Underdoped Cuprate Superconductors Research Articles

Violation of the Onsager relation for quantum oscillations in superconductors

We numerically study the quantum oscillations in superconducting vortex-mixed states with $d$-wave pairing. We show that in the parameter range of an underdoped cuprate superconductor, the commonly held assumption that the period is given by the underlying Fermi-surface area using the Onsager relation becomes invalid. Using this result, we conclude that the interpretation of the recent experimental data on YBCO as a signal of an underlying Fermi surface with four hole pockets created by a $(\ensuremath{\pi},\ensuremath{\pi})$ folding cannot be ruled out.

Low-temperature thermal conductivity in a d-wave superconductor with coexisting charge order: Effect of self-consistent disorder and vertex corrections

Given the experimental evidence of charge order in the underdoped cuprate superconductors, we consider the effect of coexisting charge order on low-temperature thermal transport in a d-wave superconductor. Using a phenomenological Hamiltonian that describes a two-dimensional system in the presence of a Q = ( π , 0 ) charge density wave and d-wave superconducting order, and including the effects of weak impurity scattering, we compute the self-energy of the quasiparticles within the self-consistent Born approximation, and calculate the zero-temperature thermal conductivity using linear response formalism. We find that vertex corrections within the ladder approximation do not significantly modify the bare-bubble result that was previously calculated. However, self-consistent treatment of the disorder does modify the charge-order-dependence of the thermal conductivity tensor, in that the magnitude of charge order required for the system to become effectively gapped is renormalized, generally to a smaller value.

Thermal conductivity, Fermi pockets and superconductivity in underdoped cuprates

The electronic contribution to thermal conductivity is studied in models of underdopedcuprates where the normal state has a pocketed Fermi surface with circumference∼x (hole concentration) and the superconducting state is formed by opening a gap inthe Fermi pocket. The physical consequences of the Fermi pocket are studied bycomparing the thermal conductivity computed in four different models: (1) an ordinaryd-wave superconductor with four Dirac Fermi points; (2) a normal metal with apocketed Fermi surface; (3) a superconductor formed by spinon–holon binding in thet–J model; (4) a phenomenological d-wave Bardeen–Cooper–Schrieffer (BCS) superconductorwith superconductivity formed by opening a gap on the pocketed Fermi surface. Our resultssuggest that thermal conductivity provides useful information to distinguish betweendifferent scenarios of the normal-to-superconducting transition in underdoped cuprates.

Nonmonotonic pseudogap in high-Tccuprates

The mechanism of high-temperature superconductivity has not been resolved for so long because the normal state of cuprates, which exhibits enigmatic pseudogap phenomena, is not yet understood. We performed careful temperature- and momentum-resolved photoemission experiments to show that the depletion of the spectral weight in slightly underdoped cuprate superconductor, usually called the “pseudogap,” exhibits an unexpected nonmonotonic temperature dependence: decreases linearly approaching T at which it reveals a sharp transition but does not vanish and starts to increase gradually again at higher temperature. The low-temperature behavior of the pseudogap is remarkably similar to one of the incommensurate charge ordering gap in the transitionmetal dichalcogenides, while the reopening of the gap at room temperature fits the scenario of temperaturedriven metal-insulator transition. This observation suggests that two phenomena, the electronic instability to density-wave formation and the entropy-driven metal-to-insulator crossover, may coexist in the normal state of cuprates.

Universal behaviour and the two-component character of magnetically underdoped cuprate superconductors

We present a detailed review of scaling behaviour in the magnetically underdoped cuprate superconductors (hole dopings less than 0.20) and show that it reflects the presence of two coupled components throughout this doping regime: a non-Landau Fermi liquid and a spin liquid whose behaviour maps onto the theoretical Monte Carlo calculations of the two-dimensional Heisenberg model of localized Cu spins for most of its temperature domain. We use this mapping to extract the doping dependence of the strength, f(x) of the spin liquid component and the effective interaction, J eff(x) between the remnant localized spins that compose it; we find that both decrease linearly with x as the doping level increases. We discuss the physical origin of pseudogap behaviour and conclude that it is consistent with scenarios in which the both the large energy gaps found in the normal state and their subsequent superconductivity are brought about by the coupling between the Fermi liquid quasiparticles and the spin liquid excitations, and that differences in this coupling between the 1–2–3 and 2–1–4 materials can explain the measured differences in their superconducting transition temperatures and other properties.

Spin susceptibility of underdoped cuprate superconductors: Insights from a stripe-ordered crystal

We report a detailed study of the temperature and magnetic-field dependence of the spin susceptibility for a single crystal of ${\text{La}}_{1.875}{\text{Ba}}_{0.125}{\text{CuO}}_{4}$. From a quantitative analysis, we find that the temperature-dependent anisotropy of the susceptibility, observed in both the paramagnetic and stripe-ordered phases, directly indicates that localized Cu moments dominate the magnetic response. A field-induced spin-flop transition provides further corroboration for the role of local moments. Contrary to previous analyses of data from polycrystalline samples, we find that a commonly assumed isotropic and temperature-independent contribution from free carriers, if present, must be quite small. Our conclusion is strengthened by extending the quantitative analysis to include crystals of ${\text{La}}_{2\ensuremath{-}x}{\text{Ba}}_{x}{\text{CuO}}_{4}$ with $x=0.095$ and 0.155. On the basis of our results, we present a revised interpretation of the temperature and doping dependence of the spin susceptibility in ${\text{La}}_{2\ensuremath{-}x}{(\text{Sr},\text{Ba})}_{x}{\text{CuO}}_{4}$.

