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The optical conductivity is a material property, which links the current density to the electric field for general frequencies.^[1] In this sense, this linear response function is a generalization of the electrical conductivity, which is usually considered in the static limit, i.e., for a time-independent (or sufficiently slowly varying) electric field. While the static electrical conductivity is vanishingly small in insulators (such as Diamond or Porcelain), the optical conductivity always remains finite in some frequency intervals (above the optical gap in the case of insulators); the total optical weight can be inferred from sum rules. The optical conductivity is closely related to the dielectric function, the generalization of the dielectric constant to arbitrary frequencies.

Only in the simplest case (coarse-graining, long-wavelength limit, cubic symmetry of the material), these properties can be considered as (complex-valued) scalar functions of the frequency only. Then, the electric current density $\mathbf {J}$ (a three-dimensional vector), the scalar optical conductivity $\sigma$ and the electric field vector $\mathbf {E}$ are linked by the equation

\mathbf {J} (\omega )=\sigma (\omega )\mathbf {E} (\omega )

^[2]

while the dielectric function $\varepsilon$ relates the electrical displacement to the electric field:

\mathbf {D} (\omega )=\varepsilon (\omega )\mathbf {E} (\omega )

^[3]

In SI units, this implies the following connection between the two linear response functions:

\varepsilon (\omega )=\varepsilon _{0}+{\frac {i\sigma (\omega )}{\omega }}

,

where $\varepsilon _{0}$ is the vacuum permittivity and $i$ denotes the imaginary unit.

The optical conductivity is most often measured in the optical frequency ranges via the reflectivity of polished samples under normal incidence (in combination with a Kramers–Kronig analysis) or using variable incidence angles.^[4] For samples that can be prepared in thin slices, higher precision is usually obtainable using optical transmission experiments. In order to get more complete information about the electronic properties of the material of interest, such measurements have to be combined with other techniques that work in remaining frequency ranges, e.g., in the static limit or at microwave frequencies.

References

^ J. Robert Schrieffer; J.S. Brooks (2007). Handbook of High -Temperature Superconductivity: Theory and Experiment. Springer Publishing. p. 299. ISBN 9780387687346.
^ Paola Di Pietro (2013). Optical Properties of Bismuth-Based Topological Insulators. Springer International Publishing. p. 64. ISBN 9783319019918.
^ Jia-Ming Liu; I-Tan Lin (2018). Graphene Photonics. Cambridge University Press. p. 70. ISBN 9781108476683.
^ Hari Singh Nalwa, ed. (2000). Handbook of Advanced Electronic and Photonic Materials and Devices, Ten-Volume Set. Elsevier Science. p. 66.

External links

Lecture notes Optical Properties of Solids by E. Y. Tsymbal

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[1] J. Robert Schrieffer; J.S. Brooks (2007). Handbook of High -Temperature Superconductivity: Theory and Experiment. Springer Publishing. p. 299. ISBN 9780387687346.

[2] Paola Di Pietro (2013). Optical Properties of Bismuth-Based Topological Insulators. Springer International Publishing. p. 64. ISBN 9783319019918.

[3] Jia-Ming Liu; I-Tan Lin (2018). Graphene Photonics. Cambridge University Press. p. 70. ISBN 9781108476683.

[4] Hari Singh Nalwa, ed. (2000). Handbook of Advanced Electronic and Photonic Materials and Devices, Ten-Volume Set. Elsevier Science. p. 66.

