Re: About the imaginary part of the optical conductivity ( No.1 ) 
 Date: 2024/01/30 19:58
 Name: YungTing Lee
 Dear Y. Zhang,
Due to (omega) = _0 + ( i (omega) / omega ) in [1], optical conductivity is related to dielectric function. The real part of optical conductivity in a material corresponds to the imaginary part of dielectric function and vice versa.
The real part of the dielectric function is associated with the polarization of a material, which allows it to store electrical energy in response to external fields. The imaginary part of dielectric function corresponds to energy dissipation of a light through a medium, such as energy loss in materials.
In [2] (below Eq. 15), for optical conductivity, it mentions that "The real part represents the inphase current which produces the resistive joule heating, while the imaginary part represents the /2 outofphase inductive current."
In [3], the sentences in the introduction describe "The real part 1 of the optical conductivity contributes 2 which determines the amount of absorption inside the medium, while the imaginary part 2 provides 1 and, therefore to the amount of polarization."
and
"The complex dielectric function is used to describe the dispersive properties of a material. It is an intrinsic property of a material that accounts for its behavior under an applied electric field. The 1 and 2 provide the information about the retardation of the velocity of light and absorption loss of light due to polarization, respectively while propagating through the material medium."
One may search or check similar sentences about the explanation of dielectric function in textbooks. ......................................... Notes: _0 = Vacuum Permittivity. = 1 + i2. 1 = real part of dielectric function, 2 = imaginary part of dielectric function. = 1 + i2. 1 = real part of optical conductivity, 2 = imaginary part of optical conductivity. ......................................... References: [1] Optical conductivity in wiki : https://en.wikipedia.org/wiki/Optical_conductivity#cite_note4 [2] https://unlcms.unl.edu/cas/physics/tsymbal/teaching/SSP927/Section%2013_Optical_Properties_of_Solids.pdf [3] Physica B: Condensed Matter Volume 655, 15 April 2023, 414723. ( https://doi.org/10.1016/j.physb.2023.414723 )
Best regards, Y.T. Lee

Re: About the imaginary part of the optical conductivity ( No.2 ) 
 Date: 2024/01/30 21:24
 Name: Ye Zhang
 Dear YungTing Lee,
Thank you very much for your reply.
Through your explanation, I understood that the imaginary part of the optical conductivity is related to the real part of the dielectric function, which is related to the polarization of the material. The imaginary part 2 provides 1 and, therefore, the amount of polarization.
Can I consider that the larger the absolute value of the imaginary part of the optical conductivity, the greater the degree of polarization inside the material? At the same time, I still donft understand the meaning of the positive or negative values of the imaginary part of the optical conductivity.
I used openmx3.9 to calculate the optical conductivity of SiC. Its imaginary part gradually decreases from zero under 06eV, and it is always negative. After it is greater than 6eV, it gradually increases and then becomes positive. I canft understand this phenomenon well.
I also read your gDielectric function and optical conductivityh, but because my knowledge of optical properties is weak, I didnft understand it well.
Best regards, Ye Zhang

Re: About the imaginary part of the optical conductivity ( No.3 ) 
 Date: 2024/01/30 23:47
 Name: YungTing Lee
 Dear Y. Zhang,
Q1. The larger value of 2 will have larger electronic polarization in a material. I think this is correct.
Q2. I try to explain below.
(1) Polarization is induced when light penetrates a medium. For a better understanding of electronic polarization, refer to Fig.2 in [1].
(2) The magnitude of polarization caused by an external field is determined by the energy of light (E_light = E_l) and the optical transition energy (E_medium = E_m) from an occupied state to an unoccupied state in a material.
(3) The dielectric function can be divided into five regions to explain its positive or negative values:
 (a) When E_l is close to E_m (before the maximum peak of 1) and E_l < E_m, electronic polarization increases as the electromagnetic wave and electronic polarization in materials are in phase. The value in the real part of the dielectric function increases at the same time, as shown in the dielectric function 1 figure in [2].
 (b) When E_l is at the maximum peak of the dielectric function and E_l < E_m, the electromagnetic wave and electronic polarization in materials gradually become in phase completely. The value of the dielectric function reaches a maximum.
 (c) When E_l = E_m, the phase between the electromagnetic wave and electronic polarization in materials is canceled with each other. It is noticeable that the imaginary part of the dielectric function reaches its maximum peak at this point, as shown in the dielectric function 2 figure in [2].
 (d) When E_l > E_m and E_l is at the minimum peak of the dielectric function, the electromagnetic wave and electronic polarization in materials remain outofphase. The value of the dielectric function is the minimum.
 (e) When E_l > E_m and E_l is beyond the minimum peak of the dielectric function 1, electrons in materials at the E_m are not gradually influenced by the electromagnetic wave.
Notice that polarization caused by an external field / an electromagnetic wave [3] is a dynamic behavior (with t). As time progresses, the bound charges undergo oscillation.
This explanation for the dielectric function may not be perfect or complete. I recommend consulting the textbook [4] or asking professors in person for a more comprehensive understanding of polarization and dielectric function.
Q3. Optical transitions in a material take place at different energy ranges (based on the eigenstates at different kpoints). Actually, optical transitions can be decomposed based on [5]. One can decompose optical transitions to figure out what's going on. However, it is quite complicated to do analysis one by one. One may focus on an energy range, such as from 3 eV to 5 eV.
Before calculating optical conductivity or dielectric function, I prefer to check the electronic band structure of a material first. Once the electronic band structure is obtained, I can approximately infer the characteristics of optical properties because optical transitions occur on these eigenstates at different kpoints.
Best regards, YungTing Lee
......................................... References: [1] B. Wang et. al., Chem. Rev. 118, 11, 56905754 (2018). [2] http://www.superstrate.net/pv/optical/absorption.html [3] https://en.wikipedia.org/wiki/Electromagnetic_radiation [4] Neil W. Ashcroft and N. David Mermin, "Solid State Physics", Chapter 27 "Dielectric properties of Insulators" on Page 534 and Appendix K "Optical Properties of Solids" on Page 776. [5] Physical Review B 102 (7), 075143 (2020). .........................................

Re: About the imaginary part of the optical conductivity ( No.4 ) 
 Date: 2024/02/01 01:49
 Name: Ye Zhang
 Dear YungTing Lee,
I would like to express my special thanks for your timely reply and your patient explanation.
Through your explanation, I have gained some understanding of optical conductivity and dielectric function.
Thank you again.
Best regards, Ye Zhang

