Pseudogap Phenomena Research Articles

Valence Bond Glass Theory of Electronic Disorder and the Pseudogap State of High-Temperature Cuprate Superconductors

We show that the low-energy fluctuations of the valence bond due to the superexchange are pinned by the electronic disorder from off-stoichiometric dopants, leading to a valence bond glass (VBG) pseudogap phase in underdoped high-T_{c} cuprates. The antinodal Fermi surface sections are gapped out, giving rise to a normal state Fermi arc whose length shrinks with underdoping. Below T_{c}, the superexchange interaction induces a d-wave superconducting gap that coexists with the VBG pseudogap. The evolution of the local and momentum-space spectroscopy with doping and temperature captures the salient properties of the pseudogap phenomena and the electronic disorder.

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.

Fermi arc formation by chiral spin textures in high-temperature superconductors

In angle-resolved photoemission spectroscopy pseudogap phenomenon in high-temperature superconductors is observed as Fermi arcs, or truncated Fermi surface. Here I argue that the hole induced chiral spin texture scenario naturally leads to Fermi arcs by including hole hopping processes. Disappearance of part of the Fermi surface is associated with the effect of the coherence factor. Suppressed spectral weight of the holes turns out to be an electron-like component which has weight near ( π , 0 ) only and has some charge instability.

Contrasting spin dynamics in Zn- and Ni-dopedNdBa2Cu3O6+ysingle crystals from Cu nuclear quadrupole resonance: Evidence for correlations between antiferromagnetism and pseudogap effects

We report $^{63,65}\mathrm{Cu}$ nuclear quadrupole resonance (NQR) measurements on slightly underdoped $\mathrm{Nd}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6+y}$ heavily doped by Ni and Zn impurities. Owing to the impurity doping, superconductivity is fully suppressed in both cases. The Ni strongly enhances magnetic correlations and induces a wipeout of the NQR signal comparable to that found in stripe ordered lanthanum cuprates. In contrast, the magnetism is suppressed in the Zn doped sample where no wipeout effect is observed and the nuclear spin relaxation rate is reduced. Our findings are in a striking correspondence with the different impact of Ni and Zn impurities on the charge pseudogap evidenced by recent optical data, uncovering thereby a close relationship between the magnetic correlations and pseudogap phenomena.

Fluctuating superconductivity in organic molecular metals close to the Mott transition

On cooling through the transition temperature T(c) of a conventional superconductor, an energy gap develops as the normal-state charge carriers form Cooper pairs; these pairs form a phase-coherent condensate that exhibits the well-known signatures of superconductivity: zero resistivity and the expulsion of magnetic flux (the Meissner effect). However, in many unconventional superconductors, the formation of the energy gap is not coincident with the formation of the phase-coherent superfluid. Instead, at temperatures above the critical temperature a range of unusual properties, collectively known as 'pseudogap phenomena', are observed. Here we argue that a key pseudogap phenomenon-fluctuating superconductivity occurring substantially above the transition temperature-could be induced by the proximity of a Mott-insulating state. The Mott-insulating state in the kappa-(BEDT-TTF)2X organic molecular metals can be tuned, without doping, through superconductivity into a normal metallic state as a function of the parameter t/U, where t is the tight-binding transfer integral characterizing the metallic bandwidth and U is the on-site Coulomb repulsion. By exploiting a particularly sensitive probe of superconducting fluctuations, the vortex-Nernst effect, we find that a fluctuating regime develops as t/U decreases and the role of Coulomb correlations increases.

