Suggestion by Dr. Rodrigo Huerta Quintanilla.

intro.tex

@@ -53,12 +53,13 @@ \section{Overview}
 The existence of these dynamical inhomogeneities suggests that a complete theory of superconductivity is unrechable assuming a perfect crystal structure without consideration for local real-space variations.
 
 Another important aspect to take into consideration is the role of electron-lattice interaction in cuprate superconductors.
-One strong motivation for Bednorz and M\"{u}ller to search for superconductivity in Ba$_x$La$_{5-x}$Cu$_5$O$_{5(3-y)}$ was the possibility of strong electron-phonon interactions in oxides due to polaron\footnote{A \textit{polaron} is an elementary excitation formed by the correlated movement betwen a charge and a distortion in the ionic lattice.} formation \cite{Bednorz1986}.
-Later X-ray absorption experiments found a large oxygen-isotope effect on the pseudogap onset temperature $T^*$ which is sign reversed with respect to the isotope effect on $T_c$.
+One strong motivation for Bednorz and M\"{u}ller to search for superconductivity in Ba$_x$La$_{5-x}$Cu$_5$O$_{5(3-y)}$ was the possibility of strong electron-phonon interactions in oxides due to polaron\footnote{A \textit{polaron} is a quasiparticle formed by correlated movement bewteen a charge carrier and a lattice distortion.}
+formation \cite{Bednorz1986}.
+Later, X-ray absorption experiments found a large oxygen-isotope effect on the pseudogap onset temperature $T^*$ which is sign reversed with respect to the isotope effect on $T_c$.
 It was also found that there were local deviations on the Cu-O bond lengths appearing at $T^*$.
 This evidence points to the significance of electron-lattice interactions in the pseudogap phase
 In particular the local deviations on the Cu-O bond lengths has been interpreted in terms of polaron formation \cite{MustredeLeon1992}.
-The formation of polaronic states is a nonadiabatic phenomenon which breaks the Born-Oppenheimer approximation \cite{Born1927}.
+Since in a polaronic state the lattice and charge degrees of freedom can not be separated, it is not possible to apply the Born-Oppenheimer approximation \cite{Born1927}.
 Thus, for a complete description of cuprate superconductors, it is impossible to separate the ionic and the electronic motions.
 
 The Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity \cite{Bardeen1957} was developed for and successfully applied to metals within the Fermi-liquid approximation. In its current formulation, it seems to lack an appropriate foundation to describe high-temperature superconductivity in copper oxides \cite{Damascelli2003}.