Motivated by quantum oscillations observed in highly ordered ortho-II YBa_2Cu_3O_6.5, we study the Fermi surface topology of d-density wave (ddw) or antiferromagnetic (AF) ordering in the presence of the ortho-II potential. We find that the electron pocket is unaffected by the presence of the ortho-II potential. This further strengthens the proposal that quantum oscillations observed in ortho-II-free YBa_2Cu_4O_8 arise from an electron pocket. On the other hand, the hole pocket topology is sensitive to the ortho-II potential. We show there exist generically three distinct quantum oscillations associated with one electron-like and two hole-like Fermi pockets. We compare our results to the quantum oscillations observed in experiments. We discuss possible ways to distinguish between ddw and antiferromagnetic orders in a potential single-layer ortho-II material.
We study underdoped high-Tc superconductors YBa2Cu3O6.5 and YBa2Cu4O8 using first-principles pseudopotential methods with additional Coulomb interactions at the Cu atoms, and obtain Fermi-surface pocket areas in close agreement with measured Shubnikov-de Haas and de Haas-van Alphen oscillations. With antiferromagnetic order in CuO2 planes, stable in the calculations, small hole pockets are formed near the so-called Fermi-arc positions in the Brillouin zone which reproduce the low-frequency oscillations. A large electron pocket, necessary for the negative Hall coefficient, is also formed in YBa…
We measure magnetic quantum oscillations in the underdoped cuprates YBa$_2$Cu$_3$O$_{6+x}$ with $x=0.61$, 0.69, using fields of up to 85 T. The quantum-oscillation frequencies and effective masses obtained suggest that the Fermi energy in the cuprates has a maximum at $p\approx 0.11-0.12$. On either side, the effective mass may diverge, possibly due to phase transitions associated with the T=0 limit of the metal-insulator crossover (low-$p$ side), and the postulated topological transition from small to large Fermi surface close to optimal doping (high $p$ side).
Fermi surface pockets in ortho-II YBa$_2$Cu$_3$O$_{6.5}$: the origin of quantum oscillations?
在本文中，我们探讨是否可以用传统的密度泛函能带结构理论解释最近观察到的ortho-II YBa $_2$ Cu $_3$ O $_{6.5}$的量子振荡信号。计算结果表明，$_2$ O $_{6.5}$的费米面对能带相对位置的微小位移极为敏感.随着刚性带位移约30 meV的小管状袋费米表面周围的Y点的布里渊区的发展。这些口袋上的量子振荡轨道的横截面积和带质量接近观察到的。讨论了$_2$ O $_3$和$_2$ CuPDMATHABMP O $_{8}$能带结构的差异。
de Haas-van Alphen oscillations in the underdoped cuprate YBa$_2$Cu$_3$O$_{6.5}$
利用转矩技术在高达59 T的脉冲磁场中观察到欠掺杂铜氧化物YBa $_2$ Cu $_3$ O $_{6.5}$的de Haas van Alphen效应。在$\sim$ 30 T的不可逆性场以上，磁化强度表现出明显的量子振荡，单频为540 T，回旋质量为自由电子质量的1.76倍，与先前观察到的Shubnikov-de Haas振荡非常一致。振荡遵循费米液体理论的标准Lifshitz-Kosevich公式。这种量子振荡的热力学观测证实了在铜酸盐的赝能隙相中存在一个定义明确、紧密且相干的费米面。
According to the celebrated Onsagar-Lifshitz paradigm, the observation of Shubnikov de-Haas and de-Haas van Alphen (SdHvA) oscillations is an indication of the presence of `closed' orbit Fermi surface in the bulk. We present a real-space based calculation of SdHvA oscillations in generalized quasi-one-dimensional lattices by relaxing the quasi-classical approximations embedded in this decades old Onsagar-Lifshitz paradigm. We find that sizable quantum oscillation can arise from `open' Fermi surfaces as long as cyclotron orbits can form in real-space with finite, but not necessarily equal, elec…
