Muon Spin Relaxation and fluctuating magnetism in the pseudogap phase of YBa$_{2}$Cu$_{3}$O$_{y}$
Zihao Zhu, Jian Zhang, Zhaofeng Ding, Cheng Tan, Changsheng Chen, Qiong Wu, Yanxing Yang, Oscar O. Bernal, Pei-Chun Ho, Gerald D. Morris, Akihiro Koda, Adrian D… 展开作者
Zihao Zhu, Jian Zhang, Zhaofeng Ding, Cheng Tan, Changsheng Chen, Qiong Wu, Yanxing Yang, Oscar O. Bernal, Pei-Chun Ho, Gerald D. Morris, Akihiro Koda, Adrian D. Hillier, Stephen P. Cottrell, Peter J. Baker, Pabitra K. Biswas, Jun Qian, Xin Yao, Douglas E. MacLaughlin, Lei Shu
We report results of a muon spin relaxation study of slow magnetic fluctuations in the pseudogap phase of underdoped single-crystalline YBa$_{2}$Cu$_{3}$O$_{y}$, $y = 6.77$ and 6.83. The dependence of the dynamic muon spin relaxation rate on applied magnetic field yields the rms magnitude~$B\mathrm{_{loc}^{rms}}$ and correlation time~$τ_c$ of fluctuating local fields at muon sites. The observed relaxation rates do not decrease with decreasing temperature~$T$ below the pseudogap onset at $T^\ast$, as would be expected for a conventional magnetic transition; both $B\mathrm{_{loc}^{rms}}$ and $τ_c$ are roughly constant in the pseudogap phase down to the superconducting transition. Corresponding NMR relaxation rates are estimated to be too small to be observable. Our results put strong constraints on theories of the anomalous pseudogap magnetism in YBa$_{2}$Cu$_{3}$O$_{y}$.
We report $^{17}$O(2,3) and $^{63}$Cu(2) spin-lattice relaxation rates and the $^{17}$O(2,3) spin-spin relaxation rate in different magnetic fields in YBa$_2$Cu$_3$O$_7$ near $T_c$. Together these measurements enable us to test the magnetic field dependence of the pseudogap effect on the spin susceptibility in different regions of the Brillouin zone using the known form factors for different nuclei as filters. Thus, we study the momentum dispersion of the pseudogap behavior. We find that near the antiferromagnetic wave vector the pseudogap is insensitive to magnetic fields up to 15 T. In the r…
The hypothesis regarding the existence of uncorrelated pre-formed pairs in the pseudogap regime of superconducting $YBa_2Cu_3O_y$ is tested experimentally using bilayers of $YBa_2Cu_3O_y$ and the itinerant ferromagnet $SrRuO_3$. In our study, we monitor the influence of $YBa_2Cu_3O_y$ on $T_p$, the ferromagnetic ordering temperature of $SrRuO_3$. Here, $T_p$ is the temperature of maximum dM/dT or dR/dT where M and R are the magnetization and resistance of $SrRuO_3$, respectively. We compare the results with similar measurements carried out on bilayers of $La_{1.88}Sr_{0.12}CuO_{4-y}$, $Au$ and…
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 $μ$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 p…
The temperature dependence of the Hall coefficient is measured with a high accuracy in a series of Zn-doped YBCO_{6.78} crystals with the Zn concentration from 0% to 1.3%. We found that the cotangent of the Hall angle, cot(θ_H), starts to deviate upward from the T^2 dependence below T_0 (which is roughly 130 K), regardless of the Zn concentration. We discuss that this deviation is caused by the pseudogap; the direction of the deviation and its insensitivity to the Zn doping suggest that the pseudogap affects cot(θ_H) through a change in the effective mass, rather than through a change in the H…
The phase diagram of cuprate high-temperature superconductors features an enigmatic pseudogap region that is characterized by a partial suppression of low energy electronic excitations. Polarized neutron diffraction, Nernst effect, THz polarimetery and ultrasound measurements on YBa$_2$Cu$_3$O$_y$ suggest that the pseudogap onset below a temperature T* coincides with a bona fide thermodynamic phase transition that breaks time-reversal, four-fold rotation and mirror symmetries respectively. However, the full point group above and below T* has not been resolved and the fate of this transition as…
