Table 1.

Conductivity and surface impedance in the different regimes and their regions of validity

Regime	Valid when	Conductivity $\sigma (q,\omega )$	Surface impedance $Z(\omega )$
Low-frequency normal	$q^2{v}^2\ll {\mathrm{\Gamma }}_{\text{inter}}{\mathrm{\Gamma }}_{\text{mr}}$ $\omega \ll {\mathrm{\Gamma }}_{\text{inter}}$	$\epsilon \hspace{0.17em}{\omega }_{\text{P}}^2\left[\frac{2}{{\mathrm{\Gamma }}_{\text{mr}}}+{\alpha }^2\frac{3}{{\mathrm{\Gamma }}_{\text{inter}}}-{\alpha }^2\frac{66}{15}\frac{1}{{\mathrm{\Gamma }}_{\text{mr}}}\right]$	$e^{i\pi /4}\mu \sqrt{\frac{\omega c^2}{{\omega }_{\text{P}}^2}}{\left(\frac{2}{{\mathrm{\Gamma }}_{\text{mr}}}+{\alpha }^2\frac{3}{{\mathrm{\Gamma }}_{\text{inter}}}-{\alpha }^2\frac{66}{15}\frac{1}{{\mathrm{\Gamma }}_{\text{mr}}}\right)}^{-\frac{1}{2}}$
Anomaly-induced nonlocal	${\mathrm{\Gamma }}_{\text{inter}}{\mathrm{\Gamma }}_{\text{mr}}\ll q^2{v}^2\ll {\mathrm{\Gamma }}_{\text{mr}}^2$ $\omega \ll q^2{v}^2/{\mathrm{\Gamma }}_{\text{mr}}$	$\epsilon \hspace{0.17em}{\omega }_{\text{P}}^2\left[\frac{2}{{\mathrm{\Gamma }}_{\text{mr}}}+{\alpha }^2\frac{18{\mathrm{\Gamma }}_{\text{mr}}}{q^2{v}^2}\right]$	See Eq. 56
Hydrodynamic	${\mathrm{\Gamma }}_{\text{mr}}{\mathrm{\Gamma }}_{\text{tot}}\ll q^2{v}^2\ll {\mathrm{\Gamma }}_{\text{tot}}^2$ $\omega \ll q^2{v}^2/{\mathrm{\Gamma }}_{\text{tot}}$	$\epsilon \hspace{0.17em}{\omega }_{\text{P}}^2\frac{{\mathrm{\Gamma }}_{\text{tot}}}{q^2{v}^2}\left[9.0-26{\alpha }^2\right]$	$\frac{1}{2}\left(e^{i\pi /8}+e^{i5\pi /8}\right)\mu {\left(\frac{{\omega }^3{v}^2{c}^2}{{\omega }_{\text{P}}^2{\mathrm{\Gamma }}_{\text{tot}}\left[9.0-26{\alpha }^2\right]}\right)}^{1/4}$
Ballistic	${\mathrm{\Gamma }}_{\text{tot}}\ll qv$ $\omega \ll qv$	$\epsilon \hspace{0.17em}{\omega }_{\text{P}}^2\frac{1}{qv}\left[4.5+4.3{\alpha }^2\right]$	$\frac{4\sqrt{3}}{9}{e}^{i\pi /3}\mu {\left(\frac{{\omega }^{2}v{c}^2}{{\omega }_{\text{P}}^2\left[4.5+4.3{\alpha }^2\right]}\right)}^{1/3}$
High-frequency normal	$qv\ll \omega$ ${\mathrm{\Gamma }}_{\text{tot}}\ll \omega$	$-i\epsilon \hspace{0.17em}{\omega }_{\text{P}}^2\frac{1}{\omega }\left[2+\frac{8}{5}{\alpha }^2\right]$	$-i\mu \frac{\omega c}{{\omega }_{\text{P}}}{\left(2+\frac{8}{5}{\alpha }^2\right)}^{-\frac{1}{2}}$

The numerical coefficients in the hydrodynamic and ballistic regimes are rounded up to two significant numbers.