Phase fluctuations and pseudogap phenomena

This article reviews the current status of precursor superconducting phase fluctuations as a possible mechanism for pseudogap formation in high-temperature superconductors. In particular we compare this approach which relies on the two-dimensional nature of the superconductivity to the often used T-matrix approach. Starting from simple pairing Hamiltonians we present a broad pedagogical introduction to the BCS–Bose crossover problem. The finite temperature extension of these models naturally leads to a discussion of the Berezinskii–Kosterlitz–Thouless superconducting transition and the related phase diagram including the effects of quantum phase fluctuations and impurities. We stress the differences between simple Bose–BCS crossover theories and the current approach where one can have a large pseudogap region even at high carrier density where the Fermi surface is well-defined. Green's function and its associated spectral function, which explicitly show non-Fermi liquid behavior, is constructed in the presence of vortices. Finally different mechanisms including quasi-particle–vortex and vortex–vortex interactions for the filling of the gap above T_c are considered.     

Evidence for a metallic–like state in the T=0 K phase diagram of a high temperature superconductor

We examine the effects of a phenomenological pseudogap on the T=0 K phase diagram of a high temperature superconductor within a self-consistent model which exhibits a d-wave pairing symmetry. At the mean-field level the presence of a pseudogap in the normal phase of the high temperature superconductor is proved to be essential for the existence of a metallic–like state in the density versus interaction phase diagram. In the small density limit, at high attractive interaction, bosonic–like degrees of freedom are likely to emerge. Our result should be relevant for underdoped high temperature superconductors, where there is a strong evidence for the presence of a pseudogap in the excitation spectrum of the normal state quasiparticles.     

The vortex-like excitations detected by Nernst signals in high-T c superconductors

The nature of the pseudogap state and its relation to the d-wave superconductivity in high-T _c superconductors is still an open issue. The vortex-like excitations detected by the Nernst effect measurements exist in a certain temperature range above superconducting transition temperature T _c, which strongly support that the pseudogap phase is characterized by finite pairing amplitude with strong phase fluctuations and imply that the phase transition at T _c is driven by the loss of long-range phase coherence. We first briefly introduce the electronic phase diagram and pseudogap state of high-T _c superconductors, and then review the results of Nernst effect for different high-T _c superconductors. Related theoretical models are also discussed.     

The vortex-like excitations detected by Nernst signals in high-Tc superconductors

The nature of the pseudogap state and its relation to the d-wave superconductivity in high-T _c superconductors is still an open issue. The vortex-like excitations detected by the Nernst effect measurements exist in a certain temperature range above superconducting transition temperature T _c, which strongly support that the pseudogap phase is characterized by finite pairing amplitude with strong phase fluctuations and imply that the phase transition at T _c is driven by the loss of long-range phase coherence. We first briefly introduce the electronic phase diagram and pseudogap state of high-T _c superconductors, and then review the results of Nernst effect for different high-T _c superconductors. Related theoretical models are also discussed.     

高温超导体中的赝隙与超导位相涨落

高温超导体赝隙态与超导态之间的关系一直是研究的焦点.交流电导和能斯特（Nernst）效应测量相继探测到超导转变温度Tc0以上温区一定范围内存在磁通涡旋激发,利用力矩技术的磁化率测量则探测到超导涨落引起的弱抗磁性.这些发现都支持了高温超导体赝隙相中存在有限的超导序参量振幅和强烈的位相涨落的图像,说明Tc0处的相变是由库珀对之间长程位相关联的消失所驱动的.文章首先简短地介绍高温超导体的电子态相图和赝隙态,以及能斯特效应的原理和测量方法,然后对能斯特效应的测量结果作一评述性介绍,还讨论了相关的理论模型.     

Tetracritical point and staggered vortex currents in superconducting state

A phase diagram reflecting the main features of the typical phase diagram of cuprate superconductors has been studied within the framework of the Ginzburg-Landau phenomenology in the vicinity of a tetracritical point, which appears as a result of the competition of the superconducting and insulating pairing channels. The superconducting pairing under repulsive interaction corresponds to a two-component order parameter, whose relative phase is related to the orbital antiferromagnetic insulating ordering. Under weak doping, the insulating order coexists with the superconductivity at temperatures below the superconducting phase transition temperature and is manifested as a weak pseudogap above this temperature. A part of the pseudogap region adjacent to the superconducting state corresponds to developed fluctuations of the order parameter in the form of quasi-stationary states of noncoherent superconducting pairs and can be interpreted as a strong pseudogap. As the doping level is increased, the system exhibits a phase transition from the region of coexistence of the superconductivity and the orbital antiferromagnetism to the usual superconducting state. In this state, a region of developed fluctuations of the order parameter in the form of quasi-stationary states of uncorrelated orbital circular currents exists near the phase transition line.     

