Pseudogap Phase In Underdoped Cuprates Research Articles

Anomalous softening of phonon dispersion in cuprate superconductors

A softening of phonon-dispersion has been observed experimentally in under-doped cuprate superconductors at the charge-density wave (CDW) ordering wave vector. Interestingly, the softening occurs below the superconducting (SC) transition temperature T$_{c}$, in contrast to the metallic systems, where the softening occurs usually below the CDW onset temperature T$_{\text{CDW}}$. An understanding of the `anomalous' nature of the phonon-softening and its connection to the pseudo-gap phase in under-doped cuprates remain open questions. Within a perturbative approach, we show that a complex interplay among the ubiquitous CDW, SC orders and life-time of quasi-particles associated to thermal fluctuations, can explain the anomalous phonon-softening below T$_{c}$. Furthermore, our formalism captures different characteristics of the low temperature phonon-softening depending on material specificity.

Fluctuations and the Higgs Mechanism in Underdoped Cuprates

The physics of the pseudogap phase of high-temperature cuprate superconductors has been an enduring mystery over the past 30 years. The ubiquitous presence of the pseudogap phase in underdoped cuprates suggests that understanding it is key to unraveling the origin of high-temperature superconductivity. We review various theoretical approaches to this problem, emphasizing the concept of emergent symmetries in the underdoped region of those compounds. We differentiate these theories by considering a few fundamental questions related to the rich phenomenology of these materials. Lastly, we discuss a recent idea regarding two kinds of entangled preformed pairs that open a gap at the pseudogap onset temperature, T*, through a specific Higgs mechanism. We review the experimental consequences of this line of thought.

Bond particle theory for the pseudogap phase of underdoped cuprates

We present a theory for the lightly doped t-J model which is of possible relevance for the normal state of underdoped cuprates. Starting from an arbitrary dimer covering of the plane an exact representation of the t-J Hamiltonian in terms of bond bosons and fermions can be derived. Since all dimer coverings must give identical results for observable quantities we construct an approximate but translationally invariant Hamiltonian by averaging the bond particle Hamiltonian over all possible dimer coverings. Treating the resulting Hamiltonian in mean-field approximation we find fermi pockets centered near (pi/2,pi/2) with a total area of x/2 (with x the hole concentration) and a gapped spin-wave-like band of triplet excitations.

Pseudo-spin skyrmions in the phase diagram of cuprate superconductors

Topological states of matter are at the root of some of the most fascinating phenomena in condensed matter physics. Here we argue that skyrmions in the pseudo-spin space related to an emerging SU(2) symmetry enlighten many mysterious properties of the pseudogap phase in under-doped cuprates. We detail the role of the SU(2) symmetry in controlling the phase diagram of the cuprates, in particular how a cascade of phase transitions explains the arising of the pseudogap, superconducting and charge modulation phases seen at low temperature. We specify the structure of the charge modulations inside the vortex core below Tc, as well as in a wide temperature region above Tc, which is a signature of the skyrmion topological structure. We argue that the underlying SU(2) symmetry is the main structure controlling the emergent complexity of excitations at the pseudogap scale T*. The theory yields a gapping of a large part of the anti-nodal region of the Brillouin zone, along with q = 0 phase transitions, of both nematic and loop currents characters.

Magnetism and Superconductivity in the Pseudogap Phase of Underdoped Cuprates

The theoretical description of the anomalous properties of the pseudogap phase in the underdoped region of the cuprate phase diagram lags behind the progress in spectroscopic and other experiments. A phenomenological ansatz, based on analogies to the approach to Mott localization at weak coupling in lower dimensional systems, for the single particle propagator in the pseudogap phase has been proposed by Yang, Rice and Zhang. This ansatz has had success in describing a range of experiments, especially spectroscopies such as ARPES and aspects of STM results. Recently this approach has been extended to successfully interpret the magnetic excitations in the spin response response. In the charge channel, d-wave cooperon excitations accompany the opening of the pseudogap and they generate an additional d-wave attraction for quasiparticles at the remnant nodal Fermi surfaces.

Determination of boson spectrum from optical data in pseudogap phase of underdoped cuprates

Information on the nature of the dominant inelastic processes operative in correlated metallic systems can be obtained from an analysis of their AC optical response. An electron-boson spectral density can usefully be extracted. This density is closely related to the optical scattering rate. However, in the underdoped region of the high Tc cuprate phase diagram a new energy scale (the pseudogap) emerges, which alters the optical scattering and needs to be taken into account in any fit to data. This can influence the shape and strength of the recovered boson spectral function. Including a pseudogap in an extended maximum entropy inversion for optimally doped Bi-2212 is more consistent with existing data than when it is left out as done previously.