X-ray diffraction measurements show that the high-temperature superconductor YBa$_2$Cu$_3$O$_{6.54}$, with ortho-II oxygen order, has charge density wave order (CDW) in the absence of an applied magnetic field. The dominant wavevector of the CDW is $\mathbf{q}_{\mathrm{CDW}} = (0, 0.328(2), 0.5)$, with the in-plane component parallel to the $\mathbf{b}$-axis (chain direction). It has a similar incommensurability to that observed in ortho-VIII and ortho-III samples, which have different dopings and oxygen orderings. Our results for ortho-II contrast with recent high-field NMR measurements, whic…
Recent observations of slow magneto-oscillations in some underdoped cuprate superconductors are one of the most striking discoveries in the field of superconductivity since many probes of underdoped cuprates clearly point to a non Fermi-liquid normal state. We show that a large magnitude and strong magnetic-field dependence of the residual resistance invalidate the conventional interpretation of the magneto-oscillations as a normal-state dHvA effect. We propose that the oscillations are most likely caused by a quantum interference of vortex and crystal lattice modulations of the order paramete…
NMR evidence for Friedel-like oscillations in the CuO chains of ortho-II YBa$_2$Cu$_3$O$_{6.5}$
对去孪晶的Ortho-II型$_2$ O $_{6.5}$（YBCO 6.5）单晶的CuO链的核磁共振（NMR）测量揭示了不寻常的和显著的性质。链Cu共振显着加宽，但逐渐，从室温冷却。其线形及其温度依赖性与常规自旋/电荷密度波（S/CDW）相变的线形及其温度依赖性显著不同。相反，线加宽归因于小振幅静态自旋和电荷密度振荡，其具有与有限长度链的末端连接的空间变化的振幅。这种CuO链现象的影响也清楚地表现在平面Cu NMR中。
本文报道了在欠掺杂铜氧化物超导体YBa $_2$ Cu $_4$ O $_8$（Y 124）中观察到的Shubnikov-de Haas振荡。对于沿c轴排列的场，振荡的频率是$660\pm 30$ T，其对应于第一布里渊区的总面积的$\sim 2.4$ %。这个轨道上准粒子的有效质量被测量为$2.7\pm0.3$乘以自由电子质量。频率和质量都与最近观察到的ortho-II YBa $_2$ Cu $_3$ O $_{6.5}$（Y123-II）相当。我们表明，虽然小费米表面口袋可以预期从能带结构计算在Y123-II，没有这样的口袋预测Y124。因此，我们的研究结果意味着这些小口袋是一个通用的功能的氧化铜平面在欠掺杂的铜酸盐。
We report quantum oscillations in underdoped YBa2Cu3O6.56 over a significantly large range in magnetic field extending from 24 to 101 T, enabling three well-spaced low frequencies at 440 T, 532 T, and 620 T to be clearly resolved. We show that a small nodal bilayer coupling that splits a nodal pocket into bonding and antibonding orbits yields a sequence of frequencies, F0 - ΔF, F0, and F0 + ΔF and accompanying beat pattern similar to that observed experimentally, on invoking magnetic breakdown tunneling at the nodes. The relative amplitudes of the multiple frequencies observed experimentally i…
The mystery of the normal state in the underdoped cuprates has deepened with the use of newer and complementary experimental probes. While photoemission studies have revealed solely `Fermi arcs' centered on nodal points in the Brillouin zone at which holes aggregate upon doping, more recent quantum oscillation experiments have been interpreted in terms of an ambipolar Fermi surface, that includes sections containing electron carriers located at the antinodal region. To address the question of whether an ambipolar Fermi surface truly exists, here we utilize measurements of the second harmonic q…
By improving the experimental conditions and extensive data accumulation, we have achieved very high-precision in the measurements of the de Haas-van Alphen effect in the underdoped high-temperature superconductor YBa$_{2}$Cu$_{3}$O$_{6.5}$. We find that the main oscillation, so far believed to be single-frequency, is composed of three closely spaced frequencies. We attribute this to bilayer splitting and warping of a single quasi-2D Fermi surface, indicating that \emph{c}-axis coherence is restored at low temperature in underdoped cuprates. Our results do not support the existence of a larger…
