# 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.

## Key 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 $x_{c1} \approx 0.15$.