Electronic specific heat and low energy quasiparticle excitations in superconducting state of $La_{2-x}Sr_xCuO_4$ single crystals

TL;DR

This study measures low temperature specific heat in La_{2-x}Sr_xCuO_4 single crystals across doping levels, analyzing quasiparticle excitations and scaling laws to understand the interplay of superconductivity and competing orders.

Contribution

It provides detailed analysis of the doping-dependent validity of d-wave scaling laws and reveals deviations linked to competing orders and core size effects.

Findings

Scaling law holds well in optimally doped samples.

Degradation of scaling quality in underdoped samples.

Zero-temperature data follow Volovik's relation across all doping levels.

Abstract

Low temperature specific heat has been measured and extensively analyzed on a series of $La_{2-x}Sr_xCuO_4$ single crystals from underdoped to overdoped regime. From these data the quasiparticle density of states (DOS) in the mixed state is derived and compared to the predicted scaling law $C_{vol}/T\sqrt{H}=f(T/\sqrt{H})$ of d-wave superconductivity. It is found that the scaling law can be nicely followed by the optimally doped sample (x=0.15) in quite wide region of ($T/\sqrt{H} \leq 8 K /\sqrt{T}$). However, the region for this scaling becomes smaller and smaller towards more underdoped region: a clear trend can be seen for samples from x=0.15 to 0.069. Therefore, generally speaking, the scaling quality becomes worse on the underdoped samples in terms of scalable region of $T/\sqrt{H}$. This feature in the underdoped region is explained as due to the low energy excitations from a second order (for example, anti-ferromagnetic correlation, d-density wave, spin density wave or charge density wave order) that may co-exist or compete with superconductivity. Surprisingly, deviations from the d-wave scaling law have also been found for the overdoped sample (x=0.22). While the scaling law is reconciled for the overdoped sample when the core size effect is taken into account. An important discovery of present work is that the zero-temperature data follow the Volovik's relation $\Delta \gamma(T=0)=A\sqrt{H}$ quite well for all samples investigated here although the applicability of the d-wave scaling law to the data at finite temperatures varies with doped hole concentration. Finally we present the doping dependence of some parameters, such as, the residual linear term $\gamma_0$, the $\alpha$ value, etc. ...