Optical Conductivity of Ortho-II YBa$_2$Cu$_3$O$_6.5$
$_2$ O $_6.5$的Ortho-II相的特征在于空Cu和填充Cu-O b轴的周期性交替使晶胞在a方向上加倍。在完整的链中的额外的氧产生了一个有吸引力的潜力，在飞机上的孔。在新的布里渊区边界$k_x=\pm pi/2$，我们估计从LDA计算的间隙开口的平面带分裂成两个。使用一个平面模型，它对待的d-波超导平均场近似，我们表明，带间跃迁产生强烈的各向异性特征的光学电导率控制的区域在k空间接近（$π/2,π/2$）。该特征的边缘位置给出了该区域准粒子谱随温度变化的信息。双层分裂将显示为双边形状。
We show that the distribution of quantum oscillation frequencies observed over a broad range of magnetic field can be reconciled with the wavevectors of charge modulations found in nuclear magnetic resonance and resonant x-ray spectroscopy experiments in underdoped YBa2Cu3O6+x within a model of biaxial charge ordering occurring in a bilayer CuO2 planar system. Bilayer coupling introduces the possibility of different period modulations and quantum oscillation frequencies corresponding to each of the bonding and antibonding bands, which can be reconciled with recent experimental observations
Shubnikov-de Haas and de Haas-van Alphen effects have been measured in the underdoped high temperature superconductor YBa$_2$Cu$_3$O$_{6.51}$. Data are in agreement with the standard Lifshitz-Kosevitch theory, which confirms the presence of a coherent Fermi surface in the ground state of underdoped cuprates. A low frequency $F = 530 \pm 10$ T is reported in both measurements, pointing to small Fermi pocket, which corresponds to 2% of the first Brillouin zone area only. This low value is in sharp contrast with that of overdoped Tl$_2$Ba$_2$CuO$_{6+δ}$, where a high frequency $F = 18$ kT has bee…
Recently, charge density wave (CDW) order in the CuO$_2$ planes of underdoped YBa$_2$Cu$_3$O$_{6+δ}$ was detected using resonant soft x-ray scattering. An important question remains: is the chain layer responsible for this charge ordering? Here, we explore the energy and polarization dependence of the resonant scattering intensity in a detwinned sample of YBa$_2$Cu$_3$O$_{6.75}$ with ortho-III oxygen ordering in the chain layer. We show that the ortho-III CDW order in the chains is distinct from the CDW order in the planes. The ortho-III structure gives rise to a commensurate superlattice refl…
We show that lightly doped YBa$_2$Cu$_3$O$_{6+y}$ has multiple holon pockets with different areas, which lead to multiple frequencies of magnetic quantum oscillations. Using neutron scattering data on incommensurate spin ordering we determine these areas, which yields frequencies in good agreement with experiments. Divergence of the effective mass observed in magnetic quantum oscillations indicates a quantum phase transition at the oxygen content $y\approx 0.48$. We argue that the transition is the onset of quasistatic incommensurate magnetic order predicted by theory and observed in neutron s…
On the basis of negative transport coefficients, it has been argued that the quantum oscillations observed in underdoped YBa(2)Cu(3)O(6+x) in high magnetic fields must be due to antinodal electron pockets. We point out a counter example in which electron-like transport in a hole-doped cuprate is associated with Fermi-arc states. We also present evidence that the antinodal gap in YBa(2)Cu(3)O(6+x) is robust to modest applied magnetic fields. We suggest that these observations should be taken into account when interpreting the results of the quantum oscillation experiments.