Particle-hole mixing driven by the superconducting fluctuations

Development of the STM and ARPES spectroscopy enabled to reach the resolution sufficient for probing the particle-hole entanglement in superconducting materials, even above the critical temperature T_c. On a quantitative level one can characterize such entanglement in terms of the Bogoliubov angle which determines to what extent the particles and holes constitute the effective quasiparticles. In classical superconductors, where the phase transition is related to formation of the Cooper pairs almost simultaneously accompanied by onset of their long-range phase coherence, the Bogoliubov angle is slanted (due to finite particle-hole mixing) all the way up to T_c. In the high temperature superconductors and in superfluid ultracold fermion atoms near the Feshbach resonance the situation is different because the preformed pairs can exist above T_c albeit loosing coherence due to the strong quantum fluctuations. We discuss a generic temperature dependence of the Bogoliubov angle in such pseudogap state indicating a novel, non-BCS behavior. For analysis we use the two-component model describing the pairs coexisting with single fermions and study selfconsistently their feedback effects by the similarity transformation originating from the renormalization group approach.     

Temperature and doping dependent flat-band superconductivity on the Lieb-lattice

We consider the superconducting properties of Lieb lattice, which produces a flat-band energy spectrum in the normal state under the strong electron–electron correlation. Firstly, we show the hole-doping dependent superconducting order amplitude with various electron–electron interaction strengths in the zero-temperature limit. Secondly, we obtain the superfluid weight and Berezinskii–Kosterlitz–Thouless(BKT) transition temperature with a lightly doping level. The large ratio between the gap-opening temperature and BKT transition temperature shows similar behavior to the pseudogap state in high-T_c superconductors. The BKT transition temperature versus doping level exhibits a dome-like shape in resemblance to the superconducting dome observed in the high-T_c superconductors. However, unlike the exponential dependence of T_c on the electron–electron interaction strength in the conventional high-T_c superconductors, the BKT transition temperature for a flat band system depends linearly on the electron–electron interaction strength. We also show the doping-dependent superconductivity on a lattice with the staggered hoping parameter in the end. Our predictions are amenable to verification in the ultracold atoms experiment and promote the understanding of the anomalous behavior of the superfluid weight in the high-T_c superconductors.     

Common phase diagram for low-dimensional superconductors

A phenomenological phase diagram which has been derived for high-temperature superconductors from NMR Knight-shift measurements of the pseudogap is compared to the phase diagram that is obtained for organic superconductors and spin-ladder superconductors, both low-dimensional systems. This is contrasted to the phase diagram of some Heavy Fermion superconductors, i.e. superconductors not constrained to a low dimensionality.     

Interplay between superconductivity and pseudogap state in bilayer cuprate superconductors

The interplay between the superconducting gap and normal-state pseudogap in the bilayer cuprate superconductors is studied based on the kinetic energy driven superconducting mechanism. It is shown that the charge carrier interaction directly from the interlayer coherent hopping in the kinetic energy by exchanging spin excitations does not provide the contribution to the normal-state pseudogap in the particle–hole channel and superconducting gap in the particle–particle channel, while only the charge carrier interaction directly from the intralayer hopping in the kinetic energy by exchanging spin excitations induces the normal-state pseudogap in the particle–hole channel and superconducting gap in the particle–particle channel, and then the two-gap behavior is a universal feature for the single layer and bilayer cuprate superconductors.     

铜氧化物超导体两能隙问题的电子拉曼散射理论研究

电子拉曼实验表明在空穴型掺杂的铜氧化物超导体中存在两能隙行为,即在欠掺杂区,随着掺杂浓度的降低,一个能隙逐渐增大而且在超导转变温度以上仍然存在,而另一个能隙逐渐减小且在DDW态依然存在.解释两能隙行为非常重要因为它与赝能隙的机理密切相关.本文计算了超导序和d-density-wave(DDW)序竞争机理下相图上不同区域的电子拉曼谱,发现欠掺杂区能隙表现出两能隙行为,与实验一致.特别地,本文发现B_1g峰对应能量由超导和DDW序共同决定,且随着掺杂浓度的降低而增大,在D 关键词： 两能隙 电子拉曼散射 竞争序     

Hot spots and pseudogaps for hole- and electron-doped high-temperature superconductors

Using cluster perturbation theory, it is shown that the spectral weight and pseudogap observed at the Fermi energy in recent angle resolved photoemission spectroscopy of both electron- and hole-doped high-temperature superconductors find their natural explanation within the t-t(')-t(")-U Hubbard model in two dimensions. The value of the interaction U needed to explain the experiments for electron-doped systems at optimal doping is in the weak to intermediate coupling regime where the t-J model is inappropriate. At strong coupling, short-range correlations suffice to create a pseudogap, but at weak-coupling long correlation lengths associated with the antiferromagnetic wave vector are necessary.     

Magnetic order in the pseudogap phase of high-Tc superconductors

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 YB(2)Cu(3)O(6+) system. The observed magnetic order preserves translational symmetry of the lattice as proposed for orbital moments in the circulating current theory of the pseudogap state. To date, it is the first direct evidence of a hidden order parameter characterizing the pseudogap phase in high-T(c) cuprates.     