Nature of the superconductor–insulator transition in disordered superconductors

The interplay of superconductivity and disorder has intrigued scientists for several decades. Disorder is expected to enhance the electrical resistance of a system, whereas superconductivity is associated with a zero-resistance state. Although superconductivity has been predicted to persist even in the presence of disorder, experiments performed on thin films have demonstrated a transition from a superconducting to an insulating state with increasing disorder or magnetic field. The nature of this transition is still under debate, and the subject has become even more relevant with the realization that high-transition-temperature (high-T(c)) superconductors are intrinsically disordered. Here we present numerical simulations of the superconductor-insulator transition in two-dimensional disordered superconductors, starting from a microscopic description that includes thermal phase fluctuations. We demonstrate explicitly that disorder leads to the formation of islands where the superconducting order is high. For weak disorder, or high electron density, increasing the magnetic field results in the eventual vanishing of the amplitude of the superconducting order parameter, thereby forming an insulating state. On the other hand, at lower electron densities or higher disorder, increasing the magnetic field suppresses the correlations between the phases of the superconducting order parameter in different islands, giving rise to a different type of superconductor-insulator transition. One of the important predictions of this work is that in the regime of high disorder, there are still superconducting islands in the sample, even on the insulating side of the transition. This result, which is consistent with experiments, explains the recently observed huge magneto-resistance peak in disordered thin films and may be relevant to the observation of 'the pseudogap phenomenon' in underdoped high-T(c) superconductors.

Effects of competing orders and quantum phase fluctuations on the low-energy excitations and pseudogap phenomena of cuprate superconductors

We investigate the low-energy quasiparticle excitation spectra of cuprate superconductors by incorporating both superconductivity (SC) and competing orders (CO) in the bare Green’s function and quantum phase fluctuations in the proper self-energy. Our approach provides consistent explanations for various empirical observations, including the excess subgap quasiparticle density of states, “dichotomy” in the momentum-dependent quasiparticle coherence and the temperature-dependent gap evolution, and the presence (absence) of the low-energy pseudogap in hole- (electron-) type cuprates depending on the relative scale of the CO and SC energy gaps.

LOWERING OF BOSON-FERMION SYSTEM ENERGY WITH A GAPPED COOPER RESONANT-PAIR DISPERSION RELATION

Applying two-time Green-function techniques to the Friedberg-T.D. Lee phenomenological Hamiltonian of a many-fermion system, it is shown that positive-energy resonant bosonic pairs associated with four-fermion excitations above the Fermi sea are energetically lower in a ground-state that is a mixture of two coexisting and dynamically interacting many-particle subsystems: a) unpaired fermions and b) composite bosons. It is argued that an interaction between free fermions and bosons excited above the Fermi sea in the mixture, namely, the continuous processes of pair-formation from, and disintegration into, two unpaired electrons, results in a substantially lowering the total system energy. The positive-energy composite bosons begin to appear incoherently below a depairing temperature T* as their coupling- and temperature-dependent number density gradually increases from zero. This leads quite naturally to the pseudogap phenomenon observed in high-Tccuprates.

Destruction of the Fermi surface due to pseudogap fluctuations in correlated systems

Pseudogap phenomena in strongly correlated systems have essential spatial length scale dependence [M.V. Sadovskii, Physics – Uspekhi 44 (2001) 515]. To merge pseudogap physics and strong electron correlations we generalize the dynamical-mean field theory (DMFT) [A. Georges, G. Kotliar, W. Krauth, M.J. Rozenberg, Rev. Mod. Phys. 68 (1996) 13]. Dependence on correlation length of pseudogap fluctuations via additional (momentum dependent) self-energy Σ k is included into conventional DMFT equations. The self-energy Σ k describes non-local dynamical correlations induced either by short-ranged collective SDW-like antiferromagnetic spin or CDW-like charge fluctuations [J. Schmalian, D. Pines, B. Stojkovic, Phys. Rev. B 60 (1999) 667; E.Z. Kuchinskii, M.V. Sadovskii, JETP 88 (1999) 347]. Weakly doped one-band Hubbard model with repulsive Coulomb interaction on a square lattice with nearest and next nearest neighbour hopping is numerically investigated within this generalized DMFT + Σ k approach [E.Z. Kuchinskii, I.A. Nekrasov, M.V. Sadovskii, JETP Lett. 82 (2005) 198; M.V. Sadovskii, I.A. Nekrasov, E.Z. Kuchinskii, Th. Prushke, V.I. Anisimov, Phys. Rev. B 72 (2005) 155105]. Both types of strongly correlated metals, namely (i) doped Mott insulator and (ii) the case of bandwidth W < U ( U – value of local Coulomb interaction) were considered. Energy dispersions, quasiparticle damping, spectral functions and ARPES spectra calculated within DMFT + Σ k, all show a pseudogap effects close to the Fermi level of quasiparticle band. Finally we demonstrate the qualitative picture of quasiparticle band dispersion, Fermi surface “destruction” and “Fermi arcs” formation due to pseudogap fluctuations, which agrees well with observations by ARPES.

