Competing orders and inter-layer tunnelling in cuprate superconductors: A finite temperature Landau theory

TL;DR

This paper develops a finite temperature Landau theory for cuprate superconductors that accounts for competing orders and interlayer tunneling, accurately predicting transition temperatures and their dependence on layer number, aligning with experimental observations.

Contribution

It extends a zero-temperature Landau theory to finite temperatures, providing a clear method to determine $T_c$ and explaining layer-dependent effects in cuprates.

Findings

The theory predicts $T_c$ without ambiguity for given parameters.

It explains the high pseudo-gap temperature relative to energy scales.

Results agree with experimental layer-number dependence of $T_c$.

Abstract

We propose a finite temperature Landau theory that describes competing orders and interlayer tunneling in cuprate superconductors as an important extension to a corresponding theory at zero temperature [Nature {\bf 428}, 53 (2004)], where the superconducting transition temperature $T_c$ is defined in three possible ways as a function of the zero temperature order parameter. For given parameters, our theory determines $T_c$ without any ambiguity. In mono- and double-layer systems we discuss the relation between zero temperature order parameter and the associated transition temperature in the presence of competing orders, and draw a connection to the puzzling experimental fact that the pseudo-gap temperature is much higher than the corresponding energy scale near optimum doping. Applying the theory to multi-layer systems, we calculate the layer-number dependence of $T_c$. In a reasonable parameter space the result turns out to be in agreement with experiments.