Here is a daily log for Daria Satco from 2018.9.4 to 2018.11.29 in Saito Lab in Tohoku Univ.

## Daily schedule (tentative)†

• 09:00-11:00 Finishing/continuing any work from previous day
• 11:00-12:00 Discussion with Nugraha-san
• 12:00-13:00 Lunch
• 13:00-15:00 Prepare for daily report presentation
• 15:00-16:00 Meeting with Saito-sensei
• 16:00-17:30 Start working on work for tomorrow's presentation and updating Pukiwiki

## Goal of the project†

• To explain the origin of new peak in doped CNT optical spectra.

This section is for posting questions from Daria-san and answers from other group members.

• Please list here with some simple reasons or details.
• For every problem, give a tag double asterisks (**) in the code so that it will appear in the table of contents.
• For the answer, give a tag triple asterisks (***) in the code below the problem in order to make a proper alignment.
• List from new to old.

## Report†

This part is basically written by Daria-san. Any other people can add this. Here the information should be from new to old so that we do not need to scroll.

### November 1†

Visited Naruko-onsen.

### October 31†

• Started to read papers on plasmons in CNT and choose the information to include in paper introduction.

To do:

• Calculate charge density as a function of Fermi level.

Visited Nikko.

### October 29†

• Changed program to make use of virtual memory more saving.

To do:

• Process data after calculation finished.

To do:

• Apply linear fitting to Fermi energy dependence.

WEEKEND

### October 25-26†

• Changed the approach of Drude conductivity calculation.
• Considered cos3t, Ef and diameter dependence of plasmon for different chiralities.

To do:

• Start writing a paper.

### October 24†

• Tried to obtain Drude conductivity.
• Got Fermi energy dependence for (16,0) and (10,10) CNTs in power law model.

To do:

• Apply linear fitting to Fermi energy dependence.

### October 23†

• Got the plasmon vs diameter dependence in leading order.

To do:

• Get the Fermi energy dependence and chiral angle dependence.
• Choose plots that could be used in the paper.

### October 22†

• Performed more accurate plasmon vs diameter data fitting.

To do:

• Add Fermi energy dependence to fitting.

WEEKEND

### October 19†

• Performed plasmon vs diameter data fitting.

To do:

• Continue playing with fitting.

### October 18†

• Checked STB result for plasmon.
• Checked negative values of Fermi energy.

To do:

• To fit plasmon vs diameter data.

To do:

• Assign points on plasmon plot with certain chiralities.

### October 17†

To do:

• To approximate plasmon as a function of diameter and plasmon as a function of fermi level.
• To include Drude-conductivity to our calculation.
• To check how different are STB and 3rd nearest neighbor TB in case of plasmons study.

### October 16†

• Calculated Eii which correspond to the model used in our calculation.

To do:

• Assign points on plasmon plot with certain chiralities.

### October 15†

• Ran program for all chiralities for CNT with d = 0.5 .. 2 nm.
• Made plot for plasmons for different chiralities.

To do:

• Check the family pattern for Eii energies, which are calculated in our program.

WEEKEND

### October 12†

• Examined the origin of plasmons in terms of possible intersubbband transitions.
• Chose the best way to plot plasmons.

To do:

• Run the program for all chiralities for 0.5 - 2 nm CNTs.

### October 11†

• Studied different main contributions to plasmons for (10,10) and (16,0) CNT.
• The results show that usually there are up to 3 main contributions, there are no interband contributions, only intraband (perpendicular polarization).
• Made the plot where scatters point the plasmon position and their size symbolizes plasmon magnitude.

To do:

• To check why we have sometimes one branch and sometimes two.

### October 10†

• Added to the program the possibility to automatically look for plasmon positions and main contributions in it.

To do:

• To check the correctness of present plasmon-looking algorithm.
• To have a look at less intensive contributions.
• To separate intra- and interband contributions.
• To show somehow the magnitude of different plasmons on the plot of their positions.

### October 9†

• Created the subroutine which matches all cutting lines numbers with certain Eii transitions.

To do:

• To automate search of plasmon position and corresponding dominant transition.

LONG WEEKEND

### October 5†

• It was concluded the the contributions from different cutting lines can be clearly observed in total plasmic absorption.
• Different chiralities which correspond to experimentally studied CNT were considered and plasmons calculated for different energy positions.
• The rule to assign the contributions to particular transitions was agreed, i and j should be taken according to Eii transitions.

To do:

• Modify the code in such a way as to make possible to assign automatically the plasmon to mainly contributing cutting lines.

To do:

• Continue analyzing contributions from different cutting lines.

### October 4†

• Created the output for different cutting lines contributions in permittivity, conductivity and absorption.
• Changed the code structure to make it work faster.

To do:

• Continue analyzing contributions from different cutting lines.

### October 3†

• Changed program to have possibility to estimate each cutting line contribution separately.
• Changed the way of plotting absorption at different Fermi levels to cascade plot.
• Got the contributions from some particular cutting lines into absorption.
• Understood that there exist one more plasmon in absorption spectra (calculated).

To do:

• Separate contributions from different cutting lines to dielectric function, conductivity, absorption.

### October 2†

• The question about computational accuracy was closed.

To do:

• Separate contributions from different transitions to the resulting absorption.

### October 1†

• Reproduced Fig.6 from Sasaki-san's paper.

To do:

• Calculate convergence function in another form (discussed on meeting).
• Separate contributions from different transitions to the resulting absorption.

WEEKEND

### September 28†

• Checked the convergence of the calculations according with nearest points distance.
• Read the paper by Senga-san on EELS of SWCNT.
• Plotted the dielectric features in 0..6 eV energy range.

