deletions | additions       diff --git a/When_applied_an_electric_field__.tex b/When_applied_an_electric_field__.tex  index 5af92fe..81ffa54 100644  --- a/When_applied_an_electric_field__.tex  +++ b/When_applied_an_electric_field__.tex 
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When applied an electric field along the quasi-1D direction on CDW materials, nonlinear motion of CDW appears and nonlinear current and conductance can be observed \cite{Fleming_1979}. There are two problems of interest. (i) What is the conductance if applied a DC electric field? (ii) What is the frequency dependence of conductance for an AC electric field? For CDW state, the band structure breaks apart by the band gap energy $E_g$ at the Fermi surface in the k-space since the lattice is distorted in real space with lattice constant from $a \rightarrow 2a$. The wavelength of the potential or the CDW $\lambda = 2a =\frac{\pi}{k_F}$ where $k_F = \frac{\pi}{2a}$ is the Fermi wave vector. Therefore we can write the expression for the charge density as a function of position x and time t:  \begin{equation}  \rho(x) = \rho_0 + \rho_1 e^{i [2k_F(x-vt)+\phi]},  \end{equation}  The v in the expression denotes the velocity of the right moving CDW while $\phi$ is the phase or shift in x. And the distortion potential:  \begin{equation}  V(x) = V_0 cos(2k_{F}r+\phi)  \end{equation}  Since the charge density is dictated by potential in the absence of electric fields, thermal fluctuations and scattering events, the CDW is "pinned" on the potential.