Toward a topological scenario for high-temperature superconductivity of copper oxides

TL;DR

This paper explores the topological origins of high-temperature superconductivity in copper oxides, linking non-Fermi-liquid behavior and resistivity crossover to a topological phase transition in the Landau state.

Contribution

It introduces a topological scenario based on interaction-induced flat bands to explain the phase diagram and resistivity behavior of cuprates, challenging conventional quantum-critical models.

Findings

Resistivity shows a crossover from linear to quadratic with doping.

The linear coefficient in resistivity decomposes into a doping-dependent and a universal Planckian factor.

Topological rearrangement of the Landau state underpins the non-Fermi-liquid behavior.

Abstract

The structure of the joint phase diagram demonstrating high-$T_c$ superconductivity of copper oxides is studied on the basis of the theory of interaction-induced flat bands. Prerequisites of an associated topological rearrangement of the Landau state are established, and related non-Fermi-liquid (NFL) behavior of the normal states of cuprates is investigated. We focus on manifestations of this behavior in the electrical resistivity $\rho(T)$, especially the observed gradual crossover from normal-state $T$-linear behavior $\rho(T,x)=A_1(x)T$ at doping $x$ below the critical value $x_c^h$ for termination of superconductivity, to $T$-quadratic behavior at $x>x_c^h$, which is incompatible with predictions of the conventional quantum-critical-point scenario. It is demonstrated that at $x<x^h_c$, in agreement with available experimental data, the coefficient $A_1( x)$ is decomposed into the product of two factors, one of which changes linearly with doping $x$, while the second is universal, being of the Planckian form.