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Yen-Lin Chen edited When_applied_an_electric_field__.tex
over 8 years ago
Commit id: f9427a482b7c70b7aeda09ffa22ee12b700ef8ea
deletions | additions
diff --git a/When_applied_an_electric_field__.tex b/When_applied_an_electric_field__.tex
index 791cd7d..e6e7502 100644
--- a/When_applied_an_electric_field__.tex
+++ b/When_applied_an_electric_field__.tex
...
E(t) = E_0 cos(\omega t)
\end{equation}
there will be DC and AC
currents. current contributions. The empirical DC conductance is of the form\cite{Bardeen_1979}:
\begin{equation}
\sigma(E) = \sigma_a + \sigma_b exp(-E_0/E)
\end{equation}
CDW was modeled as a classical particle moving in a "wash board" potential, which was approximated by parabolic and sinusoidal potentials.
The particle was overdamped and subjected to electric force $e E$. Only when the applied
DC electric field exceeds some threshold value $E_th$ will the CDW "particle" start to
"slide". This is "slide", also known as the "depinning" process of CDW \cite{Gr_ner_1981}.
The conductance Once depinned, the equation of motion can be written in
this case terms of position x or the phase shift $\phi$.
\begin{equation}
\frac{d^{2}\phi}{dt^{2}} + \Gamma \frac{d\phi}{dt} + 2k_F V_0 sin(2k_F \phi) =\frac{e E_0}{m}cos(\omega t)
\end{equation}
where \Gamma is
"diode-like". the damping coefficient determined by experiment and m is the collective mass of CDW. By