Pseudogap Phase Research Articles

A-b Anisotropy of the Intra-Unit-Cell Magnetic Order in YBa_{2}Cu_{3}O_{6.6}.

Within the complex phase diagram of the hole-doped cuprates, seizing the nature of the mysterious pseudogap phase is essential for unraveling the microscopic origin of high-temperature superconductivity. Below the pseudogap temperature T^{⋆}, evidence for intra-unit-cell orders breaking the fourfold rotation symmetry have been provided by neutron diffraction and scanning tunneling spectroscopy. Using polarized neutron diffraction on a detwinned YBa_{2}Cu_{3}O_{6.6} sample, we here report a distinct a-b anisotropy of the intra-unit-cell magnetic structure factor below T^{⋆}, highlighting that intra-unit-cell order in this material breaks the mirror symmetry of the CuO_{2} bilayers. This is likely to originate from a crisscrossed arrangement of loop currents within the CuO_{2} bilayer, resulting in a bilayer mean toroidal axis along the b direction.

Normal state pair nematicity and hidden magnetic order and metal-insulator (fermionboson) crossover origin of pseudogap phase of cuprates II

In the present paper II, we will gain an understanding of the nematicity, insulating ground state (IGS), nematicity to stripe phase transition, Fermi pockets evolution, and resistivity temperature upturn, as to be metal - insulator (fermion-boson)- crossover (MIC) phenomena for the pseudogap (PG) region of cuprates. While in the paper I [1], we obtained an understanding of the observed heat conductivity downturn, anomalous Lorentz ratio, insulator resistivity boundary, nonlinear entropy as manifestations of the same MIC. The recently observed nematicity and hidden magnetic order are related to the PG pair intra charge and spin fluctuations. We will try to obtain an answer on the question: why ground state of YBCO is Fermi liquid oscillating and of Bi-2212 is insulating? We will also clarify the physics of the recently observed MIC results of Lalibert\'e et al. [2] and explain the long-discussed transition of the electric charge density from doping to doping+1 dependence at the critical doping. We predict that at the upturns this density should have the temperature dependence $n\sim T^3n_2$ for $T\rightarrow 0$, where $n_2$ is density for dopings close to the critical value. We understood that the upturns before and after the first critical doping have the same nature. We will find understanding of all above mentioned phenomena within the PG pair physics.

Pseudogap-generated a coexistence of Fermi arcs and Fermi pockets in cuprate superconductors

One of the most intriguing puzzle is why there is a coexistence of Fermi arcs and Fermi pockets in the pseudogap phase of cuprate superconductors? This puzzle is calling for an explanation. Based on the t−J model in the fermion-spin representation, the coexistence of the Fermi arcs and Fermi pockets in cuprate superconductors is studied by taking into account the pseudogap effect. It is shown that the pseudogap induces an energy band splitting, and then the poles of the electron Green’s function at zero energy form two contours in momentum space, however, the electron spectral weight on these two contours around the antinodal region is gapped out by the pseudogap, leaving behind the low-energy electron spectral weight only located at the disconnected segments around the nodal region. In particular, the tips of these disconnected segments converge on the hot spots to form the closed Fermi pockets, generating a coexistence of the Fermi arcs and Fermi pockets. Moreover, the single-particle coherent weight is directly related to the pseudogap, and grows linearly with doping. The calculated result of the overall dispersion of the electron excitations is in qualitative agreement with the experimental data. The theory also predicts that the pseudogap-induced peak-dip-hump structure in the electron spectrum is absent from the hot-spot directions.

Dynamical decoherence of the light induced interlayer coupling in YBa2Cu3O6+δ

Optical excitation of apical oxygen vibrations in YBa$_{2}$Cu$_{3}$O$_{6+\delta}$ 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$_{6+\delta}$. However, despite the similarities between the above T$_{c}$ transient plasma mode and the equilibrium Josephson plasmon, alternative explanations involving high mobility quasiparticle transport should be considered. Here, we report an extensive study of the relaxation of the light-induced plasmon into the equilibrium incoherent phase. These new experiments allow for a critical assessment of the nature of this mode. We determine that the transient plasma relaxes through a collapse of its coherence length rather than its carrier (or superfluid) density. These observations are not easily reconciled with quasiparticle interlayer transport, and rather support transient superfluid tunneling as the origin of the light-induced interlayer coupling in YBa$_{2}$Cu$_{3}$O$_{6+\delta}$.

