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Register a new userUniversal relationship between the energy scales of the pseudogap phase, the superconducting state and the charge density wave order in copper oxide superconductors
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We report the hole doping dependencies of the pseudogap phase energy scale, $2Delta_{rm PG}$, the anti-nodal (nodal) superconducting energy scales $2Delta^{AN}_{rm SC}$ ($2Delta^{N}_{rm SC}$) and the charge density wave energy scale, $2Delta_{rm CDW}$. They have been extracted from the electronic Raman responses of distinct copper oxide families. For all the cuprates studied, we reveal universal doping dependencies which suggest that $2Delta_{rm PG}$, $2Delta^{AN}_{rm SC}$ and $2Delta_{rm CDW}$ are governed by common microscopic interactions and that these interactions become relevant well above the superconducting transition at $T_c$. In sharp contrast, $2Delta^N_{rm SC}$ tracks the doping dependence of $T_c$, appearing to be controlled by a different kind of interactions than the energy scales above.
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The cuprate high temperature superconductors develop spontaneous charge density wave (CDW) order below a temperature $T_{CDW}$ and over a wide range of hole doping (p). An outstanding challenge in the field is to understand whether this modulated phase is related to the more exhaustively studied pseudogap and superconducting phases. To address this issue it is important to extract the energy scale $Delta_{CDW}$ associated with the charge modulations, and to compare it with the pseudogap (PG) $Delta_{PG}$ and the superconducting gap $Delta_{SC}$. However, while $T_{CDW}$ is well-characterized from earlier works little has been known about $Delta_{CDW}$ until now. Here, we report the extraction of $Delta_{CDW}$ for several cuprates using electronic Raman spectroscopy. Crucially, we find that, upon approaching the parent Mott state by lowering $p$, $Delta_{CDW}$ increases in a manner similar to the doping dependence of $Delta_{PG}$ and $Delta_{SC}$. This shows that CDW is an unconventional order, and that the above three phases are controlled by the same electronic correlations. In addition, we find that $Delta_{CDW} approx Delta_{SC}$ over a substantial doping range, which is suggestive of an approximate emergent symmetry connecting the charge modulated phase with superconductivity.
In a multiorbital model of the cuprate high-temperature superconductors soft antiferromagnetic (AF) modes are assumed to reconstruct the Fermi surface to form nodal pockets. The subsequent charge ordering transition leads to a phase with a spatially modulated transfer of charge between neighboring oxygen p_x and p_y orbitals and also weak modulations of the charge density on the copper d_{x^2-y^2} orbitals. As a prime result of the AF Fermi surface reconstruction, the wavevectors of the charge modulations are oriented along the crystalline axes with a periodicity that agrees quantitatively with experiments. This resolves a discrepancy between experiments, which find axial order, and previous theoretical calculations, which find modulation wavevectors along the Brillouin zone (BZ) diagonal. The axial order is stabilized by hopping processes via the Cu4s orbital, which is commonly not included in model analyses of cuprate superconductors.
Charge-density-wave (CDW) correlations within the quintessential CuO$_2$ planes have been argued to either cause [1] or compete with [2] the superconductivity in the cuprates, and they might furthermore drive the Fermi-surface reconstruction in high magnetic fields implied by quantum oscillation (QO) experiments for YBa$_2$Cu$_3$O$_{6+{delta}}$ (YBCO) [3] and HgBa$_2$CuO$_{4+{delta}}$ (Hg1201) [4]. Consequently, the observation of bulk CDW order in YBCO was a significant development [5,6,7]. Hg1201 features particularly high structural symmetry and recently has been demonstrated to exhibit Fermi-liquid charge transport in the relevant temperature-doping range of the phase diagram, whereas for YBCO and other cuprates this underlying property of the CuO$_2$ planes is partially or fully masked [8-10]. It therefore is imperative to establish if the pristine transport behavior of Hg1201 is compatible with CDW order. Here we investigate Hg1201 ($T_c$ = 72 K) via bulk Cu L-edge resonant X-ray scattering. We indeed observe CDW correlations in the absence of a magnetic field, although the correlations and competition with superconductivity are weaker than in YBCO. Interestingly, at the measured hole-doping level, both the short-range CDW and Fermi-liquid transport appear below the same temperature of about 200 K. Our result points to a unifying picture in which the CDW formation is preceded at the higher pseudogap temperature by $q$ = 0 magnetic order [11,12] and the build-up of significant dynamic antiferromagnetic correlations [13]. Furthermore, the smaller CDW modulation wave vector observed for Hg1201 is consistent with the larger electron pocket implied by both QO [4] and Hall-effect [14] measurements, which suggests that CDW correlations are indeed responsible for the low-temperature QO phenomenon.
Charge density wave (CDW) correlations feature prominently in the phase diagram of the cuprates, motivating competing theories of whether fluctuating CDW correlations aid superconductivity or whether static CDW order coexists with superconductivity in inhomogeneous or spatially modulated states. Here we report Cu $L$-edge resonant x-ray photon correlation spectroscopy (XPCS) measurements of CDW correlations in superconducting La$_{2-x}$Ba$_x$CuO$_4$ $x=0.11$. Static CDW order is shown to exist in the superconducting state at low temperatures and to persist up to at least 85% of the CDW transition temperature. We discuss the implications of our observations for how emph{nominally} competing order parameters can coexist in the cuprates.
Kagome metals AV3Sb5 (A = K, Rb, and Cs) exhibit superconductivity at 0.9-2.5 K and charge-density wave (CDW) at 78-103 K. Key electronic states associated with the CDW and superconductivity remain elusive. Here, we investigate low-energy excitations of CsV3Sb5 by angle-resolved photoemission spectroscopy. We found an energy gap of 70-100 meV at the Dirac-crossing points of linearly dispersive bands, pointing to an importance of spin-orbit coupling. We also found a signature of strongly Fermi-surface and momentum-dependent CDW gap characterized by the larger energy gap of maximally 70 meV for a band forming a saddle point around the M point, the smaller (0-18 meV) gap for a band forming massive Dirac cones, and a zero gap at the Gamma-centered electron pocket. The observed highly anisotropic CDW gap which is enhanced around the M point signifies an importance of scattering channel connecting the saddle points, laying foundation for understanding the nature of CDW and superconductivity in AV3Sb5.
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