# The influence of topological phase transition on the superfluid density of overdoped copper oxides

## TL;DR

This paper links a topological quantum phase transition to the unusual superconducting properties of overdoped copper oxides, explaining experimental phenomena with a new theoretical framework that diverges from traditional BCS theory.

## Contribution

It introduces a topological phase transition as the key factor behind the exotic behavior of overdoped cuprates, providing a new theoretical explanation aligned with recent experiments.

## Key findings

- Superfluid density is much smaller than total electron density at T=0.
- Critical temperature T_c is linearly related to superfluid density n_s.
- Resistivity transitions from linear T dependence to T^2 in the normal overdoped region.

## Abstract

We show that a topological quantum phase transition, generating flat bands and altering Fermi surface topology, is a primary reason for the exotic behavior of the overdoped high-temperature superconductors represented by $\rm La_{2-x}Sr_xCuO_4$, whose superconductivity features differ from what is described by the classical Bardeen-Cooper-Schrieffer theory [J.I. Bo\^zovi\'c, X. He, J. Wu, and A. T. Bollinger, Nature 536, 309 (2016)]. We demonstrate that 1) at temperature $T=0$, the superfluid density $n_s$ turns out to be considerably smaller than the total electron density; 2) the critical temperature $T_c$ is controlled by $n_s$ rather than by doping, and is a linear function of the $n_s$; 3) at $T>T_c$ the resistivity $\rho(T)$ varies linearly with temperature, $\rho(T)\propto \alpha T$, where $\alpha$ diminishes with $T_c\to 0$, while in the normal overdoped (non superconducting) region with $T_c=0$, the resistivity becomes $\rho(T)\propto T^2$. The theoretical results presented are in good agreement with recent experimental observations, closing the colossal gap between these empirical findings and Bardeen-Cooper-Schrieffer-like theories.