Effect of Uniaxial and Hydrostatic Strain on the Optical Constants and the Electronic Structure of Copper

TLDR: The linear response of the optical constants of Cu to a general strain is presented for the range $1.5 to 4.15 eV in this paper, with the assumption that direct interband transitions dominate the absorption above 2 eV.

Abstract: The linear response of the optical constants of Cu to a general strain is presented for the range $1.5\ensuremath{\le}\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\le}5.5$ eV. The transitions ${X}_{5}\ensuremath{\rightarrow}{{X}_{4}}^{\ensuremath{'}}$ at 4.0 eV and ${E}_{F}\ensuremath{\rightarrow}{L}_{1}$ at 4.15 eV are identified. The deformation potentials $\frac{\ensuremath{\partial}({E}_{F}\ensuremath{-}{{L}_{3}}^{\mathrm{upper}})}{\ensuremath{\partial}e}=\ensuremath{-}(1.1\ifmmode\pm\else\textpm\fi{}0.1)$ eV and $\frac{\ensuremath{\partial}({L}_{1}\ensuremath{-}{E}_{F})}{\ensuremath{\partial}e}=\ensuremath{-}(9.6\ifmmode\pm\else\textpm\fi{}1.5)$ eV with $e=\frac{\ensuremath{\Delta}V}{V}$, and $\frac{\ensuremath{\partial}{L}_{1}}{\ensuremath{\partial}{e}_{\mathrm{yz}}}=\ensuremath{-}(72\ifmmode\pm\else\textpm\fi{}12)$ eV with ${e}_{\mathrm{xy}}={e}_{\mathrm{yz}}={e}_{\mathrm{zx}}$, ${e}_{\mathrm{xx}}={e}_{\mathrm{yy}}={e}_{\mathrm{zz}}=0$ for k\ensuremath{\parallel}[111] are evaluated from the measurements. They are used to derive the volume coefficients of the Fermi energy, $\frac{\ensuremath{\partial}(\mathrm{ln}{E}_{F})}{\ensuremath{\partial}e}=\ensuremath{-}1.1\ifmmode\pm\else\textpm\fi{}0.3$, and of the position of the $d$ bands, $\frac{\ensuremath{\partial}(\mathrm{ln}{E}_{d})}{\ensuremath{\partial}e}=\ensuremath{-}1.2\ifmmode\pm\else\textpm\fi{}0.5$, with respect to ${\ensuremath{\Gamma}}_{1}$. The measurements are consistent with the assumption that direct interband transitions dominate the absorption above 2 eV.