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

TL;DR

This paper investigates how the electronic structure and Fermi surface of high-$T_c$ cuprates evolve with hole doping, identifying Lifshitz quantum phase transitions at specific doping levels and comparing theoretical predictions with experimental data.

Contribution

It introduces a detailed theoretical analysis of Fermi surface topology changes in cuprates due to doping, highlighting Lifshitz quantum phase transitions in the normal state.

Findings

Identification of two critical doping concentrations with Fermi surface topology changes

Theoretical prediction of specific heat behavior near quantum critical points

Agreement of theoretical results with ARPES and quantum oscillation experiments

Abstract

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