Fermi surface reconstruction in high-T(c) superconductors

Magnetic field reveals vanishing Hall response in the normal state of stripe-ordered cuprates

The origin of the weak insulating behavior of the resistivity, i.e. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rho }_{xx}\propto {\mathrm{ln}}\,(1/T)$$\end{document}ρxx∝ln(1/T), revealed when magnetic fields (H) suppress superconductivity in underdoped cuprates has been a longtime mystery. Surprisingly, the high-field behavior of the resistivity observed recently in charge- and spin-stripe-ordered La-214 cuprates suggests a metallic, as opposed to insulating, high-field normal state. Here we report the vanishing of the Hall coefficient in this field-revealed normal state for all \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T\ <\ (2-6){T}_{{\rm{c}}}^{0}$$\end{document}T<(2−6)Tc0, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T}_{{\rm{c}}}^{0}$$\end{document}Tc0 is the zero-field superconducting transition temperature. Our measurements demonstrate that this is a robust fundamental property of the normal state of cuprates with intertwined orders, exhibited in the previously unexplored regime of T and H. The behavior of the high-field Hall coefficient is fundamentally different from that in other cuprates such as YBa₂Cu₃O_6+x and YBa₂Cu₄O₈, and may imply an approximate particle-hole symmetry that is unique to stripe-ordered cuprates. Our results highlight the important role of the competing orders in determining the normal state of cuprates.

The Hall effect has been used as a probe of the normal state of cuprates, when superconductivity is supressed by a magnetic field. Here, the authors report the vanishing of the Hall coefficient at high magnetic field in cuprates with stripe order and interpret it as a signature of the stripe-ordered phase.

Calculations of quantum oscillations in cuprate superconductors considering the pseudogap

The observations of quantum oscillations frequencies in overdoped cuprates were in agreement with a charge density contained in a cylindrical Fermi surface but the measured frequencies of underdoped compounds were much smaller than expected. This was attributed to a topological transition into small pockets of Fermi surface associated with the existence of charge density waves. On the other hand, spectroscopic measurements suggested that the large two-dimensional Fermi surface changes continuously into a set of four disconnected arcs. Here we take into account the effect of the pseudogap that limits the availablek-space area where the Landau levels are developed on the Luttinger theorem and obtain the correct total carrier densities. The calculations show how the disconnected arcs evolve into a closed Fermi surface reconciling the experiments.

Unusual Interplay between Superconductivity and Field-Induced Charge Order in YBa_{2}Cu_{3}O_{y}

We present a detailed study of the temperature (T) and magnetic field (H) dependence of the electronic density of states (DOS) at the Fermi level, as deduced from specific heat and Knight shift measurements in underdoped YBa_{2}Cu_{3}O_{y}. We find that the DOS becomes field independent above a characteristic field H_{DOS}, and that the H_{DOS}(T) line displays an unusual inflection near the onset of the long-range 3D charge-density wave order. The unusual S shape of H_{DOS}(T) is suggestive of two mutually exclusive orders that eventually establish a form of cooperation in order to coexist at low T. On theoretical grounds, such a collaboration could result from the stabilization of a pair-density wave state, which calls for further investigation in this region of the phase diagram.

Two-component energy spectrum of cuprates in the pseudogap phase and its evolution with temperature and at charge ordering

In the search for mechanisms of high-temperature superconductivity it is critical to know the electronic spectrum in the pseudogap phase from which superconductivity evolves. The lack of angle-resolved photoemission data for every cuprate family precludes an agreement as to its structure, doping and temperature dependence and the role of charge ordering. Here we show that, in the entire Fermi-liquid-like regime that is ubiquitous in underdoped cuprates, the spectrum consists of holes on the Fermi arcs and an electronic pocket. We argue that experiments on the Hall coefficient identify the latter as a permanent feature at doped hole concentration x > 0.08-0.10, in contrast to the idea of the Fermi surface reconstruction via charge ordering. The longstanding issue of the origin of the negative Hall coefficient in YBCO and Hg1201 at low temperature is resolved: the electronic contribution prevails as mobility of the latter (evaluated by the Dingle temperature) becomes temperature independent, while the mobility of holes scattered by the short-wavelength charge density waves decreases.

Evidence for a small hole pocket in the Fermi surface of underdoped YBa2Cu3Oy

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 evidence for a second Fermi pocket in underdoped YBa2Cu3Oy, detected as a small quantum oscillation frequency in the thermoelectric response and in the c-axis resistance. The field-angle dependence of the frequency shows that it is a distinct Fermi surface, and the normal-state thermopower requires it to be a hole pocket. A Fermi surface consisting of one electron pocket and two hole pockets with the measured areas and masses is consistent with a Fermi-surface reconstruction by the charge-density-wave order observed in YBa2Cu3Oy, provided other parts of the reconstructed Fermi surface are removed by a separate mechanism, possibly the pseudogap.