Experiments have revealed multiple quantum oscillation frequencies in underdoped high temperature superconductor $\mathrm{YBa_{2}Cu_{3}O_{6+δ}}$, corresponding to approximately 10% doping, which contain $\mathrm{CuO}$ bilayers in the unit cell. These unit cells are further coupled along the c-axis by a tunneling matrix element. A model of the energy dispersion that has its roots in the previously determined electronic structure, combined with two-fold commensurate density waves, reveals multiple electron and hole pockets. To the extent that quasiparticles of the reconstructed Fermi surface hav…
Evidence for Static Magnetism in the Vortex Cores of Ortho-II YBa$_2$Cu$_3$O$_{6.50}$
报道了欠掺杂$_2$ O $_{6+x}$涡旋芯中存在静态交变磁场的证据。在$H = 1$ T和$H = 4$ T的外加磁场中测量了YBa $_2$ Cu $_3$ O $_{6.50}$涡旋态的内部磁场分布，发现了高场尾部磁场分布的一个特征，这一特征在最佳掺杂的YBa $_2$ Cu $_3$ O $_{6.95}$中不存在，并且很好地符合涡旋核中具有静态磁场的模型。场的大小估计为18（2）G，并在$T = 10$ K以上减小。我们在现有理论的背景下讨论了额外的涡核磁性的可能起源。
We report on the noise properties of ion-irradiated YBa$_2$Cu$_3$O$_7$ Josephson junctions. This work aims at investigating the linewidth of the Josephson oscillation with a detector response experiment at $\simeq$132 GHz. Experimental results are compared with a simple analytical model based on the Likharev-Semenov equation and the de Gennes dirty limit approximation. We show that the main source of low-frequency fluctuations in these junctions is the broadband Johnson noise and that the excess ($\frac{1}{f}$) noise contribution does not prevail in the temperature range of interest, as report…
Measurements of quantum oscillations in the cuprate superconductors afford a new opportunity to assess the extent to which the electronic properties of these materials yield to a description rooted in Fermi liquid theory. However, such an analysis is hampered by the small number of oscillatory periods observed. Here we employ a genetic algorithm to globally model the field, angular, and temperature dependence of the quantum oscillations observed in the resistivity of YBa2Cu3O6.59. This approach successfully fits an entire data set to a Fermi surface comprised of two small, quasi-2-dimensional …
Magnetic correlations on the full chains of Ortho-II YBa$_2$Cu$_3$O$_{6.5}$
我们提出，在化学计量比高的$T_c$超导体Ortho-II YBa $_2$ Cu $_3$ O $_{6.5}$中，Cu链上的NMR谱线形状是由O空位附近的Cu上的感应磁化决定的，这是由于链中强的磁相关.对具有最近邻d波对相互作用的耦合链-平面哈伯德模型的非限制性Hartree-Fock计算表明，低温下NMR谱线的展宽与无序诱导磁化相一致.此外，我们给出了一个可能的解释，在高温下观察到的反常双峰线形状的不均匀的Cu价在链。链和CuO平面之间的接近诱导平面Cu上的各向异性磁化，并根据链线的平面NMR线加宽，与实验一致。我们讨论了欠掺杂YBCO的其他实验模型的影响。
Static charge-density wave (CDW) and spin-density wave (SDW) order has been convincingly observed in La-based cuprates for some time. However, more recently it has been suggested by quantum oscillation, transport and thermodynamic measurements that density wave order is generic to underdoped cuprates and plays a significant role in YBa_2Cu_3O_{6+delta} (YBCO). We use resonant soft x-ray scattering at the Cu L and O K edges to search for evidence of density wave order in Ortho-II and Ortho-VIII oxygen-ordered YBCO. We report a null result -- no evidence for static CDW order -- in both Ortho-II …
The anisotropy in the microwave conductivity of the ortho-II YBa$_2$Cu$_3$O$_{6.50}$ is studied within the kinetic energy driven superconducting mechanism. The ortho-II YBa$_2$Cu$_3$O$_{6.50}$ is characterized by a periodic alternative of filled and empty $\hat{b}$-axis CuO chains. By considering the CuO chain induced extended anisotropy impurity scattering, the main features of the anisotropy in the microwave conductivity of the ortho-II YBa$_2$Cu$_3$O$_{6.50}$ are reproduced based on the nodal approximation of the quasiparticle excitations and scattering processes, including the intensity an…
We use quantum oscillation measurements to distinguish between spin and orbital components of the lowest energy quasiparticle excitations in YBa2Cu3O6.54, each of which couple differently to a magnetic field. Our measurements reveal the phase of the observed quantum oscillations to remain uninverted over a wide angular range, indicating that the twofold spin degeneracy of the Landau levels is virtually unaltered by the magnetic field. The inferred suppression of the spin degrees of freedom indicates a spin density-wave is responsible for creation of the small Fermi surface pockets in underdope…
