# Thermodynamic evidence for nematic phase transition at the onset of pseudogap in YBa$_2$Cu$_3$O$_y$

## TL;DR

This study provides thermodynamic evidence that the pseudogap phase in cuprate superconductors involves a second-order nematic phase transition characterized by rotational symmetry breaking, distinct from charge density wave order.

## Contribution

The paper presents high-precision thermodynamic measurements revealing a nematic phase transition at the pseudogap onset in YBa$_2$Cu$_3$O$_y$, establishing a thermodynamic link between nematicity and the pseudogap.

## Key findings

- In-plane magnetic susceptibility anisotropy increases below T*
- Anisotropy exhibits a kink at T* and scales with T/T*
- Nematic transition is distinct from charge density wave transition

## Abstract

A central issue in the quest to understand the superconductivity in cuprates is the nature and origin of the pseudogap state, which harbours anomalous electronic states such as Fermi arc, charge density wave (CDW), and $d$-wave superconductivity. A fundamentally important, but long-standing controversial problem has been whether the pseudogap state is a distinct thermodynamic phase characterized by broken symmetries below the onset temperature $T^*$. Electronic nematicity, a fourfold ($C_4$) rotational symmetry breaking, has emerged as a key feature inside the pseudogap regime, but the presence or absence of a nematic phase transition and its relationship to the pseudogap remain unresolved. Here we report thermodynamic measurements of magnetic torque in the underdoped regime of orthorhombic YBa$_2$Cu$_3$O$_y$ with a field rotating in the CuO$_2$ plane, which allow us to quantify magnetic anisotropy with exceptionally high precision. Upon entering the pseudogap regime, the in-plane anisotropy of magnetic susceptibility increases after exhibiting a distinct kink at $T^*$. Our doping dependence analysis reveals that this anisotropy is preserved below $T^*$ even in the limit where the effect of orthorhombicity is eliminated. In addition, the excess in-plane anisotropy data show a remarkable scaling behaviour with respect to $T/T^*$ in a wide doping range. These results provide thermodynamic evidence that the pseudogap onset is associated with a second-order nematic phase transition, which is distinct from the CDW transition that accompanies translational symmetry breaking. This suggests that nematic fluctuations near the pseudogap phase boundary have a potential link to the strange metallic behaviour in the normal state, out of which high-$T_c$ superconductivity emerges.