To do:

• Consider 2 nm CNT (particular chirality) and reproduce the plasmon in experiment.
• Reproduce Fig.6 from Sasaki-san's paper.
• Choose some chiralities according to Senga-san paper and try to reproduce their experimental results.

### September 27†

• Compared Iwasaki-san's matrix element with our dipole calculation in the same scale. Ageed that results are consistent.
• Changed the way number of k points is chosen in program. Previously it was some input parameter. Now it is varied depending on tube (n,m) and broadening factor value.

To do:

• Check the convergence of the computational results with different dk values.
• Read the paper on EELS of single carbon nanotube.
• Check if pi-plasmon appears in our calculation.
• Try to run the program for CNTs from our experiment.

### September 26†

• Rederived selection rules and dipole matrix element using Sato-san's paper.

To do:

• Change the way number of k-points is defined inside the code. Find a good value of distance between the nearest k-points, considering the dependence on the value of broadening factor gamma.
• Renormalize the result of matrix element calculation and compare with Iwasaki-san.

### September 25†

• Added one more approach to calculate dipole matrix element: the summation is performed over all hexagons in the CNT unit cell. In contrast to the previous approach, which considered the symmetry of CNT cell and the summation was replaced by one term multiplied on number of hexagons.
• Compared the results for different approaches. The direct summation is consisted with symmetry-adopted result when correct mu-value is chosen.

To do:

• Rederive the selection rules according to Satco-san's paper.

WEEKEND

### September 21†

• Tried to reproduce expressions from Popov's paper, using his notations.

To do:

• Rederive the dipole matrix element using Saito-sensei's notations.

### September 20†

• Realized that the problem is in a way how matrix elements are calculated.

To do:

• Obtain the correct expression for matrix element analytically.

### September 19†

• Plotted different terms of under integral function as a function of k at w=0.
• Found the problem in matrix element calculation, are different for i-j and j-i transitions, though in fact they should be the same (square modulus).
• Changed the type of polarization vector variable in calculation, it is more convenient to have it REAL instead of COMPLEX.
• Checked the way how matrix elements are calculated. It appeared that there are 2 subroutines in Nugraha-san's code, one is absolutely correct and gives the same result for i-j and j-i, another one works improperly. Changed the code, now correct one is used.
• Finally got zero for Im part of conductivity, the problem was in matrix elements.
• Changed the input arguments of subroutines, now energies and matrix elements are input parameters, not calculated inside.

To do:

• Reproduce again plots from Sasaki-san's paper, after the problem was solved.
• Include Georgii-san's energy bands calculation in Nugraha-san's code.

### September 18†

• Made plot of under integral function at w=0.
• Checked that Sasaki-san uses simple TB in his paper.
• Read again the paper about plasmons in double-walled CNT, checked that they observe both interbank transitions i-i and pi-plasmon.

To do:

• Plot separately square matrix element, Fermi distribution difference and lorentzian as a function of k at w=0.
• Have a look at under integral function at different gamma.

WEEKEND

### September 14†

• Reproduced Figs. 2- 9 from Sasaki's paper.
• Sent the conductivity and permittivity data to Furuta-sensei.
• Checked the Samsonidze program for energy band structure, started to think how to include his calculation in Nugraha-san program.
• Established that there is some problem in the calculation of imaginary part of conductivity, it should tends to zero, but we obtain a finite value at zero frequency.
• Discussed the way to check the mistake in calculation of imaginary part of conductivity: the maximum and minimum values of function which is integrated can be different by several orders, need to Che

To do:

• To plot the maximum-value integral function as a function of k and j for particular i (the i is chosen the one which gives the most possible maximum value).

FNTG days

### September 10†

• Reproduced Fig. 5(a,b) and Fig.9 (a,b) from Sasaki's paper.
• Observed plasmon at approximately the same position, but plots are not very similar.
• Checked the definitions of permittivity, conductivity, if they are consistent in our calculation.

To do:

• To find the source of disagreement between calculations.

WEEKENDs

### September 7†

• Implemented the calculation of dynamical conductivity and absorption with expressions from Sasaki's paper.
• Don't have agreement between my results and Sasaki's results.

To do:

• Check where is the problem.

### September 6†

• Solved the problem with oscillations in dielectric function: used the averaging of Lorentzian function which stays under the integral (Mean Value Theorem for Integrals was applied). The averaging is performed on the range of closest points to the one of the interest, which means, that when we need value for n point, we take interval [ 1/2 [n-1,n]; 1/2[n,n+1] ].
• Added to the original code one more condition (energy difference is not equal to zero, previous one was for matrix element square). In this way we avoid singularities and uncertainties under integral.

To do:

• Calculate absorption for parallel and perpendicular light polarization according to Sasaki's paper 2018.

### September 5†

• Checked how the dielectric function calculations works with different number of k-points. Understood, that the problem is not in this number, something else.
• Checked what method is used for matrix element calculation by Nugraha-san.
• Managed to run job at tube60 in background mode, changed a little bit original code to get possibility to use standard input and output files.
• Discussed with Shoufie-san the way he calculated plasmon in his thesis, also we had a look at EELS study of CNT and graphene, discussed Sasaki's paper a little.

To do:

• Add verification of energy difference in dielectric function calculation.
• Read Sasaki's latest paper, prepare a review of the paper.
• Calculate joint density of states (jDOS).

### September 4†

• Discussed with Prof. Saito and Nugraha-san, Shoufie-san the current state of the project.
• Created web-page for daily report.
• Added one more method for calculation of imaginary part of dielectric function in Nugraha's code.

To do:

• Check the dependence of dielectric function calculation on number of k-points and frequency points.
• Read Sasaki's latest paper, study and compare our results with his.
• Calculate joint density of states (jDOS).
• Study to run jobs on tube60.