Pseudogap in normal underdoped phase of Bi2212: LDA + DMFT + Σk

Pseudogap phenomena are observed for normal underdoped phase of different high- T c cuprates. Among others Bi 2Sr 2CaCu 2O 8− δ (Bi2212) compound is one of the most studied experimentally [A. Damascelli, Z. Hussain, Z.-X. Shen, Rev. Mod. Phys. 75 (2003) 473; J.C. Campuzano, M.R. Norman, M. Randeria, in: K.H. Bennemann, J.B. Ketterson (Eds.), Physics of Superconductors, vol. 2, Springer, Berlin, 2004, p. 167; J. Fink et al., cond-mat/0512307; X.J. Zhou et al., cond-mat/0604284]. To describe pseudogap regime in Bi2212, we employ novel generalized DMFT + Σ k approach [E.Z. Kuchinskii, I.A. Nekrasov, M.V. Sadovskii, JETP Lett. 82 (2005) 198; M.V. Sadovskii et al., Phys. Rev. B 72 (2005) 155105, and these proceedings, doi:10.1016/j.physc.2007.03.367]. This approach gives possibility to preserve conventional dynamical mean-field theory (DMFT) equations [A. Georges et al., Rev. Mod. Phys. 68 (1996) 13] and include an additional (momentum dependent) self-energy Σ k . In the present case, Σ k describes non-local dynamical correlations induced by short-ranged collective Heisenberg-like antiferromagnetic spin fluctuations [M.V. Sadovskii, Physics-Uspekhi 44 (2001) 515, cond-mat/0408489]. The effective single impurity problem in the DMFT + Σ k is solved by numerical renormalization group (NRG) [R. Bulla, A.C. Hewson, Th. Pruschke, J. Phys. Cond. Mat. 10 (1998) 8365; R. Bulla, Phys. Rev. Lett. 83 (1999) 136]. To take into account material specific properties of two neighboring CuO 2 layers of Bi2212 we employ local density approximation (LDA) to calculate necessary model parameters, e.g. the values of intra- and interlayer hopping integrals between Cu-sites. Onsite Coulomb interaction U for x 2– y 2 orbital was calculated in constrained LDA method [O. Gunnarsson et al., Phys. Rev. B 39 (1989) 1708]. The value of pseudogap potential Δ was obtained within DMFT(NRG) [E.Z. Kuchinskii, I.A. Nekrasov, M.V. Sadovskii, JETP Lett. 82 (2005) 198; M.V. Sadovskii et al., Phys. Rev. B 72 (2005) 155105, and these proceedings, doi:10.1016/j.physc.2007.03.367]. Here, we report theoretical LDA + DMFT + Σ k quasiparticle bands dispersion, Fermi surface (FS) and angular resolved photoemission (ARPES) spectra accounting for pseudogap and bilayer splitting effects for normal underdoped Bi2212 ( δ = 0.15). We show that LDA-calculated value of bilayer splitting (BS) is too small to describe experimentally observed peak-dip-hump structure. Fermi surface in presence of the pseudogap fluctuations is almost insensitive to the BS value. Results obtained are in good agreement with recent ARPES experiments.