Understanding the nature of the mysterious pseudogap phenomenon is one of the most important issues associated with cuprate high-$T_c$ superconductors. Here, we report $^{17}$O nuclear magnetic resonance (NMR) studies on two planar oxygen sites in stoichiometric cuprate YBa$_2$Cu$_4$O$_8$ to investigate the symmetry breaking inside the pseudogap phase. We observe that the Knight shifts of the two oxygen sites are identical at high temperatures but different below $T_{\rm nem} \sim$ 185 K, which is close to the pseudogap temperature $T^{\ast}$. Our result provides a microscopic evidence for int…
For orthorhombic superconductors we define thermodynamic anisotropy $N \equiv d T_c/d ε_{22} - dT_c/d ε_{11}$ as the difference in how superconducting $T_c$ varies with strains $ε_{ii}$, $i=(1, 2)$, along the in-plane directions. We study the hole doping ($p$) dependence of $N$ on detwinned single crystals of underdoped YBa$_2$Cu$_3$O$_y$ (YBCO) using ultrasound technique. While the structural orthorhombicity of YBCO reduces monotonically with decreasing doping over $0.065 <p<0.16$, we find that the thermodynamic anisotropy shows an intriguing enhancement at intermediate doping level, which is…
A new NMR anvil cell design is used for measuring the influence of high pressure on the electronic properties of the high-temperature superconductor YBa$_2$Cu$_4$O$_8$ above the superconducting transition temperature $T_{\rm c}$. It is found that pressure increases the spin shift at all temperatures in such a way that the pseudo-gap feature has almost disappeared at 63 kbar. This change of the temperature dependent spin susceptibility can be explained by a pressure induced proportional decrease (factor of two) of a temperature dependent component, and an increase (factor of 9) of a temperature…
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 presenc…
The magnetic spectrum at high-energies in heavily underdoped YBa$_{2}$Cu$_{3}$O$_{6.35}$ (T$_{c}$=18 K) has been determined throughout the Brillouin zone. At low-energy the scattering forms a cone of spin excitations emanating from the antiferromagnetic (0.5, 0.5) wave vector with an acoustic velocity similar to that of insulating cuprates. At high energy transfers, below the maximum energy of 270 meV at (0.5, 0), we observe zone boundary dispersion much larger and spectral weight loss more extensive than in insulating antiferromagnets. Moreover we report phenomena not found in insulators, an …
Femtosecond pump probe experiments are reported on quasiparticle relaxation and recombination in YBa2Cu4O8 as a function of temperature and polarization. The data show a 2-component relaxation similar to YBa2Cu3O7-δ, one component being assocated with the superconducting transition, and the other with the pseudogap below T* The relaxation time tau_p associated with the pseudogap is found to be T-independent, while the relaxation time tau_g of the component obseved only below Tc exhibits a clear divergence near Tc. A strong polarisation anisotropy of the picosecond transient is observed below T…
Polarized beam neutron scattering measurements on a highly perfect crystal of ${\rm YBa_2Cu_3O_{6.6}}$ show a distinct magnetic transition with an onset at about 235K, the temperature expected for the pseudogap transition. The moment is found to be about 0.1 $μ_B$ for each sublattice and have a correlation length of at least 75 Å. We found the critical exponent for the magnetic neutron intensity to be 2$β$ =0.37$\pm$ 0.12. This is the proper range for the class of transition that has no specific heat divergence possibly explaining why none is found at the pseudogap transition.