Strong pairing fluctuations and lattice anomalies in the pseudogap phase of the cuprates

The pseudogap state in underdoped cuprates shows many very anomalous features. Among them are an extended temperature region of pairing fluctuations above the superconducting transition temperature and an unusual giant phonon anomaly in the same temperature and hole density range. A recent theoretical proposal that ascribes these anomalies to the presence of strong phase fluctuations related to a Leggett mode, is summarised.

Origin of positive out-of-plane magnetoconductivity in overdoped Bi1.6Pb0.4Sr2CaCu1.96Fe0.04O8+δ

To elucidate the pseudogap phase diagram including the overdoped state of high transition temperature (high-$T_c$) cuprates, we must understand the origin of the positive out-of-plane magnetoconductivity (MC) observed in these compounds. For this purpose, the out-of-plane resistivity $\rho_c(T,H)$ of an overdoped Bi$_{1.6}$Pb$_{0.4}$Sr$_{2}$CaCu$_{1.96}$Fe$_{0.04}$O$_{8+\delta}$ (Bi-2212) single crystal is measured under pulsed magnetic fields up to 60 T. We show that the superconductive density-of-states (DOS) depletion effect, in addition to the pseudogap effect, clearly appears below the superconductive fluctuation regime, and the contribution becomes dominant in the superconducting state.

Fermi liquid behavior of the in-plane resistivity in the pseudogap state of YBa2Cu4O8

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(7144):565-568], optical conductivity [Mirzaei SI, et al. (2013) Proc Natl Acad Sci USA 110(15):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 the underdoped regime. However, the observation of a quadratic temperature dependence in the electrical resistivity at low temperatures, the hallmark of a Fermi liquid regime, is still missing. Here, we report magnetoresistance measurements in the magnetic-field-induced normal state of underdoped YBa2Cu4O8 that are consistent with a T2 resistivity extending down to 1.5 K. The magnitude of the T2 coefficient, however, is much smaller than expected for a single pocket of the mass and size observed in quantum oscillations, implying that the reconstructed Fermi surface must consist of at least one additional pocket.

Angle-resolved photoemission with circularly polarized light in the nodal mirror plane of underdoped Bi2Sr2CaCu2O8+δ superconductor

Unraveling the nature of pseudogap phase in high-temperature superconductors holds the key to understanding their superconducting mechanisms and potentially broadening their applications via enhancement of their superconducting transition temperatures. Angle-resolved photoemission spectroscopy (ARPES) experiments using circularly polarized light have been proposed to detect possible symmetry breaking state in the pseudogap phase of cuprates. The presence (absence) of an electronic order which breaks mirror symmetry of the crystal would in principle induce a finite (zero) circular dichroism in photoemission. Different orders breaking reflection symmetries about different mirror planes can also be distinguished by the momentum dependence of the measured circular dichroism. Here, we report ARPES experiment on an underdoped Bi2Sr2CaCu2O8+δ (Bi2212) superconductor in the Γ (0,0)-Y (π,π) nodal mirror plane using circularly polarized light. No circular dichroism is observed on the level of ∼2% at low temperature, which places a clear constraint on the forms of possible symmetry breaking orders in this sample. Meanwhile, we find that the geometric dichroism remains substantial very close to its perfect extinction such that a very small sample angular offset is sufficient to induce a sizeable dichroic signal. It highlights the importance to establish a perfect extinction of geometric dichroism as a prerequisite for the identification of any intrinsic circular dichroism in this material.

