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Register a new userThermodynamic evidence for nematic phase transition at the onset of pseudogap in YBa$_2$Cu$_3$O$_y$
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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.
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Using ultrasound measurements on detwinned single crystals of underdoped YBa$_2$Cu$_3$O$_y$ (YBCO) we study the hole doping ($p$) evolution of the thermodynamic anisotropy obtained by comparing the strain dependence of superconducting $T_{rm c}$ along the $a$ and $b$ crystallographic directions. While the structural orthorhombicity of YBCO reduces monotonically with decreasing $p<0.16$, we find that the thermodynamic anisotropy shows an intriguing enhancement at intermediate doping level of electronic origin. Our theoretical analysis shows that the enhancement of the electronic anisotropy can be related to the pseudogap potential that itself increases when the Mott insulating state is approached. Our results imply that the pseudogap is controlled by a local energy scale that can be tuned by varying the nearest neighbor Cu-Cu bond length. Our work opens the possibility to strain engineer the pseudogap potential to enhance the superconducting $T_{rm c}$.
Evidence for intra-unit-cell (IUC) magnetic order in the pseudogap region of high-$T_c$ cuprates below a temperature $T^ast$ is found in several studies, but NMR and $mu$SR experiments do not observe the expected static local magnetic fields. It has been noted, however, that such fields could be averaged by fluctuations. Our measurements of muon spin relaxation rates in single crystals of YBa$_2$Cu$_3$O$_y$ reveal magnetic fluctuations of the expected order of magnitude that exhibit critical slowing down at $T^ast$. These results are strong evidence for fluctuating IUC magnetic order in the pseudogap phase.
Nematicity has emerged as a key feature of cuprate superconductors, but its link to other fundamental properties such as superconductivity, charge order and the pseudogap remains unclear. Here we use measurements of transport anisotropy in YBa$_2$Cu$_3$O$_y$ to distinguish two types of nematicity. The first is associated with short-range charge-density-wave modulations in a doping region near $p = 0.12$. It is detected in the Nernst coefficient, but not in the resistivity. The second type prevails at lower doping, where there are spin modulations but no charge modulations. In this case, the onset of in-plane anisotropy - detected in both the Nernst coefficient and the resistivity - follows a line in the temperature-doping phase diagram that tracks the pseudogap energy. We discuss two possible scenarios for the latter nematicity.
We present results of Raman scattering experiments on tetragonal ${rm (Y_{1-y}Ca_{y})Ba_{2}Cu_{3}O_{6+x}}$ for doping levels $p(x,y)$ between 0 and 0.07 holes/CuO$_2$. Below the onset of superconductivity at $p_{rm sc1} approx 0.06$, we find evidence of a diagonal superstructure. At $p_{rm sc1}$, lattice and electron dynamics change discontinuously with the charge and spin properties being renormalized at all energy scales. The results indicate that charge ordering is intimately related to the transition at $p_{rm sc1}$ and that the maximal transition temperature to superconductivity at optimal doping $T_{c}^{rm max}$ depends on the type of ordering at $p>p_{rm sc1}$.
We discuss a recent resonant ultrasound spectroscopy (RUS) study of YBa$_2$Cu$_3$O$_{6+delta}$, which infers a line of phase transitions bounding the pseudogap phase and argue that this scenario is not supported by thermodynamic evidence. We show that the anomalies in RUS, heat capacity and thermal expansion at the superconducting transition temperatures agree well. But there are large discrepancies between RUS and thermodynamic measurements at $T^*$ where the pseudogap phase transitions are purported to occur. Moreover, the frequency and temperature dependence of the RUS data for the crystal with $delta = 0.98$, interpreted in terms of critical slowing down near an electronic phase transition, is five orders of magnitude smaller than what is expected. For this crystal the RUS data near $T^*$ are more consistent with non-equilibrium effects such as oxygen relaxation.
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