Despite decades of intense researches, the enigmatic pseudo-gap (PG) phase of superconducting cuprates remains an unsolved mystery. In the last 15 years, various symmetry breakings in the PG state have been discovered, spanning an intra-unit cell (IUC) magnetism, preserving the lattice translational (LT) symmetry but breaking time-reversal symmetry and parity, and an additional incipient charge density wave breaking the LT symmetry upon cooling. However, none of these states can (alone) account for the partial gapping of the Fermi surface. Here we report a hidden LT-breaking magnetism uisng po…
Thermal transport in the T -> 0 limit was measured as a function of doping in high-quality single crystals of the cuprate superconductor YBa_2Cu_3O_y. The residual linear term kappa_0/T is found to decrease as one moves from the overdoped regime towards the Mott insulator region of the phase diagram. The doping dependence of the low-energy quasiparticle gap extracted from kappa_0/T is seen to scale closely with that of the pseudogap, arguing against a non-superconducting origin for the pseudogap. The presence of a linear term for all dopings is evidence against the existence of a quantum phase…
We have measured the spin fluctuations in the YBa2Cu3O6.5 (YBCO6.5, Tc=59 K) superconductor at high-energy transfers above ~ 100 meV. Within experimental error, the momentum dependence is isotropic at high-energies, similar to that measured in the insulator for two dimensional spin waves, and the dispersion extrapolates back to the incommensurate wave vector at the elastic position. This result contrasts with previous expectations based on measurements around 50 meV which were suggestive of a softening of the spin-wave velocity with increased hole doping. Unlike the insulator, we observe a sig…
We report a $^{63}$Cu NMR investigation in detwinned YBa$_2$Cu$_3$O$_y$ single crystals, focusing on the highly underdoped regime (y=6.35-6.6). Measurements of both the spectra and the spin-lattice relaxation rates of $^{63}$Cu uncover the emergence of static order at a well-defined onset temperature $T_0$ without a known order parameter as yet. While $T_0$ is rapidly suppressed with increasing hole doping concentration $p$, the spin pseudogap was identified only near and above the doping content at which $T_0\rightarrow 0$. Our data indicate the presence of a critical hole doping $p_c\sim 0.1…
Nematicity has emerged as a key feature of cuprate superconductors, but its link to other fundamental properties such as superconductivity, charge order and the pseudogap remains unclear. Here we use measurements of transport anisotropy in YBa$_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 on…
Parametrically amplified Josephson plasma waves in YBa_2Cu_3O_(6+x): evidence for local superconducting fluctuations up to the pseudogap temperature $T^*$
Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Max Planck Institute for the Structure and Dynamics of Matter（马克斯·普朗克物质结构与动力学研究所）；ETH Zurich（苏黎世联邦理工学院）；MIT（麻省理工学院）
研究通过强太赫兹脉冲作用于欠掺杂YBa₂Cu₃O₆₊x并在Tc和伪间隙尺度T*之间温度下，发现类似超导态的反射率边缘和探针脉冲的二次谐波产生，提出通过参数放大低约瑟夫森等离子体模式解释，但本文提出另一种解释，假设在Tc < T < T*时存在局部配对幅度和相位，从而解释反射率数据。
One of the leading issues in high-$T_C$ superconductors is the origin of the pseudogap phase in underdoped cuprates. Using polarized elastic neutron diffraction, we identify a novel magnetic order in the YBa$_2$Cu$_3$O$_{6+x}$ system. The observed magnetic order preserves translational symmetry as proposed for orbital moments in the circulating current theory of the pseudogap state. To date, it is the first direct evidence of an hidden order parameter characterizing the pseudogap phase in high-$T_C$ cuprates.
As established by scanning tunneling microscopy (STM) cleaved surfaces of the high temperature superconductor YBa$_2$Cu$_2$O$_{7-δ}$ develop charge density wave (CDW) modulations in the one-dimensional (1D) CuO chains. At the same time, no signatures of the CDW have been reported in the spectral function of the chain band previously studied by photoemission. We use soft X-ray angle resolved photoemission (SX-ARPES) to detect a chain-derived surface band that had not been detected in previous work. The $2k_\textup{F}$ for the new surface band is found to be 0.55\,Å$^{-1}$, which matches the wav…
We analyze non - Fermi liquid (NFL) behavior of fluctuating gap model (FGM) of pseudogap behavior in both 1D and 2D. We discuss in detail quasiparticle renormalization (Z - factor), demonstrating a kind of "marginal" Fermi liquid or Luttinger liquid behavior and topological stability of the "bare" Fermi surface (Luttinger theorem). In 2D case we discuss effective picture of Fermi surface "destruction" both in "hot spots" model of dielectric (AFM, CDW) pseudogap fluctuations, as well as for qualitatively different case of superconducting d - wave fluctuations, reflecting NFL spectral density be…
