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Alfredo A. Correa edited The_kink_we_found_at__.tex
almost 8 years ago
Commit id: 67b3fcb57b1aa2965f85283627e941ea67ef1af0
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Taking into account that DFT band structure predicts that the $\mathrm{d}$-band edge is $\Delta_\text{DFT} = 1.6~\mathrm{eV}$ below the Fermi energy (see for example, Fig.~3(a) in Ref.~\cite{Lin_2008}),
that electron (band) effective mass close to $1$ and that $k_\text{F} = 0.72/a_0$ for the effective homogeneous electron gas of $\mathrm{Cu}$ $\mathrm{s}$-electrons \cite{Ashcroft_2003}, we can derive an approximate value of $v_\text{kink}$ caused by the participation of $\mathrm{d}$-electrons.
Based in this DFT ground state density of states plus conservation laws, we obtain an estimate of $v_\text{kink} = \Delta/(2\hbar k_\text{F}) = 0.41~\mathrm{a.u.}$ in qualitative agreement with the TDDFT prediction.
In reality, the $\mathrm{d}$-band is about $\Delta_\text{exp} = 2~\mathrm{eV}$ below the Fermi energy as indicated by ARPES ~\cite{Knapp_1979},
that which means that both the DFT-based estimate and the TDDFT result should be giving an underestimation of 25\% of the kink location.
The second (negative) kink at $v = 0.3~\mathrm{a.u.}$ is more difficult to explain precisely as the qualitative description in terms of $k_\text{F}$ (as in the homogeneous electron gas) becomes more ambiguous, but it is related to the point at which the whole conduction band ($11$ $\mathrm{s} + \mathrm{d}$ electrons) starts participating in the process.