Fluctuations and Higgs mechanism in Under-Doped Cuprates: a Review.

The physics of the pseudo-gap phase of high temperature cuprate superconductors has been an enduring mystery in the past thirty years. The ubiquitous presence of the pseudo-gap phase in under-doped cuprates suggests that its understanding holds a key in unraveling the origin of high temperature superconductivity. In this paper, we review various theoretical approaches to this problem, with a special emphasis on the concept of emergent symmetries in the under-doped region of those compounds. We differentiate the theories by considering a few fundamental questions related to the rich phenomenology of these materials. Lastly we discuss a recent idea of two kinds of entangled preformed pairs which open a gap at the pseudo-gap onset temperature $T^{*}$ through a specific Higgs mechanism. We give a review of the experimental consequences of this line of thoughts.