We consider quantum oscillation experiments in $\mathrm{YBa_{2}Cu_{3}O_{6+δ}}$ from the perspective of an incommensurate Fermi surface reconstruction using an exact transfer matrix method and the Pichard-Landauer formula for the conductivity. The specific density wave order considered is a period-8 $d$-density wave in which the current density is unidirectionally modulated. The current modulation is also naturally accompanied by a period-4 site charge modulation in the same direction, which is consistent with recent magnetic resonance measurements. In principle Landau theory also allows for a …
Hole-doped high-temperature cuprate superconductors below optimum doping have small electron-like Fermi surfaces occupying a small fraction of the Brillouin zone. There is strong evidence that this is linked to charge density wave (CDW) order, which reconstructs the large hole-like Fermi surfaces predicted by band structure calculations . Recent experiments have revealed the structure of the two CDW components in the benchmark bilayer material YBa$_2$Cu$_3$O$_{7-x}$ in high field where quantum oscillation (QO) measurements are performed. We have combined these results with a tight-binding desc…
Fermi-surface pockets in $YBa_2Cu_3O_{6.5}$ : A comparison of ab initio techniques
我们用三种不同的基于密度泛函的能带结构技术（GGA，GGA+U，PSIC）研究了金属非磁性\textit{ortho} -Ⅱ YBa $_2$ Cu $_3$ O $_{6.5}$的费米面.计算得到的费米面在GGA+U和PSIC中没有口袋，在GGA中有一个较小的口袋。当费米能级在计算值附近移动时，我们反而观察到几个口袋结构。我们计算了它们的横截面积和回旋质量。总的来说，我们的计算显示，在这个阶段，没有确凿的证据表明存在类似电子的费米表面口袋，事实上也没有任何费米表面口袋。这表明，口袋的起源应该在其他不同的阶段寻找。
We report the direct observation of multiple `spin zeroes' in angle-dependent magnetic quantum oscillations measured up to 85T in YBa2Cu3O6+x, at which the amplitude falls to a deep minimum accompanied by a phase inversion of the measured quantum oscillations, enabling the product of the effective mass and effective g-factor m*g* to be tightly constrained. We find an evolution of the location of the spin zeros with applied magnetic field, and suggest that this effect and the absence of a spin zero at low angles can be produced by more than one Fermi surface component, and an effective g-factor…
We present magneto-transport calculations for YBa$_2$Cu$_3$O$_{7-δ}$ (YBCO) materials to show that the electron-like metallic chain state gives both the negative Hall effect and in-plane anisotropic large Nernst signal. We show that the inevitable presence of the metallic 1D CuO chain layer lying between the CuO2 bilayers in YBCO renders an electron-like Fermi surface in the doping range as wide as p=0.05 to overdoping. With underdoping, a pseudogap opening in the CuO2 state reduces its hole-carrier contribution, and therefore the net electron-like quasiparticles dominate the transport propert…
The Fermi surface of a metal is the fundamental basis from which its properties can be understood. In underdoped cuprate superconductors, the Fermi surface undergoes a reconstruction that produces a small electron pocket, but whether there is another, as yet undetected portion to the Fermi surface is unknown. Establishing the complete topology of the Fermi surface is key to identifying the mechanism responsible for its reconstruction. Here we report the discovery of a second Fermi pocket in underdoped YBa2Cu3Oy, detected as a small quantum oscillation frequency in the thermoelectric response a…
Our knowledge of the ground state of underdoped hole-doped cuprates has evolved considerably over the last few years. There is now compelling evidence that inside the pseudogap phase, charge order breaks translational symmetry leading to a reconstructed Fermi surface made of small pockets. Quantum oscillations, [Doiron-Leyraud N, et al. (2007) Nature 447:564-568], optical conductivity [Mirzaei SI, et al. (2013) Proc Natl Acad Sci USA 110:5774-5778] and the validity of Wiedemann-Franz law [Grissonnache G, et al. (2016) Phys. Rev. B 93:064513] point to a Fermi liquid regime at low temperature in…
