13: (5,5) Carbon Nanotube — Transport properties¶
- Outline: Obtain the bandstructure, quantum conductance and density of states of a metallic (5,5) carbon nanotube.
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Run pwscf and
wannier90. Inspect the output filecnt55.wout. The minimisation of the spread occurs in a two-step procedure. First, we minimise \(\Omega_I\). Then, we minimise \(\Omega_D + \Omega_{OD}\).Below, an extract from the
.woutfile showing a summary of the disentanglement procedure (minimisation of \(\Omega_I\))Output fileExtraction of optimally-connected subspace ------------------------------------------ +---------------------------------------------------------------------+<-- DIS | Iter Omega_I(i-1) Omega_I(i) Delta (frac.) Time |<-- DIS +---------------------------------------------------------------------+<-- DIS 1 33.96797815 33.91073784 1.688E-03 0.00 <-- DIS 2 33.92937273 33.90274574 7.854E-04 0.02 <-- DIS . . . . . . . . . . 45 33.89889125 33.89889125 4.172E-11 0.50 <-- DIS 46 33.89889125 33.89889125 1.626E-11 0.51 <-- DIS <<< Delta < 1.000E-10 over 3 iterations >>> <<< Disentanglement convergence criteria satisfied >>> Final Omega_I 33.89889125 (Ang^2) +----------------------------------------------------------------------------+Below, an extract from the
.woutfile showing the final state for the minimisation of \(\Omega_D + \Omega_{OD}\)Output fileFinal State WF centre and spread 1 ( -6.875141, 7.935472, 7.937658 ) 0.65233309 WF centre and spread 2 ( 4.748245, 7.935472, 7.937658 ) 0.65234300 WF centre and spread 3 ( 5.809324, 6.097678, 7.937658 ) 0.65186298 WF centre and spread 4 ( 7.816785, -7.396927, 7.648002 ) 1.20135958 WF centre and spread 5 ( 7.816785, -7.396927, -7.648002 ) 1.20135948 WF centre and spread 6 ( 7.936083, 7.324218, -7.937658 ) 0.60992987 WF centre and spread 7 ( 7.935073, -6.095184, 7.937658 ) 0.65161009 WF centre and spread 8 ( 6.874208, -6.712573, 7.937658 ) 0.61134798 WF centre and spread 9 ( 6.874224, 6.850489, -7.648754 ) 1.20500764 WF centre and spread 10 ( -7.936214, 6.097679, 7.937658 ) 0.65186256 WF centre and spread 11 ( 5.813353, -6.095183, 7.937658 ) 0.65160955 WF centre and spread 12 ( 6.874224, 6.850489, 7.648754 ) 1.20500766 WF centre and spread 13 ( 5.812342, 7.324217, 7.937658 ) 0.60993084 WF centre and spread 14 ( 5.931632, -7.396946, 7.648001 ) 1.20136423 WF centre and spread 15 ( 5.931632, -7.396946, -7.648001 ) 1.20136424 Sum of centres and spreads ( 71.362557, 7.925029, 55.563607 ) 12.95829277 Spreads (Ang^2) Omega I = 10.455434168 ================ Omega D = 0.000000000 Omega OD = 2.502858604 Final Spread (Ang^2) Omega Total = 12.958292772 ------------------------------------------------------------------------------ -
Note that the initial \(p_z\) projections on the carbon atoms are oriented in the radial direction with respect to the nanotube axis.
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The interpolated bandstructure is written to
cnt55_band.agrTo plot the interpolated bands, the quantum conductance and the Density of States as shown in Fig. 6 in the
wannier90tutorial, one can use thexmgraceprogram.
XMGRACE tutorial¶
Run the xmgrace plotting program from command line as
Before importing the data to be plotted, we have to reorganize the layout by selecting
here we can generate a grid of graphs by selecting the number of columns and
rows from the drop menus. For this particular example, we want to increase the
number of columns to 3, i.e. Cols: 3 and leave the number of rows to 1 in the
Matrix section. Moreover, we don't want any gap between the graphs so we also
need to modify the value of Hgap/width in the bottom Spacing section, i.e
Hgap/width 0. Once we have generated the three graphs we need to import the
data. This can be achieved by
The three files to import are cnt_band.agr, cnt_qc.dat and cnt_dos.dat,
respectively. For each file we need to select the graph in the Read to graph:
section, i.e. G(0), G(1) and G(2), respectively.
In order to flip the x-axis with the y-axis, one need to perform the following
In the Formula: section write
and then click apply.
wannier90 tutorial.