Screening of Point Charge Impurities in Highly Anisotropic Metals: Application toμ+-Spin Relaxation in Underdoped Cuprate Superconductors

We calculate the screening charge density distribution due to a point charge, such as that of a positive muon (mu+), placed between the planes of a highly anisotropic layered metal. In underdoped hole cuprates the screening charge converts the charge density in the metallic-plane unit cells in the vicinity of the mu+ to nearly its value in the insulating state. The current-loop-ordered state observed by polarized neutron diffraction then vanishes in such cells, and also in nearby cells over a distance of order the intrinsic correlation length of the loop-ordered state. This strongly suppresses the magnetic field at the mu+ site. We estimate this suppressed field in underdoped YBa2Cu3O6+x and La2-xSrxCuO4, and find consistency with the observed approximately 0.2 G field in the former case and the observed upper bound of approximately 0.2 G in the latter case. This resolves the controversy between the neutron diffraction and mu-spin relaxation experiments.

Anomalous Nernst effect from a chirald-density-wave state in underdoped cuprate superconductors

We show that the breakdown of time-reversal invariance, confirmed by the recent polar Kerr effect measurements in the cuprates, implies the existence of an anomalous Nernst effect in the pseudogap phase of underdoped cuprate superconductors. Modeling the time-reversal-breaking ordered state by the chiral $d$-density-wave state, we find that the magnitude of the Nernst effect can be sizable even at temperatures much higher than the superconducting transition temperature. These results imply that the experimentally found Nernst effect at the pseudogap temperatures may be due to the chiral $d$-density-wave ordered state with broken time-reversal invariance.

Fermi Arcs in the Superconducting Clustered State for Underdoped Cuprate Superconductors

The one-particle spectral function of a state formed by superconducting (SC) clusters is studied via Monte Carlo techniques. The clusters have similar SC amplitudes but randomly distributed phases. This state is stabilized by competition with the antiferromagnetism expected to be present in the cuprates and after quenched disorder is introduced. A Fermi surface composed of disconnected segments, i.e., Fermi arcs, is observed between the critical temperature T_(c) and the cluster formation temperature scale T*.

Weak ferromagnetism accompanying loop current order in underdoped cuprate superconductors

We discuss the necessary symmetry conditions and the different ways in which they can be physically realized for the occurrence of ferromagnetism accompanying the loop current orbital magnetic order observed by polarized neutron-diffraction experiments (or indeed any other conceivable principal order) in the underdoped phase of cuprates. We contrast the Kerr effect experiments in single crystals observing ferromagnetism with the direct magnetization measurements in large powder samples, which do not observe it. We also suggest experiments to resolve the differences among the experiments, all of which we believe to be correct.

Spin-polaron band structure and hole pockets in underdoped cuprates

We present a variational approach based on the string picture to analyze the internal structure and dispersion of spin polarons with different symmetries in an antiferromagnet. We then use this to discuss the properties of underdoped cuprate superconductor within the ``doped insulator'' picture. The theory explains the remnant Fermi surface for the undoped compounds, as well as hole pockets, Fermi arcs, high-energy pseudogap, and the midinfrared band in doped materials. Destructive interference between the phases of a photohole near $\ensuremath{\Gamma}$ and the internal phases of the Zhang-Rice singlet combined with our theory moreover explains the ``waterfall'' phenomenon.

Phenomenological theory of the protected nodes and collapse of the Fermi arcs in underdoped cuprate superconductors

We show how recent angle resolved photoemission measurements addressing the Fermi arcs in the cuprates reveal a very natural phenomenological description of the complex superfluid phase. Importantly, this phenomenology is consistent with a previously presented microscopic theory. By distinguishing the order parameter and the excitation gap, we are able to demonstrate how the collapse of the arcs below ${T}_{c}$ into well defined nodes is associated with the smooth emergence of superconducting coherence. Comparison of this theory with experiment shows good semiquantitative agreement.

Experimental evidence of two distinct charge carriers in underdoped cuprate superconductors

We present the results on heavily underdoped ${\text{Y}}_{1\ensuremath{-}x}{\text{Ca}}_{x}{\text{Ba}}_{2}{\text{Cu}}_{3}{\text{O}}_{6+y}$, which provide the evidence that the doping mechanism (cation substitution or oxygen loading) directly determines whether the corresponding injected mobile holes contribute to superconductivity or only to high-temperature transport. We argue that this hole tagging is a signature of the complexities of single-hole doping in Mott insulators, and it calls for a subtler description of the correlated bands than the usual one. We also map in great detail the underdoped superconducting phase diagram ${T}_{c}$ vs hole doping, which shows that the total number of mobile holes is not the driving parameter for superconductivity.

