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.

## Questions and Answers†

This section is for posting questions from Jakob-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.

### 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.