Lifshitz quantum phase transitions and Fermi surface transformation with hole doping in high-$T_c$ superconductors

摘要

We study the doping evolution of the electronic structure in the normal phaseof high-$T_c$ cuprates. Electronic structure and Fermi surface of cuprates withsingle CuO$_2$ layer in the unit cell like La$_{2-x}$Sr$_x$CuO$_4$ have beencalculated by the LDA+GTB method in the regime of strong electron correlations(SEC) and compared to ARPES and quantum oscillations data. We have found twocritical concentrations, $x_{c1}$ and $x_{c2}$, where the Fermi surfacetopology changes. Following I.M. Lifshitz ideas of the quantum phasetransitions (QPT) of the 2.5-order we discuss the concentration dependence ofthe low temperature thermodynamics. The behavior of the electronic specificheat $\delta(C/T) \sim (x - x_c)^{1/2}$ is similar to the Loram and Cooperexperimental data in the vicinity of $x_{c1} \approx 0.15$.