Synchrotron x-ray scattering study of charge-density-wave order in HgBa$_2$CuO$_{4+δ}$
W. Tabis, B. Yu, I. Bialo, M. Bluschke, T. Kolodziej, A. Kozlowski, E. Blackburn, K. Sen, E. M. Forgan, M. v. Zimmermann, Y. Tang, E. Weschke, B. Vignolle, M. H… 展开作者
W. Tabis, B. Yu, I. Bialo, M. Bluschke, T. Kolodziej, A. Kozlowski, E. Blackburn, K. Sen, E. M. Forgan, M. v. Zimmermann, Y. Tang, E. Weschke, B. Vignolle, M. Hepting, H. Gretarsson, R. Sutarto, F. He, M. Le Tacon, N. Barišić, G. Yu, M. Greven
We present a detailed synchrotron x-ray scattering study of the charge-density-wave (CDW) order in simple tetragonal HgBa$_2$CuO$_{4+δ}$ (Hg1201). Resonant soft x-ray scattering measurements reveal that short-range order appears at a temperature that is distinctly lower than the pseudogap temperature and in excellent agreement with a prior transient reflectivity result. Despite considerable structural differences between Hg1201 and YBa$_2$Cu$_3$O$_{6+δ}$, the CDW correlations exhibit similar doping dependencies, and we demonstrate a universal relationship between the CDW wave vector and the size of the reconstructed Fermi pocket observed in quantum oscillation experiments. The CDW correlations in Hg1201 vanish already below optimal doping, once the correlation length is comparable to the CDW modulation period, and they appear to be limited by the disorder potential from unit cells hosting two interstitial oxygen atoms. A complementary hard x-ray diffraction measurement, performed on an underdoped Hg1201 sample in magnetic fields along the crystallographic $c$ axis of up to 16 T, provides information about the form factor of the CDW order. As expected from the single-CuO$_2$-layer structure of Hg1201, the CDW correlations vanish at half-integer values of $L$ and appear to be peaked at integer $L$. We conclude that the atomic displacements associated with the short-range CDW order are mainly planar, within the CuO$_2$ layers.
It is well established that the hole density in the prototypical superconductor La$_{2-x}$Sr$_x$CuO$_4$ is very inhomogeneous due to Sr-dopant induced disorder. On the other hand, until recently it is widely believed that the hole distribution in HgBa$_2$CuO$_{4+δ}$ and Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ doped by interstitial oxygen is much more uniform. Recent nuclear magnetic resonance measurements indicate, however, that the charge inhomogeneity in HgBa$_2$CuO$_{4+δ}$ is close to that in La$_{2-x}$Sr$_x$CuO$_4$. Calculations performed in the present paper confirm this observation. We also show t…
We develop a model for the angle-dependent magnetoresistance of HgBa$_2$CuO$_{4+δ}$ in the underdoped regime where the Fermi surface is thought to be reconstructed by an ordered state such as a charge density wave. We show that such measurements can be employed to unambiguously distinguish the form of the Fermi surface's interlayer warping, placing severe contraints on the symmetry and nature of the reconstructing order. We describe experimentally accessible conditions in which our calculations can be put to the test.
By means of local Hall probe ac and dc permeability measurements we investigated the phase diagram of vortex matter for the HgBa$_2$CuO$_{4+δ}$ superconductor in the regime near the critical temperature. The second peak line, $H_{\rm sp}$, in contrast to what is usually assumed, doesn't terminate at the critical temperature. Our local ac permeability measurements revealed pronounced hysteretic behavior and thermomagnetic history effects near the onset of the second peak, giving evidence for a phase transition of vortex matter from an ordered qausilattice state to a disordered glass.
