Pseudogap In Underdoped Cuprates Research Articles

Locating the pseudogap closing point in cuprate superconductors: Absence of entrant or reentrant behavior

Current descriptions of the pseudogap in underdoped cuprates envision a doping-dependent transition line $T^*(p)$ which descends monotonically towards zero just beyond optimal doping. There is much debate as to the location of the terminal point $p^*$ where $T^*(p)$ vanishes, whether or not there is a phase transition at $T^*$ and exactly how $T^*(p)$ behaves below $T_c$ within the superconducting dome. One perspective sees $T^*(p)$ cutting the dome and continuing to descend monotonically to zero at $p_{crit} \approx 0.19$ holes/Cu $-$ referred to here as `entrant behavior'. Another perspective derived from photoemission studies is that $T^*(p)$ intersects the dome near $p_{crit} \approx 0.23$ holes/Cu then turns back below $T_c$, falling to zero again around $p_{crit} \approx 0.19$ $-$ referred to here as `reentrant behavior'. By examining thermodynamic data for Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ we show that neither entrant nor reentrant behavior is experimentally supported. Rather, $p_{crit} \approx 0.19$ sharply delimits the pseudogap regime and for $p < 0.19$ the pseudogap is always present, independent of temperature. Similar results are found for Y$_{0.8}$Ca$_{0.2}$Ba$_2$Cu$_3$O$_{7-\delta}$. For both materials $T^*(p)$ is not a temperature but a crossover scale, $\approx E^*(p)/2k_B$, reflecting instead the underlying pseudogap energy $E^*(p)$ which vanishes as $p \rightarrow 0.19$.

Giant phonon anomaly associated with superconducting fluctuations in the pseudogap phase of cuprates

The pseudogap in underdoped cuprates leads to significant changes in the electronic structure, and was later found to be accompanied by anomalous fluctuations of superconductivity and certain lattice phonons. Here we propose that the Fermi surface breakup due to the pseudogap, leads to a breakup of the pairing order into two weakly coupled sub-band amplitudes, and a concomitant low energy Leggett mode due to phase fluctuations between them. This increases the temperature range of superconducting fluctuations containing an overdamped Leggett mode. In this range inter-sub-band phonons show strong damping due to resonant scattering into an intermediate state with a pair of overdamped Leggett modes. In the ordered state, the Leggett mode develops a finite energy, changing the anomalous phonon damping into an anomaly in the dispersion. This proposal explains the intrinsic connection between the anomalous pseudogap phase, enhanced superconducting fluctuations and giant anomalies in the phonon spectra.

Pseudogap in cuprates in the loop-current ordered state

Scanning tunneling microscopy (STM) has revealed that the magnitude of the pseudo-gap in under-doped cuprates varies spatially and is correlated with disorder. The loop-current order, characterized by the anapole vector Ω, discovered in under-doped cuprates occurs in the same region of the temperature and doping as the pseudo gap observed in STM and ARPES experiments. Since translational symmetry remains unchanged in the pure limit, no gap occurs at the chemical potential. On the other hand for disorder coupling linearly to the different possible orientations of Ω, there can only be a finite temperature dependent static correlation length for the loop-current state at any temperature. This leads to formation of domains of the ordered state with different orientation and magnitude of Ω in each. For the characteristic size of the domains much larger than the Fermi-vectors , the boundary of the domains leads to forward scattering of the Fermions. Such forward scattering is shown to push states near the chemical potential to energies both above and below it leading to a pseudo-gap with an angular dependence which is maximum in the directions because the single-particle energies are degenerate in these directions for all domains. The magnitude of the average gap systematically increases with the square of the average loop order parameter measured by polarized neutron scattering. This result is tested. A unique result of the gap due to forward scattering is the lack of a bump in the density of states at the ‘edge’ of the pseudo-gap so that the depletion of states near the chemical potential is recovered only in integration up to the edge of the band. This is also in agreement with a variety of experiments. Some predictions for further experiments are provided. Due to the finite correlation length, low frequency excitations are expected at long wavelength at all temperatures in the ‘ordered’ phase. Such fluctuations motionally average over the shifts in frequencies of local probes such as NMR and muon resonance expected for a truly static order.

What is the simplest model that captures the basic experimental facts of the physics of underdoped cuprates?

I discuss here some well established experimental facts which have been shown to be generic of the pseudogap in underdoped cuprates. Some recent developments on Cellular Dynamic Mean Field Theories of the doped Hubbard model on a square lattice are nowadays allowing one to compute physical properties and k resolved single particle spectra. At high temperatures, recent results present qualitative features which perfectly fit the experimental observations done for more than two decades on the pseudogap in the cuprates. Most various broken symmetry states detected recently at lower temperatures than the pseudogap T*, certainly require more complicated modelling, and are not necessarily generic. I suggest that various perturbations due to the order (or disorder) of chemical dopants, which can hardly be avoided in actual materials, might drive the pseudogap electronic matter into specific ground states which exhibit interesting correlated electronic orders.