Theory of the Luttinger surface in doped Mott insulators

We prove that the Mott insulating state is characterized by a divergence of the electron self energy at well-defined values of momenta in the first Brillouin zone. When particle-hole symmetry is present, the divergence obtains at the momenta of the Fermi surface for the corresponding non-interacting system. Such a divergence gives rise to a surface of zeros (the Luttinger surface) of the single-particle Green function and offers a single unifying principle of Mottness from which pseudogap phenomena, spectral weight transfer, and broad spectral features emerge in doped Mott insulators. We also show that only when particle-hole symmetry is present does the volume of the zero surface equal the particle density. We identify that the general breakdown of Luttinger's theorem in a Mott insulator arises from the breakdown of a perturbative expansion for the self energy in the single-particle Green function around the non-interacting limit. A modified version of Luttinger's theorem is derived for special cases.

Spin correlations in the electron-doped high-transition-temperature superconductor Nd2-xCexCuO4±δ

High-transition-temperature (high-T(c)) superconductivity develops near antiferromagnetic phases, and it is possible that magnetic excitations contribute to the superconducting pairing mechanism. To assess the role of antiferromagnetism, it is essential to understand the doping and temperature dependence of the two-dimensional antiferromagnetic spin correlations. The phase diagram is asymmetric with respect to electron and hole doping, and for the comparatively less-studied electron-doped materials, the antiferromagnetic phase extends much further with doping and appears to overlap with the superconducting phase. The archetypal electron-doped compound Nd2-xCexCuO4+/-delta (NCCO) shows bulk superconductivity above x approximately 0.13 (refs 3, 4), while evidence for antiferromagnetic order has been found up to x approximately 0.17 (refs 2, 5, 6). Here we report inelastic magnetic neutron-scattering measurements that point to the distinct possibility that genuine long-range antiferromagnetism and superconductivity do not coexist. The data reveal a magnetic quantum critical point where superconductivity first appears, consistent with an exotic quantum phase transition between the two phases. We also demonstrate that the pseudogap phenomenon in the electron-doped materials, which is associated with pronounced charge anomalies, arises from a build-up of spin correlations, in agreement with recent theoretical proposals.

Superconducting Fluctuation and Pseudogap in Disordered Short Coherence Length Superconductor

We investigate the role of disorder on the superconducting (SC) fluctuation in short coherence length d-wave superconductors. The particular intetest is focused on the disorder-induced microscopic inhomogeneity of SC fluctuation and its effect on the pseudogap phenomena. We formulate the self-consistent 1-loop order theory for the SC fluctuation in inhomogeneous systems and analyze the disordered $t$-$t'$-$V$ model. The SC correlation function, electronic DOS and the critical temperature are estimated. The SC fluctuation is localized like a nanoscale granular structure when the coherence length is short, namely the transition temperature is high. This is contrasted to the long coherence length superconductors where the order parameter is almost uniform in the microscopic scale. In the former case, the SC fluctuation is enhanced by the disorder in contrast to the Abrikosov-Gorkov theory. These results are consistent with the STM, NMR and transport measurements in high-$T_{\rm c}$ cuprates and illuminate the essential role of the microscopic inhomogeneity. We calculate the spacial dependence of DOS around the single impurity and discuss the consistency with the NMR measurements.

Pseudogap behavior in Bi2Ca2SrCu2O8: Results of the generalized dynamical mean-field approach

