Optical and Transport Properties

Abstract

The iron-based superconductors are in general multiband materials with both electron and hole pockets at the Fermi surface. The presence of multiple carrier types complicates the interpretation of dc transport measurements. However, in the normal state the complex optical properties allow the different contributions to be disentangled, permitting the behavior of the electrons and the holes to be studied using the two-Drude model. The strong, broad Drude term associated with the hole pockets is essentially temperature independent and almost incoherent. Coherent transport originates from the electron pockets where the Drude term is weaker, but the temperature-dependent scattering rate is typically much smaller. The crossover in the optical scattering rates is associated with anomalies observed in transport measurements. Interestingly, the electron pocket can display either a Fermi liquid or a non-Fermi liquid behavior, depending on the nature of the chemical substitution. In the superconducting state the strength of the condensate may be determined as well as the magnitude of the superconducting energy gaps.

Appendix

The relationship between the complex dielectric constant $\tilde{\epsilon }=\epsilon _{1} + i\epsilon _{2}$ and the complex optical conductivity $\tilde{\sigma }=\sigma _{1} + i\sigma _{2}$ is given by the following (SI) expression:

$$\displaystyle{ \tilde{\sigma }= i\epsilon _{0}\omega (1-\tilde{\epsilon }) }$$

(6.14)

where $\epsilon _{0} = 8.854 \times 10^{-12}$ C²/Nm² is the permittivity of free space. The real part of the optical conductivity is then

$$\displaystyle{ \sigma _{1} =\epsilon _{0}\,\omega \epsilon _{2}. }$$

(6.15)

However, we want the units for the conductivity to be in $\Omega ^{-1}$ cm⁻¹. Examining the units of $\epsilon _{0}$, and recalling that the units of resistance are $\Omega = \mathrm{m}^{2}\mathrm{kg}/\mathrm{s}\,\mathrm{C}^{2}$, we can write

$$\displaystyle\begin{array}{rcl} \frac{\mathrm{C}^{2}} {\mathrm{N}\,\mathrm{m}^{2}}& =& \frac{\mathrm{C}^{2}\,\mathrm{s}^{2}} {\mathrm{kg}\,\mathrm{m}^{3}} {}\\ & =& \left [ \frac{\mathrm{s}\,\mathrm{C}^{2}} {\mathrm{kg}\,\mathrm{m}^{2}}\right ] \frac{\mathrm{s}} {\mathrm{m}} {}\\ & =& \Omega ^{-1}\,\left ( \frac{\mathrm{s}} {\mathrm{m}}\right ). {}\\ \end{array}$$

To remove the remaining (s/m), we multiply $\epsilon _{0}$ by the speed of light c (m/s), so the units are now simply in $\Omega ^{-1}$,

$$\displaystyle\begin{array}{rcl} \epsilon _{0}c& =& (8.854 \times 10^{-12}\ \Omega ^{-1}\,\mathrm{s}/\mathrm{m})(2.997 \times 10^{8}\ \mathrm{m}/\mathrm{s}) {}\\ & =& 0.002654\ \Omega ^{-1}. {}\\ \end{array}$$

The fact that we are using an angular frequency adds a further factor of 2π, so that the final expression for the conductivity is then $\sigma _{1}(\omega ) = (2\pi \epsilon _{0}c)\,\omega \epsilon _{2}$. When the frequency is expressed in wave numbers (cm⁻¹), then $\sigma _{1}(\omega ) = (2\pi \epsilon _{0}c)\,\omega \epsilon _{2}$ has units of $\Omega ^{-1}\mathrm{cm}^{-1}$; this can now be written as $\sigma _{1}(\omega ) = 0.016678\,\omega \epsilon _{2}$ ($\Omega ^{-1}$ cm⁻¹), or

$$\displaystyle{ \sigma _{1}(\omega ) = \frac{\omega \epsilon _{2}} {59.96} \simeq \frac{\omega \epsilon _{2}} {60}\ \ (\Omega ^{-1}\mathrm{cm}^{-1}). }$$

(6.16)

As previously mentioned, ω is in cm⁻¹. This is the origin of the mysterious “1/60” term; it arises solely from a discussion of the units of the conductivity.