Theory of Pseudogap in Underdoped Cuprates

Recent theoretical studies on the origin of the pseudogap emerging in underdoped cuprate superconductors are overviewed, based on insights obtained by a cluster extension of the dynamical mean field theory (cDMFT) for the doped two-dimensional (2D) Mott insulator. The pseudogap obtained in the cDMFT shows an s-wave-like full-gap structure, distinct from the d-wave superconducting gap. The zero-temperature electronic structure supports that a non-Fermi liquid phase exists and underlies the pseudogap. The non-Fermi liquid phase is separated from the larger-doped Fermi liquid by topological transitions of the Fermi surface and an emergence of zeros of Green's function. A coexisting evolution of the poles (Fermi surface) and zeros of the Green's function is a unique feature of the pseudogap phase. The spectra well reproduce the arc/pocket formation, together with basic experimental properties of the pseudogap phase in the cuprates. Furthermore, a full-gap structure is supported by a comparison with the results of Raman experiments. The overall feature supports the proximity of the Mott insulator and the significance of the quantum criticality of the Mott transition. These numerical results are further favorably interpreted by extending the exciton concept, known in semiconductors, to doped Mott insulators. In this composite fermion (CF) theory, the pseudogap emerges as a gap arising from a hybridization of the quasiparticle (QP) with the CF. The pairing channel opening between a QP and a CF solves the puzzle of the dichotomy between the d-wave superconductivity and the precursory insulating gap in the same antinodal region. A mechanism of superconductivity emerges from this pairing.

The Superconductivity of the Double Correlated Linear Aggregations of Holes in the Cuprates

Here I extend my last work about the origin of the pseudo-gaps in underdoped cuprates (arXiv: cond-mat. 1011.3206), to include the mechanism of superconductivity. This is done by adapting the formalism of the double correlations in systems with nested Fermi surfaces to the semi one dimensional system of strings of holes. It is proposed that magnetic interaction is crucial for the establishment of the pseudogap and the high temperature superconductivity. It is shown that superconductivity disturbs the completeness of the strings of holes, and creates fluctuations in their shapes. This, in turn, reduces the magnetic interaction and the pseudogap order.

Dynamically induced Fermi arcs and pockets: A model for the pseudogap in underdoped cuprates

We investigate the effects of the dynamic bosonic fluctuations on the Fermi surface reconstruction in two dimensions as a model for the pseudogap in underdoped cuprates. At energies larger than the boson energy ωb, the dynamic nature of the fluctuations is not important and the quasi-particle dispersion exhibits the shadow feature like that induced by a static long range order. At lower energies, however, the shadow feature is pushed away by the finite ωb. The detailed low energy features are determined by the bare dispersion and the coupling of quasi-particles to the dynamic fluctuations. We present how these factors truncate the Fermi surface to produce the Fermi arcs or the Fermi pockets, or their coexistence. Our principal result is that the dynamic nature of the fluctuations, without invoking a yet-to-be-established translational symmetry breaking hidden order, can produce the Fermi arc or Fermi pocket centered away from the (π/2, π/2) towards the zone center. This is discussed in comparison with the experimental observations.

Doping and temperature dependence of the pseudogap and Fermi arcs in cuprates fromd-CDW with short-range fluctuations in the context of thet-Jmodel

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.

Pseudogap in underdoped cuprates and spin-density-wave fluctuations

We analyze fermionic spectral function in the spin-density-wave (SDW) phase of quasi-2D cuprates at small but finite T. We use a non-perturbative approach and sum up infinite series of thermal self-energy terms, keeping at each order nearly-divergent (T/J) |log epsilon| terms, where epsilon is a deviation from a pure two-dimensionality, and neglecting regular T/J corrections. We show that, as SDW order decreases, the spectral function in the antinodal region acquires peak/hump structure: the coherent peak position scales with SDW order parameter, while the incoherent hump remains roughly at the same scale as at T=0 when SDW order is the strongest. We identify the hump with the pseudogap observed in ARPES and argue that the presence of coherent excitations at low energies gives rise to magneto-oscillations in an applied field. We show that the same peak/hump structure appears in the density of states and in optical conductivity.

Two Pseudogaps in Underdoped Cuprates

Cuprate superconductivity gaps are investigated applying the interband pairing scheme to the itinerant band and a defect "band" which is created by hole doping. A pseudogap is naturally present in this model at underdoping. Vibronic hybridization of bands renormalizes the pseudogap and two superconductivity gaps. Now two pseudogaps of electronic and vibronic origin are present in the underdoped normal state as recently observed. Entering the optimally doped region (overlapping bands) there appears a joint normal state pseudogap of vibronic origin.

Néel transition, spin fluctuations, and pseudogap in underdoped cuprates by a Lorentz invariant four-fermion model in 2+1 dimensions

We show that the N\'eel transition and spin fluctuations near the N\'eel transition in planar cuprates can be described by an SU(2) invariant relativistic four-fermion model in 2+1 dimensions. Features of the pseudogap phenomenon are naturally described by the appearance of an anomalous dimension for the spinon propagator.