Investigation of potential fluctuating intra-unit cell magnetic order in cuprates byμSR

We report low temperature muon spin relaxation (muSR) measurements of the high-transition-temperature (Tc) cuprate superconductors Bi{2+x}Sr{2-x}CaCu2O{8+\delta} and YBa2Cu3O6.57, aimed at detecting the mysterious intra-unit cell (IUC) magnetic order that has been observed by spin polarized neutron scattering in the pseudogap phase of four different cuprate families. A lack of confirmation by local magnetic probe methods has raised the possibility that the magnetic order fluctuates slowly enough to appear static on the time scale of neutron scattering, but too fast to affect $\mu$SR or nuclear magnetic resonance (NMR) signals. The IUC magnetic order has been linked to a theoretical model for the cuprates, which predicts a long-range ordered phase of electron-current loop order that terminates at a quantum crictical point (QCP). Our study suggests that lowering the temperature to T ~ 25 mK and moving far below the purported QCP does not cause enough of a slowing down of fluctuations for the IUC magnetic order to become detectable on the time scale of muSR. Our measurements place narrow limits on the fluctuation rate of this unidentified magnetic order.

Engineering holographic phase diagrams

We study how to engineer holographic models with features of a high temperature superconductor phase diagram. We introduce a field in the bulk which provides a tunable "doping" parameter in the boundary theory. By designing how this field changes the effective masses of other order parameter fields, desired phase diagrams can be engineered. We give examples of generating phase diagrams with phase boundaries similar to a superconducting dome and an anti-ferromagnetic phase by including two order parameter fields. We also explore whether the pseudo gap phase can be described without adding another order parameter field and discuss the potential scaling symmetry associated with a quantum critical point hidden under the superconducting dome in this phase diagram.

Emergence of higher order rotational symmetry in the hidden order phase of URuSi

Electrical resistivity measurements were performed as functions of temperature, magnetic field, and angle between the magnetic field and the c-axis of a URuSi single crystal. The resistivity exhibits a two-fold oscillation as a function of at high temperatures, which undergoes a 180-phase shift (sign change) with decreasing temperature at around 35 K. The hidden order transition is manifested as a minimum in the magnetoresistance and amplitude of the two-fold oscillation. Interestingly, the resistivity also showed four-fold, six-fold, and eight-fold symmetries at the hidden order transition. These higher order symmetries were also detected at low temperatures, which could be a sign of the formation of another pseudogap phase above the superconducting transition, consistent with recent evidence for a pseudogap from point-contact spectroscopy measurements and NMR. Measurements of the magnetisation of single crystalline URuSi with the magnetic field applied parallel and perpendicular to the crystallographic c-axis revealed regions with linear temperature dependencies between the hidden order transition temperature and about 25 K. This T-linear behaviour of the magnetisation may be associated with the formation of a precursor phase or ‘pseudogap’ in the density of states in the vicinity of 30–35 K.

Model of electron pairs in electron-doped cuprates

In the order parameter of hole-doped cuprate superconductors in the pseudogap phase, two holes enter the order parameter from opposite sides and pass through various [Formula: see text] cells jumping from one [Formula: see text] to the other under the influence of magnetic field offered by the [Formula: see text] ions in that [Formula: see text] cell and thus forming hole pairs. In the pseudogap phase of electron-doped cuprates, two electrons enter the order parameter at [Formula: see text] sites from opposite ends and pass from one [Formula: see text] site to the diagonally opposite [Formula: see text] site. Following this type of path, they are subjected to high magnetic fields from various [Formula: see text] ions in that cell. They do not travel from one [Formula: see text] site to the other along straight path but by helical path. As they pass through the diagonal, they face high to low to very high magnetic field. Therefore, frequency of helical motion and pitch goes on changing with the magnetic field. Just before reaching the [Formula: see text] ions at the exit points of all the cells, the pitch of the helical motion is enormously decreased and thus charge density at these sites is increased. So the velocity of electrons along the diagonal path is decreased. Consequently, transition temperature of electron-doped cuprates becomes less than that of hole-doped cuprates. Symmetry of the order parameter of the electron-doped cuprates has been found to be of [Formula: see text] type. It has been inferred that internal magnetic field inside the order parameter reconstructs the Fermi surface, which is requisite for superconductivity to take place. Electron pairs formed in the pseudogap phase are the precursors of superconducting order parameter when cooled below [Formula: see text].