The pseudogap phenomenology is one of the enigmas of the physics of high-Tc superconductors. Many members of the cuprate family have now been characterized with high resolution in both real and momentum space, which revealed highly anisotropic Fermi arcs and local domain which break rotational symmetry in the CuO2 plane at the intraunit cell level. While most theoretical approaches to date have focused on the role of electronic correlations and doping-induced disorder to explain these features, we show that many features of the pseudogap phase can be reproduced by considering the interplay bet…
Cuprate superconductors have a universal tendency to form charge density-wave (CDW) order which competes with superconductivity and is strongest at a doping $p \simeq 0.12$. Here we show that in the archetypal cuprate YBa$_{2}$Cu$_{3}$O$_{y}$ (YBCO) pressure suppresses charge order, but does not affect the pseudogap phase. This is based on transport measurements under pressure, which reveal that the onset of the pseudogap at $T^*$ is independent of pressure, while the negative Hall effect, a clear signature of CDW order in YBCO, is suppressed by pressure. We also find that pressure and magneti…
Polarized and unpolarized neutron diffraction has been used to search for magnetic order in YBa$_2$Cu$_3$O$_{6+x}$ superconductors. Most of the measurements were made on a high quality crystal of YBa$_2$Cu$_3$O$_{6.6}$. It is shown that this crystal has highly ordered ortho-II chain order, and a sharp superconducting transition. Inelastic scattering measurements display a very clean spin-gap and pseudogap with any intensity at 10 meV being 50 times smaller than the resonance intensity. The crystal shows a complicated magnetic order that appears to have three components. A magnetic phase is fou…
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 electronic Raman scattering measurements on optimally doped YBa2Cu3O7 where Zn or Ni impurities have been substituted by Cu. Using Raman selection rules, we have probed the superconducting gap in the nodal and antinodal regions. We show that under impurity substitutions, the energy of the antinodal peak detected in the superconducting state is not related to the critical temperature Tc and that signatures of superconductivity disappear in the nodal regions. Our experimental findings advocate in favor of gapless arcs around the nodes. The breakdown of the relationship between the anti…
We report an inelastic-neutron-scattering and muon-spin-relaxation study of the effect of 2% spinless (Zn) impurities on the magnetic order and dynamics of YBa$_2$Cu$_3$O$_{6.6}$, an underdoped high-temperature superconductor that exhibits a prominent spin-pseudogap in its normal state. Zn substitution induces static magnetic order at low temperatures and triggers a large-scale spectral-weight redistribution from the magnetic resonant mode at 38 meV into uniaxial, incommensurate spin excitations with energies well below the spin-pseudogap. These observations indicate a competition between inco…
We report transport measurements using pulsed magnetic fields to suppress the superconducting fluctuations (SCF) conductivity in a series of YBa_2Cu_3O_(6+x) samples. These experiments allow us altogether to measure the temperature T'c at which SCF disappear, and the pseudogap temperature T*. While the latter are consistent with previous determinations of T*, we find that T'c is slightly larger than similar data taken by Nernst measurements. A careful investigation near optimal doping shows that T* becomes smaller than T'c, which is an unambiguous evidence that the pseudogap cannot be assigned…
We study the physical property of pair density wave (PDW) and fluctuating PDW, and use it to build an effective theory of the strongly interacting pseudogap phase in cuprate high temperature superconductors. In Chapter2, we study how Fulde-Ferrell state, the simplest form of PDW, responds to incident light. The collective motion of the condensate plays a key role; gauge invariance guides us to the correct result. From Chapter 3 to Chapter 7, we construct a pseudogap metallic state by considering quantum fluctuating PDW. We analyze a recent scanning tunneling microscope (STM) discovery of perio…
The origin of the pseudogap (PG) phase and superconducting behaviors in high-Tc superconductors is proposed, based on the picture of Euclidean Q-balls formation, that carry Cooper/local-pair condensates inside their volumes. Unlike the baryonic Q-balls in supersymmetric standard model, the Euclidean Q-balls describe spin-/charge densities, that oscillate in Matsubara time, and are found in the 'nested' repulsive Hubbard model of high-Tc superconductors. Euclidean Q-balls arise due to global invariance of the effective theory under the phase rotation of the Fourier amplitudes of spin-/charge fl…