Charge order driven by Fermi-arc instability and its connection with pseudogap in cuprate superconductors

The recently discovered charge order is a generic feature of cuprate superconductors, however, its microscopic origin remains debated. Within the framework of the fermion-spin theory, the nature of charge order in the pseudogap phase and its evolution with doping are studied by taking into account the electron self-energy (then the pseudogap) effect. It is shown that the antinodal region of the electron Fermi surface is suppressed by the electron self-energy, and then the low-energy electron excitations occupy the disconnected Fermi arcs located around the nodal region. In particular, the charge order state is driven by the Fermi-arc instability, with a characteristic wave vector corresponding to the hot spots of the Fermi arcs rather than the antinodal nesting vector. Moreover, although the Fermi arc increases its length as a function of doping, the charge order wave vector reduces almost linearity with the increase of doping. The theory also indicates that the Fermi arc, charge order and pseudogap in cuprate superconductors are intimately related to each other, and all of them emanates from the electron self-energy due to the interaction between electrons by the exchange of spin excitations.     

Fluctuation-exchange study of antiferromagnetism in disordered electron-doped cuprate superconductors

On the basis of the Hubbard model, we extend the fluctuation-exchange (FLEX) approach to investigating the properties of the antiferromagnetic (AF) phase in electron-doped cuprate superconductors. Furthermore, by incorporating the effect of scatterings due to the disordered dopant atoms into the FLEX formalism, our numerical results show that the antiferromagnetic transition temperature, the onset temperature of pseudogap due to spin fluctuations, the spectral density of the single particle near the Fermi surface, and the staggered magnetization in the AF phase as a function of electron doping can consistently account for the experimental measurements.     

Conservation of the particle-hole symmetry in the pseudogap state in optimally-doped Bi2Sr2CuO6+δ superconductor

The pseudogap state is one of the most enigmatic characteristics in the anomalous normal state properties of the high temperature cuprate superconductors. A central issue is to reveal whether there is a symmetry breaking and which symmetries are broken across the pseudogap transition. By performing high resolution laser-based angle-resolved photoemission measurements on the optimally-doped Bi₂Sr_1.6La_0.4CuO_6+δ superconductor, we report the observations of the particle-hole symmetry conservation in both the superconducting state and the pseudogap state along the entire Fermi surface. These results provide key insights in understanding the nature of the pseudogap and its relation with high temperature superconductivity.     

Berezinsky-Kosterlitz-Thouless transition in phase fluctuating superconductors with inhomogeneous Gaussian distributed couplings

Within the framework of phase fluctuation picture for the pseudogap state of cuprate superconductors, we study the effects of both spatial inhomogeneity of coupling strength and thermal phase fluctuations on the superconducting transition temperature. Such a Berezinsky-Kosterlitz-Thouless (BKT) transition is characterized by a two-dimensional (2D) classical XY model, in which the bond coupling is assumed to be roughly proportional to the superconducting bond order parameter. In recent STM experiments with lattice-tracking spectroscopy technique, a Gaussian-like spatially distributed pairing strength is observed. Our Monte Carlo simulations using Wolff cluster update on such 2D classical XY model, in which the bond coupling obeys a similar spatial Gaussian distribution, indicate that the enhancement of the variance of Gaussian distribution may suppress the BKT transition temperature. In addition, we calculate the related physical quantities, including the spin stiffness, free energy, specific heat, magnetization and magnetic susceptibility, by changing the inhomogeneity variance.     

Deconfinement transition in three-dimensional compact U(1) gauge theories coupled to matter fields

It is shown that permanent confinement in three-dimensional compact U(1) gauge theory can be destroyed by matter fields in a deconfinement transition. This follows from a nontrivial infrared fixed point caused by matter, and an anomalous scaling dimension of the gauge field. This leads to a logarithmic interaction between the defects of the gauge fields, which form a gas of magnetic monopoles. For logarithmic interactions, the original electric charges are unconfined. The confined phase, which is permanent in the absence of matter fields, is reached at a critical electric charge, where the interaction between magnetic charges is screened by a pair-unbinding in a Kosterlitz-Thouless-like phase transition.     

Superconductivity in the pseudogap state in the hot spot model: The influence of impurities and the phase diagram

We analyze the peculiarities of the superconducting state (s- and d-wave paring) in the model of the pseudogap state induced by Heisenberg antiferromagnetic short-range order spin fluctuations. The model is based on the pattern of strong scattering near hot spots at the Fermi surface. The analysis is based on the microscopic derivation of the Ginzburg-Landau expansion with the inclusion of all Feynman diagrams of perturbation theory for the interaction of an electron with short-range order fluctuations and in the ladder approximation for the scattering by normal (nonmagnetic) impurities. We determine the dependence of the critical superconducting transition temperature and other superconductor characteristics on the pseudogap parameters and the degree of impurity scattering. We show that the characteristic shape of the phase diagram for high-temperature superconductors can be explained in terms of the model under consideration.