Thermodynamic evidence for a nematic phase transition at the onset of the pseudogap in YBa2Cu3Oy

Abstract

A long-standing controversial issue in the quest to understand the superconductivity in cuprates is the nature of the enigmatic pseudogap region of the phase diagram 1 . Especially important is whether the pseudogap state is a distinct thermodynamic phase characterized by broken symmetries below the onset temperature T * . Here we report torque-magnetometry measurements of anisotropic susceptibility within the ab planes in orthorhombic YBa 2 Cu 3 O y with exceptionally high precision. The in-plane anisotropy displays a significant increase with a distinct kink at the pseudogap onset temperature T * , showing a remarkable scaling behaviour with respect to T/T * in a wide doping range. Our systematic analysis reveals that the rotational symmetry breaking sets in at T * in the limit where the e ect of orthorhombicity is eliminated. These results provide thermodynamic evidence that the pseudogap onset is associated with a second-order nematic phase transition, which di ers from the recently reported charge-density-wave transition that accompanies translational symmetry breaking [2][3][4][5][6][7][8][9][10] . The pseudogap state harbours anomalous electronic states such as Fermi arcs, charge density waves (CDW), and d-wave superconductivity 1 . Electronic nematicity, a four-fold (C 4 ) rotational symmetry breaking, has emerged as a key feature inside the pseudogap regime 11-14 , but the presence or absence of a nematic phase transition and its relationship to the pseudogap remain unresolved. Nematicity has been widely discussed in cuprates, and one of its mechanism is the onset of a stripe-type CDW order parameter which generally breaks rotation symmetry as well as translation symmetry with a nonzero wavenumber Q = 0 (refs 2-10,15-18). In Bi 2 Sr 2 CaCu 2 O 8+δ (BSCCO), scanning tunnelling microscopy experiments at low temperatures report an electronic state, consisting of short-range CDW of unidirectional (one-dimensional, 1D) type with a period of ∼4a 0 , where a 0 is the Cu-O-Cu distance 19,20 . This nano-stripe structure persists even well above the superconducting transition temperature T c (ref. 21). In YBa 2 Cu 3 O y (YBCO), the short-range CDW order forms a dome-shaped boundary inside the pseudogap regime 6,7 . Resonant X-ray scattering (RXS) experiments in YBCO report that the CDW is of unidirectional type with a periodicity of ∼3a 0 (ref. 4).In both BSCCO and YBCO, the CDW forms domains with a size of ∼3 nm in zero field, inside which the C 4 symmetry of the unit cell is strongly broken. In contrast to such CDW orders, the nematicity may also be caused by an instability without breaking translational symmetry, characterized by Q = 0.The measurement of the magnetic torque has a very high sensitivity for detecting magnetic anisotropy. The torque τ = µ 0 V M × H is a thermodynamic quantity, a differential of the free energy with respect to angular displacement. Here µ 0 is the permeability of vacuum, V is the sample volume, and M is the magnetization induced by the external magnetic field H. When H is rotated ...

Discovery of slow magnetic fluctuations and critical slowing down in the pseudogap phase of YBa 2 Cu 3 O y

“…[ T * is also the temperature around which changes in transport properties ( 34 ) and thermodynamic properties ( 35 , 36 ) from those of the strange metal phase begin to be observed.] The observed T mag also corresponds well to the results of recent torque magnetometry measurements, which support a second-order phase transition at T * ( 9 ). The inset of Fig.…”

“…Orange circles: T * from second harmonic generation ( 8 ). Green stars: T * from magnetic torque ( 9 ). Magenta left triangles: Charge-density-wave (CDW) onset temperatures T CDW from NMR ( 20 ).…”

“…For all y , the onset of long-range CDW order is at still lower temperatures and is only observed in high-applied magnetic fields ( 20 ). Recent torque magnetometry measurements also provide strong evidence that CDW order and the pseudogap phase are characterized by distinct broken symmetries at different temperatures ( 9 ). The detailed temperature-doping phase diagram (Fig.…”

“…Recent experiments have shown that, consistent with a phase transition, time-reversal symmetry ( 5 , 6 ) and spatial rotation and inversion symmetries ( 7 – 9 ) are broken below T * in a number of cuprate superconductors. However, lattice translational symmetry is preserved, indicating that the antiferromagnetism that lies near the pseudogap phase in the temperature-doping phase diagram is not involved.…”

Evidence for a universal Fermi-liquid scattering rate throughout the phase diagram of the copper-oxide superconductors

“…At the hole concentration p * ≈ 0.19, just above the optimal doping level at which the superconducting (SC) transition temperature (T c ) is maximized, the SC state directly evolves from the peculiar SM state. The intervening region of the phase diagram at lower doping is marked by the pseudogap (PG) phenomenon below T * (p) and by evidence for a phase transition [7][8][9][10][11][12][13][14]. These and other experimental observations have been argued to be the result of an underlying quantum critical point at p * with associated fluctuations that give rise to the extended T-linear resistive behavior and to the superconductivity [1].…”