We theoretically investigate inhomogeneity effects on the charges, electric field gradients and site-projected densities of states in HgBa$_2$CuO$_{4+δ}$. We find pronounced differences in the doping-induced number of holes at different atomic sites. The contributions of these sites to the density of states in the vicinity of the Fermi level are peaked at the same energy, but vary in magnitude by up to 70 percent and have different energy dependence. Due to this energy dependence the role of the intrinsic inhomogeneities for superconductivity strongly depends on the energy and character of the…
$^{63}$Cu and $^{199}$Hg NMR shifts for an optimally and underdoped HgBa$_{2}$CuO$_{4+δ}$ single crystal are reported, and the temperature dependence dictates a two-component description of the uniform spin susceptibility. The first component, associated with the pseudogap phenomenon in the NMR shifts, decreases already at room temperature and continues to drop as the temperature is lowered, without a drastic change at the transition temperature into the superconducting state. The second component is temperature independent above the superconducting transition temperature and vanishes rapidly …
We present the first angle-resolved photoemission measurement on the single-layer Hg-based cuprate, HgBa$_2$CuO$_{4+δ}$ (Hg1201). A quasi-particle peak in the spectrum and a kink in the band dispersion around the diagonal of the Brillouin zone are observed, whereas no structure is detected near the Brillouin zone boundary. To search for a material-dependent trend among hole-doped cuprates, including Hg1201, we use a tight-binding model to fit their Fermi surfaces. We find a positive correlation between the $T_{c,\mathrm{max}}$ and $t'/t$, consistent with theoretical predictions.
We present an inelastic neutron scattering study of the structurally simple single-layer compound HgBa$_2$CuO$_{4+δ}$ close to optimal doping ($T_c \approx 96$ K). A well-defined antiferromagnetic resonance with energy $ω_r = 56$ meV ($\approx 6.8 k_BT_c$) is observed below the superconducting transition temperature $T_c$. The resonance mode is energy-resolution limited and exhibits an intrinsic momentum width of about $0.2 \mathrm{\mathring{A}^{-1}}$, consistent with prior work on several other cuprates. However, the unusually large value of the mode energy implies a non-universal relationshi…
Novel nanoscale probes are opening new venues for understanding unconventional electronic and magnetic functionalities driven by multiscale lattice complexity in doped high temperature superconducting perovskites. In this work we focus on the multiscale texture at supramolecular level of atomic oxygen interstitials (O-i) stripes in HgBa$_2$CuO$_{4+y}$ at optimal doping for the highest superconducting critical temperature $T_C$=94K. We report compelling evidence for the nematic phase of oxygen-interstitial O-i atomic wires with fractal-like spatial distribution over multiple scales by using sca…
Nuclear magnetic resonance (NMR) experiments on single crystals of HgBa$_{2}$CuO$_{4+δ}$ are presented that identify two distinct temperature-dependent spin susceptibilities: one is due to a spin component that is temperature-dependent above the critical temperature for superconductivity ($T_{\rm c}$) and reflects pseudogap behavior; the other is Fermi-liquid-like in that it is temperature independent above $T_{\rm c}$ and vanishes rapidly below $T_{\rm c}$. In addition, we demonstrate the existence of a third, hitherto undetected spin susceptibility: it is temperature independent at higher te…