Fermi-surface reconstruction and complex phase equilibria in CaFe2As2

Fermi-surface topology governs the relationship between magnetism and superconductivity in iron-based materials. Using low-temperature transport, angle-resolved photoemission, and x-ray diffraction, we show unambiguous evidence of large Fermi-surface reconstruction in CaFe2As2 at magnetic spin-density-wave and nonmagnetic collapsed-tetragonal (cT) transitions. For the cT transition, the change in the Fermi-surface topology has a different character with no contribution from the hole part of the Fermi surface. In addition, the results suggest that the pressure effect in CaFe2As2 is mainly leading to a rigid-band-like change of the valence electronic structure. We discuss these results and their implications for magnetism and superconductivity in this material.

Direct measurement of the upper critical field in cuprate superconductors

In the quest to increase the critical temperature Tc of cuprate superconductors, it is essential to identify the factors that limit the strength of superconductivity. The upper critical field Hc2 is a fundamental measure of that strength, yet there is no agreement on its magnitude and doping dependence in cuprate superconductors. Here we show that the thermal conductivity can be used to directly detect Hc2 in the cuprates YBa2Cu3Oy, YBa2Cu4O8 and Tl2Ba2CuO6+δ, allowing us to map out Hc2 across the doping phase diagram. It exhibits two peaks, each located at a critical point where the Fermi surface of YBa2Cu3Oy is known to undergo a transformation. Below the higher critical point, the condensation energy, obtained directly from Hc2, suffers a sudden 20-fold collapse. This reveals that phase competition-associated with Fermi-surface reconstruction and charge-density-wave order-is a key limiting factor in the superconductivity of cuprates.

Bond order in two-dimensional metals with antiferromagnetic exchange interactions

We present an unrestricted Hartree-Fock computation of charge-ordering instabilities of two-dimensional metals with antiferromagnetic exchange interactions, allowing for arbitrary ordering wave vectors and internal wave functions of the particle-hole pair condensate. We find that the ordering has a dominant d symmetry of rotations about lattice points for a range of ordering wave vectors, including those observed in recent experiments at low temperatures on YBa2Cu3O(y). This d symmetry implies the charge ordering is primarily on the bonds of the Cu lattice, and we propose incommensurate bond order parameters for the underdoped cuprates. The field theory for the onset of Néel order in a metal has an emergent pseudospin symmetry which "rotates" d-wave Cooper pairs to particle-hole pairs [M. A. Metlitski and S. Sachdev, Phys. Rev. B 82, 075128 (2010)]; our results show that this symmetry has consequences even when the spin correlations are short ranged and incommensurate.

Quantum oscillations in YBa2Cu3O(6+δ) from period-8 d-density wave order

We consider quantum oscillation experiments in YBa(2)Cu(3)O(6+δ) from the perspective of Fermi surface reconstruction using an exact transfer matrix method and the Pichard-Landauer formula for the conductivity. The specific density wave order responsible for reconstruction is a period-8 d-density wave in which the current density is unidirectionally modulated, which is also naturally accompanied by a period-4 charge order, consistent with recent nuclear magnetic resonance experiments. This scenario leads to a natural explanation as to why only oscillations from a single electron pocket of a frequency of about 500 T is observed, and a hole pocket of roughly twice the frequency as dictated by the twofold commensurate order and the Luttinger sum rule is not observed. In contrast period-8 d-density wave leads to a hole pocket of roughly half the frequency of the electron pocket. The observation of this slower frequency will require higher, but not unrealistic, magnetic fields than those commonly employed. There is already some suggestion of the slower frequency in a measurement in fields as high as 85 T.

Interplay between charge stripes and sign reversals of Hall and Seebeck effects in stripe-ordered La(1.6-x)Nd0.4Sr(x)CuO4 superconductors

The Hall and Seebeck effects of the stripe-ordered superconductor La(1.6-x)Nd(0.4)Sr(x)CuO(4) single crystals (x = 0.10, 0.12 and 0.15) were investigated systematically. The sign change of Hall and Seebeck coefficients (R(H) and S) from positive to negative with decreasing temperature suggests the presence of electron pockets in the Fermi surface due to the stripe ordering. We successfully tune this behavior through an epitaxial strain induced by the mismatch between the thin film and the substrate. The negative R(H) disappears in the thinner film in which the static charge stripe is greatly suppressed by the strong epitaxial strain, and for a strain released thicker film the negative R(H) recovers. These results indicate the possibility of Fermi surface reconstruction caused by the static charge stripe order in the system.