Short-range spin correlations and pseudogap in underdoped cuprates

In this paper we show that local spin-singlet amplitude with d-wave symmetry can be induced by short-range spin correlations even in the absence of pairing interactions. In the present scenario for the pseudogap, the normal state pseudogap is caused by the induced local spin-singlet amplitude due to short-range spin correlations, which compete in the low energy sector with superconducting correlations to make T c go to zero near half-filling.

D x2− y2-wave pairing fluctuations and spin pseudogap in high- Tc cuprates

Pseudogap phenomena in high- T c cuprates are examined. The effective action for 2D electron systems with antiferromagnetic (AFM) and d x 2− y 2 -wave superconducting (dSC) fluctuations is considered. By the SCR (self-consistent renormalization), the spin and the pairing correlation lengths, ξ σ and ξ d, and 1/ T 1 T are calculated. The pseudogap (PG) emerges when dSC short-range order (SRO) dominates over AFM-SRO. When damping for the spin wave strongly depends on ξ d through the formation of precursor singlets around (π, 0) and (0, π) points, the spin PG in underdoped cuprates is reproduced. Otherwise, the PG region shrinks as in overdoped cuprates.

Study on the anomalies of thermoelectric power due to the normal-state pseudogap in underdoped cuprates

The thermoelectric power of underdoped Gd 1− x Pr x Ba 2Cu 3O 7− δ with different Pr contents is measured. The experiments indicate that a hump in the temperature dependence of TEP appears above T c. This is considered to be associated with the opening of the normal-state pseudogap. The present experimental results and those reported by Tallon et al . [J.L. Tallon et al., Phys. Rev. Lett. 75 (1995) 4114.] are analyzed based on the opening of the pseudogap. The pseudogap excitation energy E G is obtained. Furthermore, a phase diagram of E G versus hole concentration p is given. The analysis may provide an effective way to estimate E G.

Changes in irreversibility line, anisotropy, and condensation energy by oxygen depletion ofYBa2Cu3O7−δ

We report results of magnetization measurements on the same ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ crystal for a range of $\ensuremath{\delta}$ values $0.03&lt;~\ensuremath{\delta}&lt;~0.35,$ in magnetic fields up to 120 kOe, applied parallel or perpendicular to the ${\mathrm{CuO}}_{2}$ planes. Zero-field resistivity anisotropy measurements have also been made for the same values of $\ensuremath{\delta}.$ The irreversibility line ${H}_{\mathrm{irr}}$ falls by over a factor of 10 in the range of $\ensuremath{\delta}$ studied, and there is a similar strong decrease in superconducting condensation energy associated with the growth of the normal-state pseudogap in under-doped cuprates. On the other hand, the anisotropy in ${H}_{\mathrm{irr}}$ and the room-temperature resistivity anisotropy only increase by a factor of 2. Evidence that for our crystals the so-called ``vortex lattice melting line'' ${H}_{m}(T)\ensuremath{\approx}{H}_{\mathrm{irr}}(T)$ is presented. There is also a large field and temperature region where the reversible magnetization varies as ${H}^{\ensuremath{-}1/2}$ and its magnitude corresponds to a free-energy density of ${k}_{B}T$ in a certain field-dependent correlation volume. Many of the results are consistent with the presence of critical thermodynamic fluctuations described by the three-dimensional $\mathrm{XY}$ model; these are probably enhanced when the field along the c axis is greater than 10 kOe.

Pseudogaps in underdoped cuprates

It has become clear in the past several years that the cuprates show many unusual properties, both in the normal and superconducting (SC) states, especially in the underdoped region. In particular, gap-like behavior is observed in magnetic properties, c-axis conductivity and photoemission, whereas in-plane transport properties are only slightly affected by the pseudogap. I shall argue that these experimental evidences must be viewed in the context of the physics of a doped Mott insulator and that they support the notion of spin charge separation. I shall review recent theoretical developments, concentrating on studies based on the t– J model. I shall describe a model based on quasiparticle (qp) excitations, which predicts the doping dependence of T c and anomalous energy-gap-to- T c ratios. Finally, I shall outline how the model may be derived from a microscopic formulation of the t– J model. After a brief review of the U(1) formulation, I shall explain some of the difficulties encountered there, and how a new SU(2) formulation can resolve some of the difficulties.

Temperature variation of the pseudogap in underdoped cuprates

We consider thermal evolution of the spectral function A(Omega, T) in underdoped cuprates at T >Tc. We find that in the strong coupling limit, the fermionic Green's function near (0,\pi) behaves as G^{-1} (Omega) ~ \sqrt{Omega} in the whole frequency range relevant to photoemission experiments. The analysis of the pairing problem with this form of G yields a leading edge gap in A(\Omega) and a broad maximum at larger frequencies. We find that classical fluctuations predominantly add a frequency independent term to G^{-1} (Omega). This term destroys the leading edge gap at T =T* (k)$which has a maximum value of about 200K near (0,\pi).