this is for holding javascript data
Alfredo A. Correa edited We_observe_in_Figure_ref__.tex
over 8 years ago
Commit id: e99cb65c9777bf323c23d8d0c17d03180d7cd144
deletions | additions
diff --git a/We_observe_in_Figure_ref__.tex b/We_observe_in_Figure_ref__.tex
index 4e8bb29..91be2eb 100644
--- a/We_observe_in_Figure_ref__.tex
+++ b/We_observe_in_Figure_ref__.tex
...
Due to Pauli exclusion only electrons in the energy range $E_\text{F} \pm 2\hbar k_\text{F} v$ can participate in the stopping process.
Taking into account that DFT band structure predicts that the $\mathrm{d}$-band 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 are close to $1$ for and $k_\text{F} = 0.72$ for $\mathrm{Cu}$ $\mathrm{s}$-electrons \cite{Ashcroft_2003}.
Based in this DFT ground state density of states plus conservation laws we obtain an estimate of $v_\text{kink} = \Delta/\hbar/k_\text{F} =
0.081~\mathrm{a.u.}$ 0.082~\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 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 $k_\text{F}$ become more ambiguous, but it is related to the point at which the whole conduction band (11 electrons) starts participating in the process.
In reality, the $\mathrm{d}$-band is about $\Delta_\text{exp} = 2~\mathrm{eV}$ below the Fermi energy, that means that both the DFT-based estimate and the TDDFT result should be giving an underestimation of 25\% of the kink location.