Fermi-surface reconstruction by stripe order in cuprate superconductors

The origin of pairing in a superconductor resides in the underlying normal state. In the cuprate high-temperature superconductor YBa₂Cu₃O_y (YBCO), application of a magnetic field to suppress superconductivity reveals a ground state that appears to break the translational symmetry of the lattice, pointing to some density-wave order. Here we use a comparative study of thermoelectric transport in the cuprates YBCO and La_1.8−xEu_0.2Sr_xCuO₄ (Eu-LSCO) to show that the two materials exhibit the same process of Fermi-surface reconstruction as a function of temperature and doping. The fact that in Eu-LSCO this reconstruction coexists with spin and charge modulations that break translational symmetry shows that stripe order is the generic non-superconducting ground state of hole-doped cuprates.

An electron pocket exists in the Fermi-surface of the high temperature superconductor YBa₂Cu₃O_y, but its origin is unknown. Here, YBa₂Cu₃O_y and La_1.8−xEu_0.2Sr_xCuO₄ are both shown to exhibit Fermi-surface reconstruction, and in the latter, this is due to stripe order, suggesting that the same mechanism exists in YBa₂Cu₃O_y.

Fermi-liquid behavior of the normal phase of a strongly interacting gas of cold atoms

We measure the magnetic susceptibility of a Fermi gas with tunable interactions in the low-temperature limit and compare it to quantum Monte Carlo calculations. Experiment and theory are in excellent agreement and fully compatible with the Landau theory of Fermi liquids. We show that these measurements shed new light on the nature of the excitations of the normal phase of a strongly interacting Fermi gas.

Dynamic charge inhomogeneity in cuprate superconductors

The inelastic x-ray scattering spectrum for phonons of Δ(1) symmetry, including the CuO bond-stretching phonon dispersion, is analyzed by means of Lorentz fitting for HgBa(2)CuO(4) and Bi(2)Sr(2)CuO(6), 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 case for the second-highest Δ(1) branch compromising the bond-stretching modes, which disagrees for both compounds with the calculations. This branch shows an anomalous softening with a minimum around the wavevector [Formula: see text], at variance with the calculation predictions. Such a disparity with the calculated results, that are based on the assumption of an undisturbed translation and point group invariant electronic structure of the CuO plane, indicates some static charge inhomogeneities in the measured probes. Most likely these will be charge stripes along the CuO bonds which have the strongest coupling to certain longitudinal bond-stretching modes, that in turn self-consistently induce corresponding dynamic charge inhomogeneities. The symmetry breaking by the mix of dynamic and static charge inhomogeneities can lead to a reconstruction of the Fermi surface into small pockets.

Broken rotational symmetry in the pseudogap phase of a high-T(c) superconductor

The nature of the pseudogap phase is a central problem in the effort to understand the high-transition-temperature (high-T(c)) copper oxide superconductors. A fundamental question is what symmetries are broken when the pseudogap phase sets in, which occurs when the temperature decreases below a value T*. There is evidence from measurements of both polarized neutron diffraction and the polar Kerr effect that time-reversal symmetry is broken, but at temperatures that differ significantly from one another. Broken rotational symmetry was detected from both resistivity measurements and inelastic neutron scattering at low doping, and from scanning tunnelling spectroscopy at low temperature, but showed no clear relation to T*. Here we report the observation of a large in-plane anisotropy of the Nernst effect in YBa(2)Cu(3)O(y) that sets in precisely at T* throughout the doping phase diagram. We show that the CuO chains of the orthorhombic lattice are not responsible for this anisotropy, which is therefore an intrinsic property of the CuO(2) planes. We conclude that the pseudogap phase is an electronic state that strongly breaks four-fold rotational symmetry. This narrows the range of possible states considerably, pointing to stripe or nematic order.

Nernst and Seebeck coefficients of the cuprate superconductor YBa2Cu3O6.67: a study of Fermi surface reconstruction

The Seebeck and Nernst coefficients S and nu of the cuprate superconductor YBa{2}Cu{3}O{y} (YBCO) were measured in a single crystal with doping p=0.12 in magnetic fields up to H=28 T. Down to T=9 K, nu becomes independent of field by H approximately 30 T, showing that superconducting fluctuations have become negligible. In this field-induced normal state, S/T and nu/T are both large and negative in the T-->0 limit, with the magnitude and sign of S/T consistent with the small electronlike Fermi surface pocket detected previously by quantum oscillations and the Hall effect. The change of sign in S(T) at T approximately 50 K is remarkably similar to that observed in La2-xBaxCuO4, La{2-x-y}Nd{y}Sr_{x}CuO{4}, and La{2-x-y}Eu{y}Sr{x}CuO{4}, where it is clearly associated with the onset of stripe order. We propose that a similar density-wave mechanism causes the Fermi surface reconstruction in YBCO.

Multiple quantum oscillations in the de Haas-van Alphen spectra of the underdoped high-temperature superconductor YBa2Cu3O6.5

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 YBa2Cu3O6.5. 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 c axis coherence is restored at low temperature in underdoped cuprates. Our results do not support the existence of a larger frequency of the order of 1650 T reported recently in the same compound [S. E. Sebastian, Nature (London) 454, 200 (2008)].