Pseudogap phenomena are observed for the normal underdoped phase of different high-T c cuprates. Among others, the Bi2Sr2CaCu2O8 − δ (Bi2212) compound is one of the most studied experimentally. To describe the pseudogap regime in Bi2212, we use a novel generalized ab initio LDA + DMFT + Σk hybrid scheme. This scheme is based on the strategy of one of the most powerful computational tools for real correlated materials: the local density approximation (LDA) + dynamical mean-field theory (DMFT). Conventional LDA + DMFT equations are here supplied with an additional (momentum-dependent) self-energy Σk in the spirit of our recently proposed DMFT + Σk approach taking into account pseudogap fluctuations. In the present model, Σk describes nonlocal correlations induced by short-range collective Heisenberg-like antiferromagnetic spin fluctuations. The effective single-impurity problem of the DMFT is solved by the numerical renormalization group (NRG) method. Material-specific model parameters for the effective x 2 − y 2 orbital of Cu-3d shell of the Bi2212 compound, e.g., the values of intra-and interlayer hopping integrals between different Cu sites, the local Coulomb interaction U, and the pseudogap potential Δ were obtained within the LDA and LDA + DMFT schemes. Here, we report on the theoretical LDA + DMFT + Σk quasiparticle band dispersion and damping, Fermi surface renormalization, momentum anisotropy of (quasi)static scattering, densities of states, spectral densities, and angular-resolved photoemission (ARPES) spectra, taking into account pseudogap and bilayer splitting effects for normal (slightly) underdoped Bi2212 (δ = 0.15). We show that LDA + DMFT + Σk successfully describes strong (pseudogap) scattering close to Brillouin zone boundaries. Our calculated LDA + DMFT + Σk Fermi surfaces and ARPES spectra in the presence of pseudogap fluctuations are almost insensitive to the bilayer splitting strength. However, our LDA-calculated value of bilayer splitting is rather small to describe the experimentally observed peak-dip-hump structure. The results obtained are in good semiquantitative agreement with various recent ARPES experiments.

The short-range correlations of a doped Mott insulator

This paper presents numerical studies of the single hole tt't''J model that address the interplay between the kinetic energy of itinerant electrons and the exchange energy of local moments as of interest to doped Mott insulators. Due to this interplay, two different spin correlations coexist around a mobile vacancy. These local correlations provide an effective two-band picture that explains the two-band structure observed in various theoretical and experimental studies, the doping dependence of the momentum space anisotropic pseudogap phenomena and the asymmetry between hole and electron doped cuprates.

Mottness

We review several of the normal state properties of the cuprates in an attempt to establish an organizing principle from which pseudogap phenomena, broad spectral features, T-linear resistivity, and spectral weight transfer emerge. We first show that standard field theories with a single critical length scale cannot capture the T-linear resistivity as long as the charge carriers are critical. What seems to be missing is an additional length scale, which may or may not be critical. Second, we prove a generalised version of Luttinger’s theorem for a Mott insulator. In particular, we show that for Mott insulators, regardless of the spatial dimension, the Fermi surface of the non-interacting system is converted into a surface of zeros of the single-particle Green function when the underlying band structure has particle-hole symmetry. Only in the presence of particle-hole symmetry does the volume of the surface of zeros equal the particle density. The surface of zeros persists at finite doping and is shown to provide a framework from which pseudogaps, broad spectral features, spectral weight transfer on the Mott gap scale, and the additional length scale required to capture T-linear resistivity can be understood.

Pseudogap induced by short-range spin correlations in a doped Mott insulator

We study the evolution of a Mott-Hubbard insulator into a correlated metal upon doping in the two-dimensional Hubbard model using the cellular dynamical mean-field theory. Short-range spin correlations create two additional bands apart from the familiar Hubbard bands in the spectral function. Even a tiny doping into this insulator causes a jump of the Fermi energy to one of these additional bands and an immediate momentum-dependent suppression of the spectral weight at this Fermi energy. The pseudogap is closely tied to the existence of these bands. This suggests a strong-coupling mechanism that arises from short-range spin correlations and large scattering rates for the pseudogap phenomenon seen in several cuprates.