We use magnetic quantum oscillations in the underdoped high Tc superconductor YBa_2Cu_3O_(6+x) (x=0.56) measured over a broad range of temperatures 100 mK<T<18 K to extract the form of the distribution function describing the low-lying quasiparticle excitations in high magnetic fields. Despite the proximity of YBa_2Cu_3O_(6+x) (x=0.56) to a Mott insulating state, various broken symmetry ground states and/or states with different quasiparticle statistics, we find that our experimental results can be understood in terms of quasiparticle excitations obeying Fermi-Dirac statistics as in the Landau…
We study the temperature dependence of the low energy phonons in the $(H, 0, L)$ reciprocal plane of the highly ordered ortho-II YBa$_2$Cu$_3$O$_{6.55}$ cuprate high temperature superconductor by means of high-resolution inelastic x-ray scattering. Anomalies associated with the emergence of long-range charge density wave (CDW) fluctuations are observed, and are qualitatively similar to those previously observed in the $(0, K, L)$ plane. This confirms the unconventional nature of this bi-dimensional CDW, which is not soft-phonon driven. With the support of first principles calculations, the sym…
The metallic state of the underdoped high-Tc cuprates has remained an enigma: How may seemingly disconnected Fermi surface segments, observed in zero magnetic field as a result of the opening of a partial gap (the pseudogap), possess conventional quasiparticle properties? How do the small Fermi-surface pockets evidenced by the observation of quantum oscillations (QO) emerge as superconductivity is suppressed in high magnetic fields? Such QO, discovered in underdoped YBa2Cu3O6.5 (Y123) and YBa2Cu4O8 (Y124), signify the existence of a conventional Fermi surface (FS). However, due to the complexi…
The Fourier transform of the observed magnetic quantum oscillations (MQO) in YBa$_{2}$Cu$_{3}$O$_{6+δ}$ high-temperature superconductors has a prominent low-frequency peak with two smaller neighbouring peaks. The separation and positions of these three peaks are almost independent of doping. This pattern has been explained previously by rather special, exquisitely detailed, Fermi-surface reconstruction. We propose that these MQO have a different origin, and their frequencies are related to the bilayer and inter-bilayer electron hopping rather than directly to the areas of tiny Fermi-surface po…
Recent experiments have revealed incommensurate charge density wave (CDW) in the pseudogap regime in underdoped cuprates, e.g. YBa$_2$Cu$_3$O$_{6+δ}$ and HgBa$_2$CuO$_{4+δ}$. However, its relationship with the pseudogap is still controversial. In this work, we take a phenomenological synthesis of the doped resonating valence bond (RVB) state and the CDW order. Starting from the Yang-Rice-Zhang Green's function ansatz for the doped RVB state [Phys. Rev. B {\bf 73}, 174501 (2006)], in which the Fermi surface is partially truncated into four nodal hole-like Fermi pockets by the antinodal RVB gap,…
Quantum oscillations in a tilted magnetic field offer the possibility of distinguishing singlet versus triplet order parameters in the particle hole channel provided the measurements reflect a putative ``normal'' state of a density wave obtained by applying by high magnetic field at low temperatures. A theoretical analysis is given that compares spin density wave, a singlet $d$-density wave, and a triplet $d$-density wave. While the existence of a spin zero in the oscillation amplitude is a necessary consequence of a singlet order parameter, a triplet order parameter may or may not exhibit a s…
The underlying physics of the magnetic-field-induced resistive state in high temperature cuprate superconductors remains a mystery. One interpretation is that the application of magnetic field destroys the d-wave superconducting gap to uncover a Fermi surface that behaves like a conventional (i.e.Fermi Liquid) metal (1). Another view is that an applied magnetic field destroys long range superconducting phase coherence, but the superconducting gap amplitude survives (2, 3). By measuring the specific heat of ultra-clean YBa2Cu3O6.56 (YBCO 6.56), we obtain a measure of the quasi-particle density …