Superconductor to Mott insulator transition in YBa2Cu3O7/LaCaMnO3 heterostructures.

The superconductor-to-insulator transition (SIT) induced by means such as external magnetic fields, disorder or spatial confinement is a vivid illustration of a quantum phase transition dramatically affecting the superconducting order parameter. In pursuit of a new realization of the SIT by interfacial charge transfer, we developed extremely thin superlattices composed of high Tc superconductor YBa2Cu3O7 (YBCO) and colossal magnetoresistance ferromagnet La0.67Ca0.33MnO3 (LCMO). By using linearly polarized resonant X-ray absorption spectroscopy and magnetic circular dichroism, combined with hard X-ray photoelectron spectroscopy, we derived a complete picture of the interfacial carrier doping in cuprate and manganite atomic layers, leading to the transition from superconducting to an unusual Mott insulating state emerging with the increase of LCMO layer thickness. In addition, contrary to the common perception that only transition metal ions may respond to the charge transfer process, we found that charge is also actively compensated by rare-earth and alkaline-earth metal ions of the interface. Such deterministic control of Tc by pure electronic doping without any hindering effects of chemical substitution is another promising route to disentangle the role of disorder on the pseudo-gap and charge density wave phases of underdoped cuprates.

Charge Order and Peak-dip-hump Structure in Pseudogap Phase of Cuprate Superconductors

Within the framework of the t-J model, the nature of the peak-dip-hump structure in the electron spectrum of cuprate superconductors in the normal-state is studied by taking into account the pseudogap effect. It is shown that in analogy to the charge-order state, the peak-dip-hump structure in the electron spectrum is also generated by the momentum dependence of the pseudogap, and therefore, there is a common origin for the emergence of the charge-order state and peak-dip-hump structure. In particular, the remarkable peak-dip-hump structure in the electron spectrum appears in the entire region of the electron Fermi surface except for the hot spots.

Structural analysis of the precursor pseudogap in cuprate superconductors

Abstract We investigate the precursor pseudogap (PP) state that emerges on the lower temperature side of the pseudogap phase in cuprate superconductors based on the characteristic layer structure. The coherence among layers in the electronic state may be broken by low energy thermal interactions, whereas the coherence within the layers remains in the phase above the superconducting (SC) phase on account of strongness of the bonding. In this state, the two-electron energy gain (TEG) is also larger than that of SC state and the one-electron energy gain (OEG) is smaller than that of the SC state. We call this incoherent ensemble of in-layer states the in-layer electronic state system (IESS). The PP state is a crossover state between IESS and the normal pseudogap (NP) state, which appears on the upper temperature side, because the d-wave pairing symmetry in cuprates inverts the sign of the difference of the total electronic energy gain between the IESS and the NP state around the nodal region, even though it is positive overall. We perform our analysis at the mean field level. We show that the relationships among the SC gap, the gap of in-layer state, and the transition temperatures in the relevant phases are compatible with existing experimental data. The proposed precursor state requires pairing models to make the SC interactions three-dimensional beyond a single layer, although the precursors have in-layer properties.

D-Density Wave Scenario Description of the New Hidden Charge Order in Cuprates

In this paper, we show that the theory of high $T_c$ superconductivity based on a microscopic model with $d$-density wave (DDW) scenario in the pseudogap phase is able to reproduce some of the most important features of the recent experimentally discovered hidden charge order in several families of Cuprates. In particular, by computing and comparing energies of charge orders of different modulation directions derived from a full microscopic theory with $d$-density wave scenario, the axial charge order $\phi_{X(Y)}$ with wavevector $\mathbf{Q}=(Q_0,0)((0,Q_0))$ is shown to be unambiguously energetically more favorable over the diagonal charge order $\phi_{X\pm Y}$ with wavevector $\mathbf{Q}=(Q_0,\pm Q_0)$ at least in commensurate limit, to be expected also to hold even to more general incommensurate case, in agreement with experiment. The two types of axial charge order $\phi_X$ and $\phi_Y$ are degenerate by symmetry. We find that within the superconducting background, biaxial (checkerboard) charge order is energetically more favorable than uniaxial (stripe) charge order, and therefore checkerboard axial charge order should be the one observed in experiments, assuming a single domain of charge ordered state on each CuO$_2$ plane.