Theory of reduced superfluid density in underdoped cuprate superconductors

The critical temperature of an underdoped cuprate superconductor is limited by its phase stiffness $\rho$. In this Letter we argue that the dependence of $\rho$ on doping $x$ should be understood as a consequence of deleterious competition with antiferromagnetism at large electron densities, rather than as evidence for pairing of holes in the $x =0$ Mott insulator state. Our proposal is based on the observation that the correlation energy of a d-wave superconductor increases in magnitude at finite pairing wavevector when antiferromagnetic fluctuations are strong.

Evidence for Two Separate Energy Gaps in Underdoped High-Temperature Cuprate Superconductors from Broadband Infrared Ellipsometry

We present broadband infrared ellipsometry measurements of the c-axis conductivity of underdoped RBa_{2}Cu_{3}O_{7-delta} (R=Y, Nd, and La) single crystals. Our data show that separate energy scales are underlying the redistributions of spectral weight due to the normal state pseudogap and the superconducting gap. Furthermore, they provide evidence that these gaps do not share the same electronic states and do not merge on the overdoped side. Accordingly, our data are suggestive of a two gap scenario with a pseudogap that is likely extrinsic with respect to superconductivity.

Quantum Oscillations in the Underdoped CuprateYBa2Cu4O8

We report the observation of quantum oscillations in the underdoped cuprate superconductor YBa2Cu4O8 using a tunnel-diode oscillator technique in pulsed magnetic fields up to 85 T. There is a clear signal, periodic in inverse field, with frequency 660+/-15 T and possible evidence for the presence of two components of slightly different frequency. The quasiparticle mass is m(*)=3.0+/-0.3m(e). In conjunction with the results of Doiron-Leyraud et al. for YBa2Cu3O6.5, the present measurements suggest that Fermi surface pockets are a general feature of underdoped copper oxide planes and provide information about the doping dependence of the Fermi surface.

Small Fermi Surface Pockets in Underdoped High Temperature Superconductors: Observation of Shubnikov–de Haas Oscillations inYBa2Cu4O8

We report the observation of Shubnikov-de Haas oscillations in the underdoped cuprate superconductor YBa2Cu4O8 (Y124). For fields aligned along the c axis, the frequency of the oscillations is 660+/-30 T, which corresponds to approximately 2.4% of the total area of the first Brillouin zone. The effective mass of the quasiparticles on this orbit is measured to be 2.7+/-0.3 times the free electron mass. Both the frequency and mass are comparable to those recently observed for ortho-II YBa2Cu3O6.5 (Y123-II). We show that although small Fermi surface pockets may be expected from band-structure calculations in Y123-II, no such pockets are predicted for Y124. Our results therefore imply that these small pockets are a generic feature of the copper oxide plane in underdoped cuprates.

Electronic Liquid Crystal State in the High-Temperature Superconductor YBa 2 Cu 3 O 6.45

Electronic phases with symmetry properties matching those of conventional liquid crystals have recently been discovered in transport experiments on semiconductor heterostructures and metal oxides at millikelvin temperatures. We report the spontaneous onset of a one-dimensional, incommensurate modulation of the spin system in the high-transition-temperature superconductor YBa2Cu3O6.45 upon cooling below approximately 150 kelvin, whereas static magnetic order is absent above 2 kelvin. The evolution of this modulation with temperature and doping parallels that of the in-plane anisotropy of the resistivity, indicating an electronic nematic phase that is stable over a wide temperature range. The results suggest that soft spin fluctuations are a microscopic route toward electronic liquid crystals and that nematic order can coexist with high-temperature superconductivity in underdoped cuprates.

Temperature scaling of Fermi arcs in the normal state of the underdoped cuprate superconductors

Recent angle resolved photoemission experiments by Kanigel et al., [Nature Physics 2 (2006) 447] show that the low energy electronic excitations in the normal state of underdoped cuprate superconductors exist on open Fermi arcs which shrink upon cooling, and appear to extrapolate to nodal points at zero temperature. We show that this non-Fermi liquid phenomenon could result from the underdoped normal state lying in the quantum critical regime of a superconductor–insulator transition, and present computational results for the electron spectral function which are in reasonable agreement with the experimental results.

Phenomenological Description of the Two Energy Scales in Underdoped Cuprate Superconductors

Raman and angle-resolved photoemission spectroscopy experiments have demonstrated that in superconducting underdoped cuprates nodal and antinodal regions are characterized by two energy scales instead of the one expected in BCS theory. The nodal scale decreases with underdoping while the antinodal one increases. Contrary to the behavior expected for an increasing energy scale, the antinodal Raman intensity decreases with decreasing doping. Using the Yang-Rice-Zhang model, we show that these features are a consequence of the nonconventional nature of the superconducting state in which superconductivity and pseudogap correlations are both present and compete for the phase space.