The strain derivatives of $T_c$ along the $a$ and $c$ axes have been determined for HgBa$_2$CuO$_{4+δ}$ (Hg1201), the simplest monolayer cuprate with the highest $T_c$ of all monolayer cuprates ($T_c$ = 97 K at optimal doping). The underdoped compound with the initial $T_c$ of 65 K has been studied as a function of pressure up to 20 GPa by magnetic susceptibility and X-ray diffraction (XRD). The observed linear increase in $T_c$ with pressure is the same as previously been found for the optimally-doped compound. The above results have enabled the investigation of the origins of the significant…
Various forms of spin and charge ordering have been identified in a wide range of cuprate superconducting materials, but whether these behaviors are ubiquitous phenomena is not established. In this work we focus on one of the simplest compounds, HgBa$_{2}$CuO$_{4+δ}$ (Hg1201), a superconductor with a high transition temperature, 97 K, having only a single layer and tetragonal structure, in contrast to one of the most extensively studied materials, YBa$_{2}$Cu$_{3}$O$_{6+y}$ (Y123). Using nuclear magnetic resonance we have discovered a coherent spatial modulation of both spin and charge that is…
Using resonant X-ray diffraction and Raman spectroscopy, we study charge correlations and lattice dynamics in two model cuprates, HgBa$_{2}$CuO$_{4+δ}$ and HgBa$_{2}$CaCu$_{2}$O$_{6+δ}$. 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 a…
While recent experiments have found that at optimum doping for the highest critical temperature in HgBa$_2$CuO$_{4+y}$ (Hg1201) the oxygen interstitials (O-i) are not homogeneously distributed but form one-dimensional atomic wires, there are no available information of its electronic structure considering self-organized O-i atomic wires. Here we report the calculated electronic structure of HgBa$_2$CuO$_{4+y}$ where oxygen interstitials form atomic wires along (1,0,0) crystal direction in the Hg layer. We find that at optimum doping for superconductivity the chemical potential is tuned near an…
The magnitude of the powder spin susceptibility of an optimally doped superconductor HgBa$_2$CuO$_{4+δ}$ (Hg1201) in the normal state is found to be nearly the same as that of La$_{2-x}$Sr$_{x}$CuO$_{4}$ near the optimally doped level. The Stoner enhancement factor of Hg1201 is larger than that of La$_{2-x}$Sr$_{x}$CuO$_{4}$. The magnitude correlation of the Stoner enhancement factor is inconsistent with the effect of the recent theoretical Coulomb repulsion between 3$d$ electrons and that of the superexchange intereraction of a charge transfer type.
We present an extensive study of vortex dynamics in a high-quality single crystal of HgBa$_2$CuO$_{4+δ}$ (Hg1201), a highly anisotropic superconductor that is a model system for studying the effects of anisotropy. From magnetization $M$ measurements over a wide range of temperatures $T$ and fields $H$, we construct a detailed vortex phase diagram. We find that the temperature-dependent vortex penetration field $H_p(T)$, second magnetization peak $H_{smp}(T)$, and irreversibility field $H_{irr}(T)$ all decay exponentially at low temperatures and exhibit an abrupt change in behavior at high temp…
We study the spin dynamics of the Resonant Excitonic State (RES) proposed, within the theory of an emergent SU(2) symmetry, to explain some properties of the pseudo-gap phase of cuprate superconductors. The RES can be described as a proliferation of particle-hole patches with an internal modulated structure. We model the RES modes as a charge order with multiple $2{\bf {p}}_{\text{F}}$ ordering vectors, where $2{\bf {p}}_{\text{F}}$ connects two opposite side of the Fermi surface. This simple modelization enables us to propose a comprehensive study of the collective mode observed at the antife…
Phonons in nearly optimally doped HgBa$_2$CuO$_{4+δ}$ 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.
