. Note that the Fermi level has been shifted by 1.06eV with respect to the bandstructure plot.

  1. Y.-S. Lee, M. B. Nardelli, and N. Marzari. Band structure and quantum conductance of nanostructures from maximally localized wannier functions: the case of functionalized carbon nanotubes. Phys. Rev. Lett., 95:076804, 2005. ↩