New Scenario for High- $T_c$ Cuprates: Electronic Topological Transition as a Motor for Anomalies in the Underdoped Regime

We have discovered a new nontrivial aspect of electronic topological transition (ETT) in a 2D free fermion system on a square lattice. The corresponding exotic quantum critical point, $\delta ={\delta }_c$, $T=0\mathrm{}$ ( $n=1-\delta$ is the electron concentration), is at the origin of anomalous behavior in the interacting system on one side of ETT, $\delta <{\delta }_c$. Most important is the appearance of the line of characteristic temperatures, $T^{*}\left(\delta \right)\propto {\delta }_c-\delta$. Application of the theory to high- $T_c$ cuprates reveals a striking similarity to the behavior observed experimentally in the underdoped regime.