We report a doping dependant Electronic Raman Scattering (ERS) study of HgBa$_2$CuO$_{4+δ}$ (Hg-1201) single crystals. We investigate the dynamics of the antinodal and nodal quasiparticles. We show that the dynamical response of the antinodal quasiparticles is strongly reduced towards the underdoped regime in both the normal and superconducting states. When probing the nodal quasiparticles, we are able to distinguish between the energy scale of the pseudogap and that of the superconducting gap. A simple model relating the suppression of the dynamical response of the antinodal quasiparticles to…
Generally strong charge and magnetic inhomogeneities are observed in NQR/NMR experiments on underdoped cuprates. It is not the case for the underdoped HgBa$_2$CuO$_{4+δ}$, the most symmetric and highest T$_c$ single layer cuprate, whose magnetic inhomogeneity is strongly suppressed. Also neutron scattering experiments reveal a unique pair of weakly dispersive magnetic modes in this material. We propose that these special properties stem from the symmetric positioning of the O-dopants between adjacent CuO$_2$ layers that lead to a strong superexchange interaction between a pair of hole spins. I…
We report a doping dependent study of the quasiparticles dynamics in HgBa$_2$CuO$_{4+δ}$ via Electronic Raman Scattering. A well-defined energy scale is found in the normal state dynamics of the quasiparticles over a broad doping range. It is interpreted as evidence for coupling between the quasiparticles and a collective bosonic mode whose energy scale depend only weakly with doping. We contrast this behavior with that of the superconducting gap whose amplitude near the node continuously decreases towards the underdoped regime. We discuss the implications of our findings on the nature of the …
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$_{4+δ}$. Here we report neutron scattering results for HgBa$_2$CuO$_{4+δ}$ (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 t…
The simple structure of HgBa$_2$CuO$_{4+δ}$ (Hg1201) is ideal among cuprates for study of the pseudogap phase as a broken symmetry state. We have performed $^{17}$O nuclear magnetic resonance (NMR) on an underdoped Hg1201 crystal with transition temperature of 74 K to look for circulating orbital currents proposed theoretically and inferred from neutron scattering. The narrow spectra preclude static local fields in the pseudogap phase at the apical site, suggesting that the moments observed with neutrons are fluctuating. The NMR frequency shifts are consistent with a dipolar field from the Cu$…
This paper is published in Advanced Materials (available at http://www3.interscience.wiley.com/cgi-bin/abstract/113511105/ABSTRACT). It has been withdrawn from the cond-mat preprint archive in order to avoid a violation of the Journal's policy.
The lamellar cuprate superconductors exhibit the highest ambient-pressure superconducting transition temperatures (T$_C$) and, after more than three decades of extraordinary research activity, continue to pose formidable scientific challenges. A major experimental obstacle has been to distinguish universal phenomena from materials- or technique-dependent ones. Angle-resolved photoemission spectroscopy (ARPES) measures momentum-dependent single-particle electronic excitations and has been invaluable in the endeavor to determine the anisotropic momentum-space properties of the cuprates. HgBa$_2$…
We report a Cu $K$-edge resonant inelastic x-ray scattering (RIXS) study of charge-transfer excitations in the 2-8 eV range in the structurally simple compound HgBa$_2$CuO$_{4+δ}$ at optimal doping ($T_{\rm c} = 96.5 $ K). The spectra exhibit a significant dependence on the incident photon energy which we carefully utilize to resolve a multiplet of weakly-dispersive ($ < 0.5$ eV) electron-hole excitations, including a mode at 2 eV. The observation of this 2 eV excitation suggests the existence of a charge-transfer pseudogap deep in the superconducting phase. Quite generally, our data demonstra…
Measurements of the $^{17}$O nuclear magnetic resonance (NMR) quadrupolar spectrum of apical oxygen in HgBa$_{2}$CuO$_{4+δ}$ were performed over a range of magnetic fields from 6.4 to 30\,T in the superconducting state. Oxygen isotope exchanged single crystals were investigated with doping corresponding to superconducting transition temperatures from 74\,K underdoped, to 78\,K overdoped. The apical oxygen site was chosen since its NMR spectrum has narrow quadrupolar satellites that are well separated from any other resonance. Non-vortex contributions to the spectra can be deconvolved in the ti…
In type-II superconductors exposed to magnetic fields between upper and lower critical values, $H_{c1}$ and $H_{c2}$, penetrating magnetic flux forms a lattice of vortices whose motion can induce dissipation. Consequently, the magnetization $M$ of superconductors is typically progressively weakened with increasing magnetic field $B \propto n_v$ (for vortex density $n_v$). However, some materials exhibit a non-monotonic $M(B)$, presenting a maximum in $M$ at what is known as the second magnetization peak. This phenomenon appears in most classes of superconductors, including low $T_c$ materials,…