Pseudogap and high-temperature superconductivity from weak to strong coupling. Towards a quantitative theory (Review Article)

This is a short review of the theoretical work on the two-dimensional Hubbard model performed in Sherbrooke in the last few years. It is written on the occasion of the twentieth anniversary of the discovery of high-temperature superconductivity. We discuss several approaches, how they were benchmarked and how they agree sufficiently with each other that we can trust that the results are accurate solutions of the Hubbard model. Then comparisons are made with experiment. We show that the Hubbard model does exhibit d-wave superconductivity and antiferromagnetism essentially where they are observed for both hole- and electron-doped cuprates. We also show that the pseudogap phenomenon comes out of these calculations. In the case of electron-doped high temperature superconductors, comparisons with angle-resolved photoemission experiments are nearly quantitative. The value of the pseudogap temperature observed for these compounds in recent photoemission experiments had been predicted by theory before it was observed experimentally. Additional experimental confirmation would be useful. The theoretical methods that are surveyed include mostly the two-particle self-consistent approach, variational cluster perturbation theory (or variational cluster approximation), and cellular dynamical mean-field theory.

Pseudogap phenomenon and superconductivity in a magnetic field

We study the effect of a magnetic field on the d-density wave (DDW) in the presence of d x 2 - y 2 superconducting order parameter (DSC) for high-temperature cuprates using a mean-field calculation of the tight binding model. The phase diagrams for the order parameter with doping are discussed. The phase diagram of the field with filling and also the dependence of the critical field ( H c ) on the critical temperature ( T c ) have been considered. The temperature dependence of the specific heat is also demonstrated. The effect of the field on the DDW order parameter and the superconducting gap are not alike. While the field suppresses the DSC gap, it tends to increase the DDW gap at the same doping. Moreover the gap to T c ratio increases with the field. The critical field has a power law dependence ( H c – T c 2 ).

Doping a Mott insulator: Physics of high-temperature superconductivity

This article reviews the physics of high-temperature superconductors from the point of view of the doping of a Mott insulator. The basic electronic structure of cuprates is reviewed, emphasizing the physics of strong correlation and establishing the model of a doped Mott insulator as a starting point. A variety of experiments are discussed, focusing on the region of the phase diagram close to the Mott insulator (the underdoped region) where the behavior is most anomalous. The normal state in this region exhibits pseudogap phenomenon. In contrast, the quasiparticles in the superconducting state are well defined and behave according to theory. This review introduces Anderson's idea of the resonating valence bond and argues that it gives a qualitative account of the data. The importance of phase fluctuations is discussed, leading to a theory of the transition temperature, which is driven by phase fluctuations and the thermal excitation of quasiparticles. However, an argument is made that phase fluctuations can only explain pseudogap phenomenology over a limited temperature range, and some additional physics is needed to explain the onset of singlet formation at very high temperatures. A description of the numerical method of the projected wave function is presented, which turns out to be a very useful technique for implementing the strong correlation constraint and leads to a number of predictions which are in agreement with experiments. The remainder of the paper deals with an analytic treatment of the $t\text{\ensuremath{-}}J$ model, with the goal of putting the resonating valence bond idea on a more formal footing. The slave boson is introduced to enforce the constraint againt double occupation and it is shown that the implementation of this local constraint leads naturally to gauge theories. This review follows the historical order by first examining the U(1) formulation of the gauge theory. Some inadequacies of this formulation for underdoping are discussed, leading to the SU(2) formulation. Here follows a rather thorough discussion of the role of gauge theory in describing the spin-liquid phase of the undoped Mott insulator. The difference between the high-energy gauge group in the formulation of the problem versus the low-energy gauge group, which is an emergent phenomenon, is emphasized. Several possible routes to deconfinement based on different emergent gauge groups are discussed, which leads to the physics of fractionalization and spin-charge separation. Next the extension of the SU(2) formulation to nonzero doping is described with a focus on a part of the mean-field phase diagram called the staggered flux liquid phase. It will be shown that inclusion of the gauge fluctuation provides a reasonable description of the pseudogap phase. It is emphasized that $d$-wave superconductivity can be considered as evolving from a stable U(1) spin liquid. These ideas are applied to the high-${T}_{c}$ cuprates, and their implications for the vortex structure and the phase diagram are discussed. A possible test of the topological structure of the pseudogap phase is described.