 Re: About the imaginary part of the optical conductivity ( No.1 ) |
- Date: 2024/01/30 19:58
- Name: Yung-Ting Lee
- Dear Y. Zhang,
Due to ε(omega) = ε_0 + ( i σ(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 in-phase current which produces the resistive joule heating,
while the imaginary part represents the π/2 out-of-phase inductive current."
In [3], the sentences in the introduction describe
"The real part σ1 of the optical conductivity contributes ε2 which determines the amount of absorption inside the medium,
while the imaginary part σ2 provides ε1 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 ε1 and ε2 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.
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Notes:
ε_0 = Vacuum Permittivity.
ε = ε1 + iε2. ε1 = real part of dielectric function, ε2 = imaginary part of dielectric function.
σ = σ1 + iσ2. σ1 = real part of optical conductivity, σ2 = imaginary part of optical conductivity.
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References:
[1] Optical conductivity in wiki : https://en.wikipedia.org/wiki/Optical_conductivity#cite_note-4
[2] https://unlcms.unl.edu/cas/physics/tsymbal/teaching/SSP-927/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
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| Re: About the imaginary part of the optical conductivity ( No.2 ) |
- Date: 2024/01/30 21:24
- Name: Ye Zhang
- Dear Yung-Ting 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 σ2 provides ε1 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 don’t 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 0-6eV, and it is always negative.
After it is greater than 6eV, it gradually increases and then becomes positive. I can’t understand this phenomenon well.
I also read your “Dielectric function and optical conductivity”, but because my knowledge of optical properties is weak, I didn’t understand it well.
Best regards,
Ye Zhang
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| Re: About the imaginary part of the optical conductivity ( No.3 ) |
- Date: 2024/01/30 23:47
- Name: Yung-Ting Lee
- Dear Y. Zhang,
Q1. The larger value of σ2 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 ε1) 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 ε1 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 ε2 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 out-of-phase. 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 ε1,
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 k-points).
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 k-points.
Best regards,
Yung-Ting Lee
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References:
[1] B. Wang et. al., Chem. Rev. 118, 11, 5690-5754 (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).
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| Re: About the imaginary part of the optical conductivity ( No.4 ) |
- Date: 2024/02/01 01:49
- Name: Ye Zhang
- Dear Yung-Ting 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
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About the imaginary part of the optical conductivity