The specific heat $C$ of the single-layer cuprate superconductor HgBa$_2$CuO$_{4 + δ}$ was measured in an underdoped crystal with $T_{\rm c} = 72$ K at temperatures down to $2$ K in magnetic fields up to $35$ T, a field large enough to suppress superconductivity at that doping ($p \simeq 0.09$). In the normal state at $H = 35$ T, a residual linear term of magnitude $γ= 12 \pm 2$ mJ/K$^2$mol is observed in $C/T$ as $T \to 0$, a direct measure of the electronic density of states. This high value of $γ$ has two major implications. First, it is significantly larger than the value measured in overd…
HgBa$_{2}$CuO$_{4+δ}$ (Hg1201) has been shown to be a model cuprate for scattering, optical, and transport experiments, but angle-resolved photoemission spectroscopy (ARPES) data are still lacking owing to the absence of a charge-neutral cleavage plane. We report on progress in achieving the experimental conditions for which quasiparticles can be observed in the near-nodal region of the Fermi surface. The d-wave superconducting gap is measured and found to have a maximum of 39 meV. At low temperature, a kink is detected in the nodal dispersion at approximately 51 meV below the Fermi level, an …
To understand the link between doping and electronic properties in high temperature superconductors, we report first-principles calculations on the oxygen doping effect for the single layer cuprate HgBa$_2$CuO$_{4+δ}$. The doping effect is studied both by supercell and single cell virtual crystal type approaches. We find ionic behavior of the dopant atom up to an optimal doping concentration of $δ=0.22$. The excess oxygen attracts electrons from the CuO$_2$ plane leading to an increase of the hole concentration in this building block. The maximum amount of holes is reached when the oxygen $p$-…
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$_{4+δ}$, 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…
We report on the temperature dependence of $^{63}$Cu and $^{199}$Hg NMR magnetic shifts and linewidths for an optimally doped and an underdoped HgBa$_{2}$CuO$_{4+δ}$ single crystal, as well as the quadrupole splitting and its distribution for $^{63}$Cu. From the $^{63}$Cu and $^{199}$Hg \textit{magnetic shifts} we have recently concluded on the existence of two spin components with different temperature dependencies [J. Haase, D. Rybicki, C. P. Slichter, M. Greven, G. Yu, Y. Li, and X. Zhao, Phys. Rev. B 85, 104517 (2012)]. Here we give a comprehensive account of all data and focus on the line…
The compound HgBa$_2$CuO$_{4+Δ}$ (Hg1201) exhibits a simple tetragonal crystal structure and the highest superconducting transition temperature (T$_c$) among all single Cu-O layer cuprates, with T$_c$ = 97 K (onset) at optimal doping. Due to a lack of sizable single crystals, experimental work on this very attractive system has been significantly limited. Thanks to a recent breakthrough in crystal growth, such crystals have now become available. Here, we demonstrate that it is possible to identify suitable heat treatment conditions to systematically and uniformly tune the hole concentration of…
Anomalously high quasiparticle thermal conductivity in the underdoped cuprate superconductor HgBa$_{2}$CuO$_{4+δ}$
Université de Sherbrooke（舍布鲁克大学）；CEA Saclay（法国原子能和替代能源委员会萨克莱中心）；CNRS UPR3228, Univ. Grenoble Alpes, Univ. Toulouse, INSA-T（法国国家科学研究中心、格勒诺布尔阿尔卑斯大学、图卢兹大学）；IRL Frontières Quantiques, Université de Sherbrooke–CNRS（量子前沿研究所，舍布鲁克大学-法国国家科学研究中心）；Canadian Institute for Advanced Research（加拿大高级研究院）
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 CD…
We have succeeded in the synthesis of Re-doped $HgBa_{2}Ca_{n-1}Cu_{n}O_{2(n+1)+δ}$ quickly by a sealed tube technique with a bit of CsCl flux. Powder X-ray diffraction measurement revealed that the single phases of Re-doped $HgBa_{2}CuO_{4+δ}$ (Hg1201), $HgBa_{2}CaCu_{2}O_{6+δ}$ (Hg1212), and $HgBa_{2}Ca_{2}Cu_{3}O_{8+δ}$ (Hg1223) formed in 4 h. The sample grains exhibited plate-like crystals with the sizes of 20$\times$20$\times$1 $μm^{3}$ and the chemical compositions of Hg1201, Hg1212, and Hg1223. The superconducting transitions were observed at 25 K for Hg1201, 122 for Hg1212, and 133 K f…
A first-order phase transition is found in the multilayer cuprate superconductor, HgBa$_2$Ca$_4$Cu$_5$O$_y$ (Hg-1245), with a superconducting transition temperature of 108 K, under zero magnetic field. We observed a hysteretic specific heat jump around 41 K. We conclude that the Bardeen-Cooper-Schrieffer pairs have a residual entropy due to fluctuations in the phase difference between the five CuO$_2$ planes in a unit cell of Hg-1245, and that this fluctuation freezes below the first-order phase transition temperature.
