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Register a new userSoftening of Cu-O bond stretching phonon in tetragonal HgBa$_2$CuO$_{4+delta}$
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Phonons in nearly optimally doped HgBa$_2$CuO$_{4+delta}$ were studied by inelastic X-ray scattering. The dispersion of the low energy modes is well described by a shell model, while the Cu-O bond stretching mode at high energy shows strong softening towards the zone boundary, which deviates strongly from the model. This seems to be common in the hole-doped high-$T_mathrm{c}$ superconducting cuprates, and, based on this work, not related to a lattice distortion specific to each material.
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The pseudogap phenomenon in cuprates is the most mysterious puzzle in the research of high-temperature superconductivity. In particular, whether the pseudogap is associated with a crossover or phase transition has been a long-standing controversial issue. The tetragonal cuprate HgBa$_2$CuO$_{4+delta}$, with only one CuO$_2$ layer per primitive cell, is an ideal system to tackle this puzzle. Here, we measure the anisotropy of magnetic susceptibility within the CuO$_2$ plane with exceptionally high-precision magnetic torque experiments. Our key finding is that a distinct two-fold in-plane anisotropy sets in below the pseudogap temperature $T^*$, which provides thermodynamic evidence for a nematic phase transition with broken four-fold symmetry. Most surprisingly, the nematic director orients along the diagonal direction of the CuO$_2$ square lattice, in sharp contrast to the bond nematicity reported in various iron-based superconductors and double-layer YBa$_2$Cu$_3$O$_{6+delta}$, where the anisotropy axis is along the Fe-Fe and Cu-O-Cu directions, respectively. Another remarkable feature is that the enhancement of the diagonal nematicity with decreasing temperature is suppressed around the temperature at which short-range charge-density-wave (CDW) formation occurs. This is in stark contrast to YBa$_2$Cu$_3$O$_{6+delta}$, where the bond nematicity is not influenced by the CDW. Our result suggests a competing relationship between diagonal nematic and CDW order in HgBa$_2$CuO$_{4+delta}$.
Using resonant X-ray diffraction and Raman spectroscopy, we study charge correlations and lattice dynamics in two model cuprates, HgBa$_{2}$CuO$_{4+delta}$ and HgBa$_{2}$CaCu$_{2}$O$_{6+delta}$. We observe a maximum of the characteristic charge order temperature around the same hole concentration ($p approx 0.09$) in both compounds, and concomitant pronounced anomalies in the lattice dynamics that involve the motion of atoms in and/or adjacent to the CuO$_2$ layers. These anomalies are already present at room temperature, and therefore precede the formation of the static charge correlations, and we attribute them to an instability of the CuO$_2$ layers. Our finding implies that the charge order in the cuprates is an emergent phenomenon, driven by a fundamental variation in both lattice and electronic properties as a function of doping.
Antiferromagnetic correlations have been argued to be the cause of the d-wave superconductivity and the pseudogap phenomena exhibited by the cuprates. Although the antiferromagnetic response in the pseudogap state has been reported for a number of compounds, there exists no information for structurally simple HgBa$_2$CuO$_{4+delta}$. Here we report neutron scattering results for HgBa$_2$CuO$_{4+delta}$ (superconducting transition temperature T$_c$ $sim$ 71 K, pseudogap temperature T* $sim$ 305 K) that demonstrate the absence of the two most prominent features of the magnetic excitation spectrum of the cuprates: the X-shaped hourglass response and the resonance mode in the superconducting state. Instead, the response is Y-shaped, gapped, and significantly enhanced below T*, and hence a prominent signature of the pseudogap state.
The cuprates exhibit a prominent charge-density-wave (CDW) instability with wavevector along [100], i.e., the Cu-O bond direction. Whereas CDW order is most prominent at moderate doping and low temperature, there exists increasing evidence for dynamic charge correlations throughout a large portion of the temperature-doping phase diagram. In particular, signatures of incipient charge order have been observed as phonon softening and/or broadening near the CDW wavevector approximately half-way through the Brillouin zone. Most of this work has focused on moderately-doped cuprates, for which the CDW order is robust, or on optimally-doped samples, for which the superconducting transition temperature ($T_c$) attains its maximum. Here we present a time-of-flight neutron scattering study of phonons in simple-tetragonal $text{HgBa}_2text{CuO}_{4+delta}$ ($T_c = 55$ K) at a low doping level where prior work showed the CDW order to be weak. We employ and showcase a new software-based technique that mines the large number of measured Brillouin zones for useful data in order to improve accuracy and counting statistics. Density-functional theory has not provided an accurate description of phonons in $text{HgBa}_2text{CuO}_{4+delta}$, yet we find the right set of parameters to qualitatively reproduce the data. The notable exception is a dispersion minimum in the longitudinal Cu-O bond-stretching branch along [100]. This discrepancy suggests that, while CDW order is weak, there exist significant dynamic charge correlations in the optic phonon range at low doping, near the edge of the superconducting dome.
High magnetic fields have revealed a surprisingly small Fermi-surface in underdoped cuprates, possibly resulting from Fermi-surface reconstruction due to an order parameter that breaks translational symmetry of the crystal lattice. A crucial issue concerns the doping extent of this state and its relationship to the principal pseudogap and superconducting phases. We employ pulsed magnetic field measurements on the cuprate HgBa$_2$CuO$_{4+delta}$ to identify signatures of Fermi surface reconstruction from a sign change of the Hall effect and a peak in the temperature-dependent planar resistivity. We trace the termination of Fermi-surface reconstruction to two hole concentrations where the superconducting upper critical fields are found to be enhanced. One of these points is associated with the pseudogap end-point near optimal doping. These results connect the Fermi-surface reconstruction to both superconductivity and the pseudogap phenomena.
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