A pronounced xy-anisotropy was observed in recent neutron scattering experiments for magnetic excitations in untwinned YBa_{2}Cu_{3}O_{6+y} (YBCO). The small anisotropy of the bare band structure due to the orthorhombic crystal symmetry seems to be enhanced by correlation effects. A natural possibility is that the system is close to a Pomeranchuk instability associated with a d-wave Fermi surface deformation (dFSD). We investigate this possibility in the bilayer t-J model within a self-consistent slave-boson mean-field theory. We show that the dFSD correlations drive a pronounced xy-anisotropy…
Cuprate high-T_c superconductors on the Mott-insulating side of "optimal doping" (with respect to the highest T_c's) exhibit enigmatic behavior in the non-superconducting state. Near optimal doping the transport and spectroscopic properties are unlike those of a Landau-Fermi liquid. For carrier concentrations below optimal doping a pseudogap removes quasi-particle spectral weight from parts of the Fermi surface, and causes a break-up of the Fermi surface into disconnected nodal and anti-nodal sectors. Here we show that the near-nodal excitations of underdoped cuprates obey Fermi liquid behavio…
The normal state of optimally doped cuprates is dominated by the "strange metal" phase that shows a linear temperature ($T$) dependence of the resistivity persisting down to the lowest $T$. For underdoped cuprates this behavior is lost below the pseudogap temperature $T^*$, where Charge Density Waves (CDW) together with other intertwined local orders characterize the ground state. Here we show that the $T$-linear resistivity of highly strained, ultrathin and underdoped YBa$_2$Cu$_3$O$_{7-δ}$ films is restored when the CDW amplitude, detected by Resonant Inelastic X-ray scattering, is suppresse…
Here we provide the first clear evidence of Fermi-liquid breakdown in an intermediate valence system. We employ high precision magnetization measurements of the valence fluctuating superconductor beta-YbAlB4 to probe the quantum critical free energy down to temperatures far below the characteristic energy scale of the valence fluctuations. The observed T/B scaling in the magnetization over three decades not only indicates unconventional quantum criticality, but places an upper bound on the critical magnetic field |B_c| < 0.2 mT, a value comparable with the Earth's magnetic field and six orders…
The pseudogap is one of the most pervasive phenomena of high temperature superconductors. It is attributed either to incoherent Cooper pairing setting in above the superconducting transition temperature Tc, or to a hidden order parameter competing with superconductivity. Here we use inelastic neutron scattering from underdoped YBa(2)Cu(3)O(6.6) to show that the dispersion relations of spin excitations in the superconducting and pseudogap states are qualitatively different. Specifically, the extensively studied "hour glass" shape of the magnetic dispersions in the superconducting state is no lo…
We have measured the spin susceptibility of the underdoped high temperature superconductor, YBa2Cu4O8 by Gd^{3+} electron spin resonance in single crystals and aligned powders at several magnetic fields between 3 and 15.4 T. At low temperatures and high fields, the spin susceptibility of the CuO2 planes is enhanced slightly in the $B\parallel c$ orientation with respect to the $B\perp c$ orientation. The enhancement in an applied field of 15.4 T ($\approx 0.15 H_{c2}$) at 16 K (0.2 $T_c$) is approximately 10 percent of the susceptibility measured at $T_c$. Such a small magnitude suggests that …
Optical excitation of apical oxygen vibrations in YBa$_{2}$Cu$_{3}$O$_{6+δ}$ has been shown to enhance its c-axis superconducting-phase rigidity, as evidenced by a transient blue shift of the equilibrium inter-bilayer Josephson plasma resonance. Surprisingly, a transient c-axis plasma mode could also be induced above T$_{c}$ by the same apical oxygen excitation, suggesting light activated superfluid tunneling throughout the pseudogap phase of YBa$_{2}$Cu$_{3}$O$_{6+δ}$. However, despite the similarities between the above T$_{c}$ transient plasma mode and the equilibrium Josephson plasmon, alte…