The charge-density-wave (CDW) instability in the underdoped, pseudogap part of the cuprate phase diagram has been a major recent research focus, yet measurements of dynamic, energy-resolved CDW correlations are still in their infancy. We report a high-resolution resonant inelastic X-ray scattering (RIXS) study of the underdoped cuprate superconductor HgBa$_{2}$CuO$_{4+δ}$ ($T_c = 70$ K). At $T=250$ K, above the CDW order temperature $T_\mathrm{CDW} \approx 200$ K, we observe significant dynamic CDW correlations at about 40 meV. This energy scale is comparable to both the superconducting gap an…
We report that planar CuO_2 hole densities in high-T_c cuprates are consistently determined by the Cu-NMR Knight shift. In single- and bi-layered cuprates, it is demonstrated that the spin part of the Knight shift K_s(300 K) at room temperature monotonically increases with the hole density $p$ from underdoped to overdoped regions, suggesting that the relationship of K_s(300 K) vs. p is a reliable measure to determine p. The validity of this K_s(300 K)-p relationship is confirmed by the investigation of the p-dependencies of hyperfine magnetic fields and of spin susceptibility for single- and b…
We have investigated the doping dependencies of the basal areas in single-layer high-T_c cuprates La_{2-x}Sr_xCuO_4 and HgBa_2CuO_x, as well as in two-layer Y_{1-y}Ca_yBa_2Cu_3O_x and HgBa_2CaCu_2O_x. The basal areas not only tend to shrink on hole doping, as expected from single electron quantum chemistry, but exhibit also a "bulge'' around optimum doping. We attribute the "bulge'' to the effects of the strongly correlated quantum liquid on the CuO_2 lattice, rendering it nearly incompressible around optimum doping, but highly compressible in the weakly overdoped regime. Inhomogenous doping c…
Band calculations show that a stripe-like anti-ferromagnetic spin wave is enforced by a 'half-breathing' phonon distortion within the CuO plane of HgBa_2CuO_4. This spin-phonon coupling is increased further by shear distortion and by increased distance between Cu and apical oxygens. The effects from spin-phonon coupling are consistent with many observations in high-T_C materials. Spin-phonon coupling can be important for the mechanism of spin fluctuations and superconductivity, although the effects are quantitatively weak when using the local density potential.
