Evidence for two competing order parameters in underdoped cuprates superconductors from a model analysis of the Fermi-arc effects

Preformed pairs above $T_c$ and the two-gap scenarios are two main proposals for describing the low doping pseudogap phase of high-$T_c$ cuprates. Very recent angle-resolved photoemission experiments have shown features which were interpreted as evidence for preformed pairs. Here it is shown that those results can be explained also in the context of the two-gap scenario if self-energy effects are considered. The discussion is based on the $d$-CDW theory or the flux phase of the $t-J$ model.Comment: 4 pages, 4 figures, accepted for publication in Phys. Rev. Let

Isotope effect on the superconducting critical temperature of cuprates in the presence of charge order

Using the large-$N$ limit of the $t$-$J$ model and allowing also for phonons and the electron-phonon interaction we study the isotope effect $\alpha$ for coupling constants appropriate for YBCO. We find that $\alpha$ has a minimum at optimal doping and increases strongly (slightly) towards the underdoped (overdoped) region. Using values for the electron phonon interaction from the local density approximation we get good agreement for $\alpha$ as a function of $T_c$ and doping $\delta$ with recent experimental data in YBCO. Our results strongly suggest that the large increase of $\alpha$ in the underdoped region is (a) caused by the shift of electronic spectral density from low to high energies associated with a competing phase (in our case a charge density wave) and the formation of a gap, and (b) compatible with the small electron phonon coupling constants obtained from the local density approximation. We propose a similar explanation for the anomalous behavior of $\alpha$ in Sr doped La$_2$CuO$_4$ near the doping 1/8.Comment: 14 pages, 6 figure

Self-energy effects in electronic Raman spectra of doped cuprates due to magnetic fluctuations

We present results for magnetic excitations in doped copper oxides using the random phase approximation and itinerant electrons. In the [1,0] direction the observed excitations resemble dispersive quasi-particles both in the normal and superconducting state similar as in recent resonant inelastic X-ray scattering (RIXS) experiments. In the [1,1] direction the excitations form, except for the critical region near the antiferromagnetic wave vector ${\bf Q}=(\pi,\pi)$, only very broad continua. Using the obtained spin propagators we calculate electron self-energies and their effects on electronic Raman spectra. We show that the recently observed additional peak at about twice the pair breaking in B$_{1g}$ symmetry below T$_c$ in HgBa$_2$CuO$_{4+\delta}$ can be explained as a self-energy effect where a broken Cooper pair and a magnetic excitation appear as final states. The absence of this peak in B$_{2g}$ symmetry, which probes mainly electrons near the nodal direction, is explained by their small self-energies compared to those in the antinodal direction.Comment: 5 pages, 5 figure

Two distinct quasiparticle inelastic scattering rates in the t−Jt-J model and their relevance for high-TcT_c cuprates superconductors

The recent findings about two distinct quasiparticle inelastic scattering rates in angle-dependent magnetoresistance (ADMR) experiments in overdoped high-$T_c$ cuprates superconductors have motivated many discussions related to the link between superconductivity, pseudogap, and transport properties in these materials. After computing dynamical self-energy corrections in the framework of the $t-J$ model the inelastic scattering rate was introduced as usual. Two distinct scattering rates were obtained showing the main features observed in ADMR experiments. Predictions for underdoped cuprates are discussed. The implicances of these two scattering rates on the resistivity were also studied as a function of doping and temperature and confronted with experimental measurements.Comment: 6 pages, 6 figure

dd-wave bond-order charge excitations in electron-doped cuprates

We study charge excitation spectra in the two-dimensional $t$-$J$ model on a square lattice to explore a charge-order tendency recently found in electron-doped cuprates around the carrier density 0.15. The static susceptibility of $d$-wave charge density, which corresponds to the nematic susceptibility at the momentum transfer ${\bf q}=(0,0)$, shows two characteristic peaks at momenta of the form ${\bf q}_{1}=(q',q')$ and ${\bf q}_{2}=(q,0)$. These two peaks originate from the so-called $2k_{F}$ scattering processes enhanced by the $d$-wave character of the bond-charge density. The peak at ${\bf q}_{1}$ is much broader, but develop to be very sharp in the vicinity of its instability, whereas the peak at ${\bf q}_{2}$ becomes sharper with decreasing temperature, but does not diverge. The equal-time correlation function, which is measured by resonant x-ray scattering, exhibits a momentum dependence similar to the static susceptibility. We also present energy-resolved charge excitation spectra. The spectra show a V-shaped structure around ${\bf q}=(0,0)$ and bend back toward close to zero energy due to the charge-order tendency at ${\bf q}_{1}$ and ${\bf q}_{2}$. The resulting spectra form gap-like features with a maximal gap at ${\bf q} \approx {\bf q}_{1}/2$ and ${\bf q}_{2}/2$. We discuss implications for the recent experiments in electron-doped cuprates.Comment: 6 pages, 4 figures, panel b of figure 1 corrected, added references, corrected typos, added a paragraph before summar