Two maxima in transverse relaxation rate of Cu(2) nuclei in YBa$_2$Cu$_3$O$_{7-y}$ are observed, at T = 35 K and T = 47 K. Comparison of the $^{63}$Cu(2) and $^{65}$Cu(2) rates at T = 47 K indicates the magnetic character of relaxation. The enhancement at T = 47 K of fluctuating local magnetic fields perpendicular to the CuO$_2$ planes is connected with the critical fluctuations of orbital currents. Maximum at T = 35 K is connected with the appearance of inhomogeneous supeconducting phase. Together with data published to date, our experimental results allow to suggest a qualitatively new phase…
Geometric orthogonal metals: Hidden antiferromagnetism and pseudogap from fluctuating stripes
Ludwig-Maximilians-Universität München（慕尼黑大学）；Arnold Sommerfeld Center for Theoretical Physics (ASC)（阿诺德·索末菲理论物理中心）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；University of Regensburg（雷根斯堡大学）
We report spatially resolved tunneling spectroscopic evidence for field-induced microscopic orders in a high-$T_c$ superconductor $\rm YBa_2Cu_3O_{7-δ}$. The spectral characteristics inside vortices reveal a pseudogap ($V_{\rm CO}$) larger than the superconducting gap ($Δ\_{\rm SC}$) as well as a subgap ($Δ\^{\prime}$) smaller than $Δ\_{\rm SC}$, and the spectral weight shifts steadily from $Δ_{\rm SC}$ to $V_{\rm CO}$ and $Δ\^{\prime}$ upon increasing magnetic field. Additionally, energy-independent conductance modulations at 3.6 and 7.1 lattice constants along the Cu-O bonding directions and…
Polarized and unpolarized neutron triple-axis spectrometry was used to study the dynamical magnetic susceptibility $χ^{\prime\prime}({\bf q},ω)$ as a function of energy ($\hbarω$) and wave vector (${\bf q}$) in a wide temperature range for the bilayer superconductor YBa$_2$Cu$_3$O$_{6+x}$ with oxygen concentrations, $x$, of 0.45, 0.5, 0.6, 0.7, 0.8, 0.93, and 0.95. The most prominent features in the magnetic spectra include a spin gap in the superconducting state, a pseudogap in the normal state, the much-discussed resonance, and incommensurate spin fluctuations below the resonance. We establi…
We used high resolution angle-resolved photoemission spectroscopy to reveal the Fermi surface and key transport parameters of the metallic state of the layered Colossal Magnetoresistive (CMR) oxide La1.2Sr1.8Mn2O7. With these parameters the calculated in-plane conductivity is nearly one order of magnitude larger than the measured DC conductivity. This discrepancy can be accounted for by including the pseudogap which removes at least 90% of the spectral weight at the Fermi energy. Key to the pseudogap and many other properties are the parallel straight Fermi surface sections which are highly su…
Pseudogap formation in the moderate correlated layered attractive Hubbard model
Russian Quantum Center（俄罗斯量子中心）；National University of Science and Technology “MISIS”（莫斯科国立科技大学 MISIS）；Department of Physics, National Research University Higher School of Economics（高等经济大学物理系）；Lomonosov Moscow State University（莫斯科国立罗蒙诺索夫大学）；London School of Economics and Political Science（伦敦政治经济学院）
The nature of the pseudogap phase is a central problem in the quest to understand high-Tc cuprate superconductors. A fundamental question is what symmetries are broken when that phase sets in below a temperature T*. There is evidence from both polarized neutron diffraction and polar Kerr effect measurements that time- reversal symmetry is broken, but at temperatures that differ significantly. Broken rotational symmetry was detected by both resistivity and inelastic neutron scattering at low doping and by scanning tunnelling spectroscopy at low temperature, but with no clear connection to T*. H…
We study the spin dynamics in underdoped cuprates at low temperatures by considering them as quasi two dimensional d-wave superconductors (dSC) with strong phase fluctuations. An effective theory of spin degrees of freedom of nodal quasiparticles coupled to vortex defects in the phase of the superconducting order parameter is formulated. It represents the minimal extension of the QED3 theory of the pseudogap phase into the superconducting region. The theory predicts a single dSC-SDW transition, which may be fluctuation induced first order, without the region of coexistence between the two orde…
Recent observations of broken symmetries have partly demystified the pseudogap phase. Here we review evidence for long-range intra-unit-cell(IUC) nematic order and its unexpectedly strong coupling to the phase of the fluctuating stripes in the pseudogap states of underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$. In particular, we focus on the analysis techniques that reveal this evidence in scanning tunneling spectroscopy data, the definition of the extracted IUC nematic order parameter, and a phenomenological theory of the coupling between the IUC nematic order and the previously reported coexisting …