We studied local magnetic properties of triple-CuO$_2$-layer superconductors HgBa$_2$Ca$_2$Cu$_3$O$_{8+δ}$ with rich $^{63}$Cu isotope (underdoped $T_\mathrm{c}$ = 124 K and optimally doped $T_\mathrm{c}$ = 134 K) by $^{63}$Cu NMR spin-echo techniques. The temperature dependences of the $^{63}$Cu nuclear spin-lattice relaxation rate $^{63}$(1/$T_1$) and the spin Knight shift $^{63}K_\mathrm{spin}$ of the inner plane Cu(1) site were nearly the same as those of the outer plane Cu(2) site in the normal states. The pseudogap temperature $T^*$ defined as the maximum temperature of $^{63}$(1/$T_1T$)…
Lattice distortions associated with charge stripe order in 1/8 hole-doped La$_{1.875}$Ba$_{0.125-x}$Sr$_{x}$CuO$_{4}$ are studied using synchrotron X-ray diffraction for $x=0.05$ and $x=0.075$. The propagation wave vector and charge order correlation lengths are determined with a high accuracy, revealing that the oblique charge stripes in orthorhombic $x=0.075$ crystal are more disordered than the aligned stripes in tetragonal $x=0.05$ crystal. The twofold periodicity of lattice modulations along the c-axis is explained by long-range Coulomb interactions between holes on neighboring CuO$_{2}$ …
Superconductivity studied by solving ab initio low-energy effective Hamiltonians for carrier doped CaCuO$_2$, Bi$_2$Sr$_2$CuO$_6$, Bi$_2$Sr$_2$CaCu$_2$O$_8$, and HgBa$_2$CuO$_4$
Phonon dynamics, charge response and the phonon density of states are calculated for the high-temperature superconductors HgBa$_{2}$CuO$_{4}$ and Bi$_{2}$Sr$_{2}$CuO$_{6}$ within a microscopic model for the electronic density response. The results are compared with previous calculations for La$_{2}$CuO$_{4}$ and Nd$_{2}$CuO$_{4}$. Our main focus is on the phononanomalies which are connected with the high-frequency oxygen bond-stretching modes (OBSM) found before in our calculations for $p$-doped La$_{2}$CuO$_{4}$ and $n$-doped Nd$_{2}$CuO$_{4}$. We investigate the question if the characteristi…
Multilayered cuprates possess not only the highest superconducting temperature transition but also offer a unique platform to study disorder-free CuO$_2$ planes and the interplay between competing orders with superconductivity. Here, we study the underdoped trilayer cuprate HgBa$_2$Ca$_2$Cu$_3$O$_{8+ δ}$ and we report the first quantum oscillation and Hall effect measurements in magnetic field up to 88 T. A careful analysis of the complex spectra of quantum oscillations strongly supports the coexistence of an antiferromagnetic order in the inner plane and a charge order in the outer planes. Th…
Band calculations on HgBa$_2$CuO$_4$ and La$_{(2-x)}$Sr$_x$CuO$_4$ with phonon and spin-waves within the CuO planes show that partial gaps are created at various energies depending on wavelengths. Spin and phonon gaps appear at different energies when the modulations are along [1,1,0], while they are at the same energy for modulations along [1,0,0]. It is shown that the ability to form gaps and antiferromagnetic waves is correlated with the strength of the interaction parameter $λ_{sf}$ for spin fluctuations. Many unusual properties of the high-T$_C$ oxides can be understood from spin-phonon c…
We perform first-principles calculation to study the electronic structure of HgBa$_{2}$Ca$_{n-1}$Cu$_{n}$O$_{2n+2+x}$ copper oxides up to $n = 6$ for the undoped parent compound $(x = 0)$ and up to $n = 3$ for the doped compound $(x > 0)$ by means of the SCAN meta-GGA density functional. Our calculations predict an antiferromagnetic insulator ground state for the parent compounds with an energy gap that decreases with the number of CuO$_{2}$ planes. We report structural, electronic and magnetic order evolution with $x$ which agree with experiments. We find an enhanced density of states at Ferm…