Self-energy effects in cuprates and the dome-shaped behavior of the superconducting critical temperature

Hole doped cuprates show a superconducting critical temperature $T_c$ which follows an universal dome-shaped behavior as function of doping. It is believed that the origin of superconductivity in cuprates is entangled with the physics of the pseudogap phase. An open discussion is whether the source of superconductivity is the same that causes the pseudogap properties. The $t$-$J$ model treated in large-N expansion shows $d$-wave superconductivity triggered by non-retarded interactions, and an instability of the paramagnetic state to a flux phase or $d$-wave charge density wave ($d$-CDW) state. In this paper we show that self-energy effects near $d$-CDW instability may lead to a dome-shaped behavior of $T_c$. In addition, it is also shown that these self-energy contributions may describe several properties observed in the pseudogap phase. In this picture, although fluctuations responsible for the pseudogap properties leads to a dome-shaped behavior, they are not involved in pairing which is mainly non-retarded.Comment: 11 pages, 7 figures, accepted for publication in Phys. Rev.

Doping and temperature dependence of the pseudogap and Fermi arcs in cuprates from dd-CDW short-range fluctuations in the context of the t-J model

At mean-field level the t-J model shows a phase diagram with close analogies to the phase diagram of hole doped cuprates. An order parameter associated with the flux or $d$ charge-density wave ($d$-CDW) phase competes and coexists with superconductivity at low doping showing characteristics identified with the observed pseudogap in underdoped cuprates. In addition, in the $d$-CDW state the Fermi surface is reconstructed toward pockets with low spectral weight in the outer part, resembling the arcs observed in angle-resolved photoemission spectroscopy experiments. However, the $d$-CDW requires broken translational symmetry, a fact that is not completely accepted. Including self-energy corrections beyond the mean, field we found that the self-energy can be written as two distinct contributions. One of these (called $\Sigma_{flux}$) dominates at low energy and originates from the scattering between carriers and $d$-CDW fluctuations in proximity to the $d$-CDW instability. The second contribution (called $\Sigma_{R\lambda}$) dominates at large energy and originates from the scattering between charge fluctuations under the constraint of non double occupancy. In this paper it is shown that $\Sigma_{flux}$ is responsible for the origin of low-energy features in the spectral function as a pseudogap and Fermi arcs. The obtained doping and temperature dependence of the pseudogap and Fermi arcs is similar to that observed in experiments. At low energy, $\Sigma_{R \lambda}$ gives an additional contribution to the closure of the pseudogap.Comment: 11 pages, 13 figure

Fermi arcs and isotope effect of the magnetic penetration depth in underdoped cuprates

The isotope coefficient $\beta$ of the magnetic penetration depth in the superconducting state is studied at T=0 for a $d$-CDW and a nodal metal model. Disregarding superconductivity the Fermi surface of the first model possesses arcs whereas the second model has no arcs. We show that a large increase of $\beta$ in the pseudogap region is generically incompatible with Fermi arcs in the pseudogap state. Thus only the second model shows a large increase of $\beta$ with decreasing doping. The required electron-phonon coupling is small and compatible with first-principles calculations based on the local density approximation (LDA).Comment: 5 pages, 3 figures, will appear as ep

Large isotope effect on TcT_c in cuprates despite of a small electron-phonon coupling

We calculate the isotope coefficients $\alpha$ and $\alpha^\ast$ for the superconducting critical temperature $T_c$ and the pseudogap temperature $T^\ast$ in a mean-field treatment of the t-J model including phonons. The pseudogap phase is identified with the $d$-charge-density wave ($d$-CDW) phase in this model. Using the small electron-phonon coupling constant $\lambda_d \sim 0.02$ obtained previously in LDA calculations in YBa$_2$Cu$_3$O$_7$, $\alpha^{\ast}$ is negative but negligible small whereas $\alpha$ increases from about 0.03 at optimal doping to values around 1 at small dopings in agreement with the general trend observed in many cuprates. Using a simple phase fluctuation model where the $d$-CDW has only short-range correlations it is shown that the large increase of $\alpha$ at low dopings is rather universal and does not depend on the existence of sharp peaks in the density of states in the pseudogap state or on specific values of the phonon cutoff. It rather is caused by the large depletion of spectral weight at low frequencies by the $d$-CDW and thus should also occur in other realizations of the pseudogap.Comment: 8 pages, 5 figures, to be publ. in PR