We apply the modified spin-wave theory with the constraint of zero staggered magnetization to investigate normal-state spectral and magnetic properties of the 2D t-J model in the paramagnetic state. A set of self-energy equations for hole and magnon Green's functions is solved numerically in the self-consistent Born approximation. The constraint can be fulfilled in the ranges of hole concentrations 0.02 < x < 0.17 and temperatures T < 150 K. In this region the hole spectrum differs from a conventional metallic spectrum which is manifested in the variation with x of the quasiparticle weights of…
We present a SU(2) gauge theory of fluctuating magnetic order in the two-dimensional Hubbard model. The theory is based on a fractionalization of electrons in fermionic chargons and bosonic spinons. The chargons undergo Néel or spiral magnetic order below a density dependent transition temperature $T^*$. Fluctuations of the spin orientation are described by a non-linear sigma model obtained from a gradient expansion of the spinon action. The spin stiffnesses are computed from a renormalization group improved random phase approximation. Our approximations are applicable for a weak or moderate H…
We have examined the magnetic properties of polycrystalline, superconducting YBa_2(Cu_0.96Ni_0.04)_3O_y (y ~ 7, T_sc ~ 75 K) using two local probe techniques: 170Yb Moessbauer down to 0.1 K and muon spin relaxation (muSR) down to 1.5 K. At 0.1 K, the 170Yb measurements show the Cu(2) over essentially all the sample volume carry magnetically correlated moments which are static on the time-scale of 10^{-9} s. The moments show a distribution in size. The correlations are probably short range. As the temperature increases, the correlated moments are observed to fluctuate with measurable rates (in …
The nature of the enigmatic pseudogap region of the phase diagram is the most important and intriguing unsolved puzzle in the field of high transition-temperature (Tc) superconductivity. This region, the temperature range above Tc and below a characteristic temperature T*, is characterized by highly anomalous magnetic, charge transport, thermodynamic and optical properties. Associated with the pseudogap puzzle are open questions pertaining to the number of distinct phases and the presence of a quantum-critical point underneath the superconducting dome. Here we use polarized neutron diffraction…
We have examined the magnetic properties of superconducting YBa_2(Cu_0.96Co_0.04)_3O_y (y ~ 7, T_sc = 65 K) using elastic neutron scattering and muon spin relaxation (muSR) on single crystal samples. The elastic neutron scattering measurements evidence magnetic reflections which correspond to a commensurate antiferromagnetic Cu(2) magnetic structure with an associated Neel temperature T_N ~ 400 K. This magnetically correlated state is not evidenced by the muSR measurements. We suggest this apparent anomaly arises because the magnetically correlated state is dynamic in nature. It fluctuates wit…
We develop a powerful numerical algorithm for calculating the density of states rho(omega) of the fluctuating gap model, which describes the low-energy physics of disordered Peierls and spin-Peierls chains. We obtain rho(omega) with unprecedented accuracy from the solution of a simple initial value problem for a single Riccati equation. Generating Gaussian disorder with large correlation length xi by means of a simple Markov process, we present a quantitative study of the behavior of rho (omega) in the pseudogap regime. In particular, we show that in the commensurate case and in the absence of…
Two contradictory phase diagrams have dominated the literature of high-$T_c$ cuprate superconductors. Does the pseudogap line cross the superconducting $T_c$-dome or not? To answer, we have revisited the experimental magnetic susceptibility and knight shift of four different compounds, La$_{1-x}$Sr$_x$CuO$_4$, Bi$_2$Sr$_2$Ca$_{1-x}$Y$_x$Cu$_2$O$_8$, Bi$_2$Sr$_2$CaCu$_2$O$_{8+y}$, and YBa$_2$Cu$_3$O$_{6+y}$, as a function of temperature and doping. The susceptibility can be described by the same function for all materials, having a magnetic and an electronic contributions. The former is the 2D …
The central issue in high-temperature cuprate superconductors is the pseudogap state appearing below the pseudogap temperature $T^*$, which is well above the superconducting transition temperature. In this study, we theoretically investigate the rapid increase of the magnetic anisotropy below the pseudogap temperature detected by the recent torque-magnetometry measurements on YBa$_2$Cu$_3$O$_y$ [Y. Sato et al., Nat. Phys., 13, 1074 (2017)]. Applying the spin Green's function formalism including the Dzyaloshinskii--Moriya interaction arising from the buckling of the CuO$_2$ plane, we obtain res…