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+{{Multiple issues|
-The '''optical conductivity''' is a material property, which links the [[Current (electricity)|current]] density to the [[electric field]] for general [[frequency|frequencies]]. In this sense, this [[linear response function]] is a generalization of the [[electrical conductivity]], which is usually considered in the static limit, i.e., for a time-independent (or sufficiently slowly varying) electric field.  While the static electrical conductivity is vanishingly small in [[insulator (electricity)|insulator]]s (such as [[Diamond]] or [[Porcelain]]), the optical conductivity always remains finite in some frequency intervals (above the '''optical gap''' in the case of insulators); the total '''optical weight''' can be inferred from [[sum rule in quantum mechanics|sum rules]]. The optical conductivity is closely related to the [[dielectric function]], the generalization of the [[dielectric constant]] to arbitrary frequencies.
+{{Original research|date=May 2021}}
+{{More citations needed|date=May 2021}}
+}}
+The '''optical conductivity''' is a material property, which links the [[Current (electricity)|current]] density to the [[electric field]] for general [[frequency|frequencies]].<ref>{{cite book |url=https://www.google.co.uk/books/edition/Handbook_of_High_Temperature_Superconduc/nLJFc_gDexcC?hl=en&gbpv=1&pg=PA299&printsec=frontcover |title=Handbook of High -Temperature Superconductivity: Theory and Experiment |author1=J. Robert Schrieffer |author2=J.S. Brooks |page=299 |year=2007 |isbn=9780387687346 |publisher=[[Springer Publishing]]}}</ref> In this sense, this [[linear response function]] is a generalization of the [[electrical conductivity]], which is usually considered in the static limit, i.e., for a time-independent (or sufficiently slowly varying) electric field.  While the static electrical conductivity is vanishingly small in [[insulator (electricity)|insulator]]s (such as [[Diamond]] or [[Porcelain]]), the optical conductivity always remains finite in some frequency intervals (above the '''optical gap''' in the case of insulators); the total '''optical weight''' can be inferred from [[sum rule in quantum mechanics|sum rules]]. The optical conductivity is closely related to the [[dielectric function]], the generalization of the [[dielectric constant]] to arbitrary frequencies.
 Only in the simplest case (coarse-graining, long-wavelength limit, cubic symmetry of the material), these properties can be considered as (complex-valued) scalar functions of the frequency only. Then, the electric current density <math>\mathbf{J}</math> (a three-dimensional vector), the scalar optical conductivity <math>\sigma</math> and the electric field vector <math>\mathbf{E}</math> are linked by the equation
+:<math>\mathbf{J}(\omega) = \sigma(\omega) \mathbf{E}(\omega)</math><ref>{{cite book |url=https://www.google.co.uk/books/edition/Optical_Properties_of_Bismuth_Based_Topo/GEa9BAAAQBAJ?hl=en&gbpv=1&pg=PA64&printsec=frontcover |page=64 |title=Optical Properties of Bismuth-Based Topological Insulators |author=Paola Di Pietro |year=2013 |isbn=9783319019918 |publisher=[[Springer International Publishing]]}}</ref>
-:<math>\mathbf{J}(\omega) = \sigma(\omega) \mathbf{E}(\omega)</math>
 while the dielectric function <math>\varepsilon</math> relates the [[electrical displacement]] to the electric field:
-:<math>\mathbf{D}(\omega) = \varepsilon(\omega) \mathbf{E}(\omega)</math>
+:<math>\mathbf{D}(\omega) = \varepsilon(\omega) \mathbf{E}(\omega)</math><ref>{{cite book |url=https://www.google.co.uk/books/edition/Graphene_Photonics/KJB2DwAAQBAJ?hl=en&gbpv=1&pg=PA70&printsec=frontcover |page=70 |title=Graphene Photonics |author1=Jia-Ming Liu |author2=I-Tan Lin |year=2018 |isbn=9781108476683 |publisher=[[Cambridge University Press]]}}</ref>
 In [[SI]] units, this implies the following connection between the two linear response functions:
@@ Line 19: / Line 23: @@
 where <math>\varepsilon_0</math> is the [[vacuum permittivity]] and <math>i</math> denotes the [[imaginary unit]].
-The optical conductivity is most often measured in the optical frequency ranges via the [[reflectivity]] of polished samples under normal incidence (in combination with a [[Kramers–Kronig relations|Kramers–Kronig analysis]]) or using variable incidence angles. For samples that can be prepared in thin slices, higher precision is usually obtainable using optical transmission experiments. In order to get more complete information about the electronic properties of the material of interest, such measurements have to be combined with other techniques that work in remaining frequency ranges, e.g., in the static limit or at [[Microwave spectroscopy|microwave]] frequencies.
+The optical conductivity is most often measured in the optical frequency ranges via the [[reflectivity]] of polished samples under normal incidence (in combination with a [[Kramers–Kronig relations|Kramers–Kronig analysis]]) or using variable incidence angles.<ref>{{cite book |url=https://www.google.co.uk/books/edition/Handbook_of_Advanced_Electronic_and_Phot/a9s4Wrl-014C?hl=en&gbpv=1&pg=PA66&printsec=frontcover |title=Handbook of Advanced Electronic and Photonic Materials and Devices, Ten-Volume Set |editor=Hari Singh Nalwa |year=2000 |page=66 |publisher=[[Elsevier Science]]}}</ref> For samples that can be prepared in thin slices, higher precision is usually obtainable using optical transmission experiments. In order to get more complete information about the electronic properties of the material of interest, such measurements have to be combined with other techniques that work in remaining frequency ranges, e.g., in the static limit or at [[Microwave spectroscopy|microwave]] frequencies.
+== References ==
+{{reflist}}
 ==External links==