Superconducting and DDW states of high-Tccuprates with Rashba and Dresselhaus spin-orbit couplings

Abstractauthoren The effects of the spin–orbit couplings (SOC) including the Rashba and the Dresselhaus interactions are considered for the high cuprates with superconducting gap (DSC) and the pseudogap (d-density wave, DDW) phase. The sole Rashba or the Dresselhaus interaction is shown to have a stronger effect on the superconducting phase when compared to the mixed SOC. The temperature dependencies of the DSC and DDW parameters along with the specific heat of both the underdoped and the overdoped cuprates were considered.

Quasistatic magnetoelectric multipoles as order parameter for pseudogap phase in cuprate superconductors

We introduce a mechanism in which coupling between fluctuating spin magnetic dipole moments and polar optical phonons leads to a non-zero ferroic ordering of quasi-static magnetoelectric multipoles. Using first-principles calculations within the LSDA$+U$ method of density functional theory, we calculate the magnitude of the effect for the prototypical cuprate superconductor, HgBa$_2$CuO$_4$. We show that our proposed mechanism is consistent, to our knowledge, with all experimental data for the onset of the pseudo-gap phase and therefore propose the quasi-static magnetoelectric multipole as a possible pseudo-gap order parameter. Finally, we show that our mechanism embraces some key aspects of previous theoretical models, in particular the description of the pseudo-gap phase in terms of orbital currents.

Quantum oscillation as diagnostics of pseudogap state in underdoped cuprates

The Fermi surface in underdoped cuprates is reconstructed by the charge density wave (CDW) order in the pseudogap phase. Theoretical proposals can be divided into two classes: one assumes the underlying Fermi surface without CDW as a conventional large surface; the other assumes small hole-like Fermi pockets. In both scenarios, we theoretically study the quantum oscillation and find three evenly spaced peaks in the oscillation spectra. The central dominant peak is induced by the CDW order. Its effective mass is strongly enhanced as the CDW vanishes in agreement with experiments. But the two scenarios have different understandings of the subdominant satellite peaks. In the large-surface scenario they are induced by the interlayer tunneling between the bilayer CuO2 planes. Their effective masses are also enhanced with descreasing CDW. In the small-pocket scenario one of the subdominant peaks comes from the original small Fermi pockets of the pseudogap state. Its effective mass is nearly independent of the CDW strength and increases monotonically with the doping. We propose future quantum oscillation experiments to test these different predictions and thus to clarify the underlying Fermi surface structure of the pseudogap state.

Detection of a Cooper-pair density wave in Bi2Sr2CaCu2O8+x.

The quantum condensate of Cooper pairs forming a superconductor was originally conceived as being translationally invariant. In theory, however, pairs can exist with finite momentum Q, thus generating a state with a spatially modulated Cooper-pair density. Such a state has been created in ultracold (6)Li gas but never observed directly in any superconductor. It is now widely hypothesized that the pseudogap phase of the copper oxide superconductors contains such a 'pair density wave' state. Here we report the use of nanometre-resolution scanned Josephson tunnelling microscopy to image Cooper pair tunnelling from a d-wave superconducting microscope tip to the condensate of the superconductor Bi2Sr2CaCu2O8+x. We demonstrate condensate visualization capabilities directly by using the Cooper-pair density variations surrounding zinc impurity atoms and at the Bi2Sr2CaCu2O8+x crystal supermodulation. Then, by using Fourier analysis of scanned Josephson tunnelling images, we discover the direct signature of a Cooper-pair density modulation at wavevectors QP ≈ (0.25, 0)2π/a0 and (0, 0.25)2π/a0 in Bi2Sr2CaCu2O8+x. The amplitude of these modulations is about five per cent of the background condensate density and their form factor exhibits primarily s or s' symmetry. This phenomenology is consistent with Ginzburg-Landau theory when a charge density wave with d-symmetry form factor and wavevector QC = QP coexists with a d-symmetry superconductor; it is also predicted by several contemporary microscopic theories for the pseudogap phase.