Modeling a striped pseudogap state

We study the electronic structure within a system of phase-decoupled one-dimensional superconductors coexisting with stripe spin and charge density wave order. This system has a nodal Fermi surface (Fermi arc) in the form of a hole pocket and an antinodal pseudogap. The spectral function in the antinodes is approximately particle-hole symmetric contrary to the gapped regions just outside the pocket. We find that states at the Fermi energy are extended whereas states near the pseudogap energy have localization lengths as short as the inter-stripe spacing. We consider pairing which has either local d-wave or s-wave symmetry and find similar results in both cases, consistent with the pseudogap being an effect of local pair correlations. We suggest that this state is a stripe ordered caricature of the pseudogap phase in underdoped cuprates with coexisting spin-, charge-, and pair-density wave correlations. Lastly, we also model a superconducting state which 1) evolves smoothly from the pseudogap state, 2) has a signature subgap peak in the density of states, and 3) has the coherent pair density concentrated to the nodal region.

Modeling the Fermi arc in underdoped cuprates

Angle resolved photoemission data in the pseudogap phase of underdoped cuprates have revealed the presence of a truncated Fermi surface consisting of Fermi arcs. We compare a number of proposed models for the arcs and find that the one that best models the data is a $d$-wave energy gap with a lifetime broadening whose temperature dependence is suggestive of fluctuating pairs.

Magnetic Order in the Pseudogap Phase of High-TCSuperconductors

One of the leading issues in high-$T_C$ superconductors is the origin of the pseudogap phase in underdoped cuprates. Using polarized elastic neutron diffraction, we identify a novel magnetic order in the YBa$_2$Cu$_3$O$_{6+x}$ system. The observed magnetic order preserves translational symmetry as proposed for orbital moments in the circulating current theory of the pseudogap state. To date, it is the first direct evidence of an hidden order parameter characterizing the pseudogap phase in high-$T_C$ cuprates.

QED3theory of underdoped high-temperature superconductors

The low-energy theory of d-wave quasiparticles coupled to fluctuating vortex loops that describes the loss of phase coherence in a two-dimensional d-wave superconductor at $T=0$ is derived from first principles. The theory has the form of (2+1) dimensional quantum electrodynamics $({\mathrm{QED}}_{3}),$ and is proposed as an effective description of the $T=0$ superconductor-insulator transition and of the pseudogap phase in underdoped cuprates. The coupling constant (``charge'') in this theory is proportional to the dual order parameter of the $\mathrm{XY}$ model, which is assumed to describe fluctuations of the phase of the superconducting order parameter. Finiteness of the charge is then tantamount to the appearance of infinitely large vortex loops, i.e., to the loss of phase coherence in the system. The principal result is that the destruction of the superconducting phase coherence in the d-wave superconductors typically, and immediately, leads to the appearance of antiferromagnetism. This transition can be understood in terms of the spontaneous breaking of an approximate ``chiral'' ${\mathrm{SU}}_{c}(2)$ symmetry, which may be discerned at low enough energies in the standard d-wave superconductor. The mechanism of this spontaneous symmetry breaking is formally analogous to the dynamical mass generation in ${\mathrm{QED}}_{3},$ with the ``mass'' here being proportional to staggered magnetization. Other phases with broken chiral symmetry include the translationally invariant $``d+ip''$ and $``d+is$'' insulators, and the one-dimensional charge-density and spin-density waves, which are all insulating descendants of the d-wave superconductor. All the insulating states have neutral spin-$1/2$ excitations that one can identify in the superconductor confined by the logarithmic potential. Electron repulsion is in this formalism represented by a particular quartic perturbation to the ${\mathrm{QED}}_{3}$ action, which breaks the chiral symmetry and selects the antiferromagnet as the preferred broken symmetry state. I formulate the mean-field theory of the antiferromagnetic instability in presence of a short-range repulsive interaction, and find the staggered magnetization to be significantly enhanced deeper inside the insulating state. The theory offers an explanation for the rounded d-wave-like dispersion seen in angle-resolved photoemission spectroscopy experiments on the insulating ${\mathrm{Ca}}_{2}{\mathrm{CuO}}_{2}{\mathrm{Cl}}_{2}$ [F. Ronning et al., Science 282, 2067 (1998)]. Relations to other theoretical approaches to the high-${T}_{c}$ problem are discussed.