Charge density-wave order has been observed in cuprate superconductors whose crystal structure breaks the square symmetry of the CuO2 planes, such as orthorhombic YBa2Cu3Oy (YBCO), but not so far in cuprates that preserve that symmetry, such as tetragonal HgBa2CuO4+d (Hg1201). We have measured the Hall (R_H), Seebeck (S), and Nernst coefficients of underdoped Hg1201 in magnetic fields large enough to suppress superconductivity. The high-field R_H(T) and S(T) are found to drop with decreasing temperature and become negative, as also observed in YBCO at comparable doping. In YBCO, the negative R…
We report resonant electronic Raman scattering in optimally doped single layer HgBa$_2$CuO$_{4+δ}$ (Hg-1201) and trilayer HgBa$_2$Ca$_2$Cu$_3$O$_{8+δ}$ (Hg-1223) single crystals. Analysis of the $B_{1g}$ and B$_{2g}$ channels in the superconducting state of Hg-1201 advocates for a gap having d-wave symmetry. In addition a resonant study $B_{1g}$ pair-breaking peak and the $A_{1g}$ peak suggests that the $A_{1g}$ peak is not directly related to the d-wave superconducting gap amplitude. Comparison with trilayer Hg-1223 demonstrates the universal behavior of this two energy scales in optimally do…
Effects of coupling between phonon distortions and stripe-like spin waves in the CuO plane of HgBa$_2$CuO$_4$ are studied by band calculations. Local exchange enhancements depend sensitively on the local structure around Cu sites. Interactions where spin waves have twice as long wave length as phonon waves can lead to a 'dip' in the density of states (DOS) below the Fermi energy, $E_F$. This type of interaction is compatible with several seemingly contradictory observations among high-$T_C$ cuprates, like the isotope effect, anti-ferromagnetic fluctuations, stripes and pseudogaps. It can also …
In order to explore the reason why the single-layered cuprates, La$_{2-x}$(Sr/Ba)$_x$CuO$_4$ ($T_c\simeq$ 40K) and HgBa$_2$CuO$_{4+δ}$ ($T_c\simeq$ 90K), have such a significant difference in $T_c$, we study a two-orbital model that incorporates the $d_{z^2}$ orbital on top of the $d_{x^2-y^2}$ orbital. It is found, with the fluctuation exchange approximation, that the $d_{z^2}$ orbital contribution to the Fermi surface, which is stronger in the La system, works against d-wave superconductivity, thereby dominating over the effect of the Fermi surface shape. The result resolves the long-standin…
One of the prime manifestations of an anisotropic electronic state in underdoped cuprates is the in-plane resistivity anisotropy $Δρ\equiv(ρ_{a}-ρ_{b})/ρ_{b}$. Here we use a Boltzmann-equation approach to compute the contribution to $Δρ$ arising from scattering by anisotropic charge and spin fluctuations, which have been recently observed experimentally. While the anisotropy in the charge fluctuations is manifested in the correlation length, the anisotropy in the spin fluctuations emerges only in the structure factor. As a result, we find that spin fluctuations favor $Δρ>0$, whereas charge flu…
The inelastic x-ray scattering spectrum for phonons of $Δ_{1}$-symmetry including the CuO bond-stretching phonon dispersion is analyzed by a Lorentz fit in HgBa$_{2}$CuO$_{4}$ and Bi$_{2}$Sr$_{2}$CuO$_{6}$, respectively, using recently calculated phonon frequencies as input parameters. The resulting mode frequencies of the fit are almost all in good agreement with the calculated data. An exception is the second highest $Δ_{1}$-branch compromising the bond-stretching modes which disagrees in both compounds with the calculations. This branch unlike the calculations shows an anomalous softening w…
The nature of charge stripe order and its relationship with structural phase transitions were studied using synchrotron X-ray diffraction in La$_{1.875}$Ba$_{0.125-x}$Sr$_{x}$CuO$_{4}$ ($0.05\leq x\leq 0.10$). For $x=0.05$, as temperature increased, incommensurate superlattice peaks associated with the charge order disappeared just at the structural phase transition temperature, $T_{\rm d2}$. However, for $x=0.075$ and 0.09, the superlattice peaks still existed as a short range correlation even above $T_{\rm d2}$, indicating a precursor of charge ordering. Furthermore, temperature dependences …
