Effect of orbital currents on the restricted optical conductivity sum rule

We derive the restricted optical-conductivity sum rule for a model with circulating orbital currents. It is shown that an unusual coupling of the vector potential to the interaction term of the model Hamiltonian results in a non-standard form of the sum rule. As a consequence, the temperature dependence of the restricted spectral weight could be compatible with existing experimental data for high-T _c cuprates above the critical temperature T _c . We extend our results to the superconducting state, and comment on the differences and analogies between these two symmetry-breaking phenomena.Received: 30 April 2004, Published online: 23 July 2004PACS: 71.10.-w Theories and models of many-electron systems - 74.25.Gz Optical properties - 72.15.-v Electronic conduction in metals and alloys - 74.72.-h Cuprate superconductors (high-T _c and insulating parent compounds)S.G. Sharapov: Present address: Institute for Scientific Interchange, via Settimio Severo 65, 10133 Torino, Italy     

An ARPES view on the high-<Emphasis Type="Italic">T</Emphasis><Subscript>c</Subscript> problem: Phonons <Emphasis Type="Italic">vs.</Emphasis> spin-fluctuations

We review the search for a mediator of high-T _c superconductivity focusing on ARPES experiment. In case of HTSC cuprates, we summarize and discuss a consistent view of electronic interactions that provides natural explanation of both the origin of the pseudogap state and the mechanism for high temperature superconductivity. Within this scenario, the spin-fluctuations play a decisive role in formation of the fermionic excitation spectrum in the normal state and are sufficient to explain the high transition temperatures to the superconducting state while the pseudogap phenomenon is a consequence of a Peierls-type intrinsic instability of electronic system to formation of an incommensurate density wave. On the other hand, a similar analysis being applied to the iron pnictides reveals especially strong electron-phonon coupling that suggests important role of phonons for high-T _c superconductivity in pnictides.     

The 3-band Hubbard-model <Emphasis Type="Italic">versus</Emphasis> the 1-band model for the high-<Emphasis Type="Bold">T</Emphasis><Subscript>c</Subscript> cuprates: Pairing dynamics,superconductivity and the ground-state phase diagram

One central challenge in high-T _c superconductivity (SC) is to derive a detailed understanding for the specific role of the Cu-d _x2-y2 and O-p _x,y orbital degrees of freedom. In most theoretical studies an effective one-band Hubbard (1BH) or t-J model has been used. Here, the physics is that of doping into a Mott-insulator, whereas the actual high-T _c cuprates are doped charge-transfer insulators. To shed light on the related question, where the material-dependent physics enters, we compare the competing magnetic and superconducting phases in the ground state, the single- and two-particle excitations and, in particular, the pairing interaction and its dynamics in the three-band Hubbard (3BH) and 1BH-models. Using a cluster embedding scheme, i.e. the variational cluster approach (VCA), we find which frequencies are relevant for pairing in the two models as a function of interaction strength and doping: in the 3BH-models the interaction in the low- to optimal-doping regime is dominated by retarded pairing due to low-energy spin fluctuations with surprisingly little influence of inter-band (p-d charge) fluctuations. On the other hand, in the 1BH-model, in addition a part comes from “high-energy” excited states (Hubbard band), which may be identified with a non-retarded contribution. We find these differences between a charge-transfer and a Mott insulator to be renormalized away for the ground-state phase diagram of the 3BH- and 1BH-models, which are in close overall agreement, i.e. are “universal”. On the other hand, we expect the differences - and thus, the material dependence to show up in the “non-universal” finite-T phase diagram (T _c-values).     

On the limits of consistency of Eliashberg theory and the density of states of high-T c superconductors

We make a detailed study of the Eliashberg theory in the coupling region where some fundamental qualitative deviations from the conventional BCS-like behavior begin to appear. These deviations are identified as the onset of a cross-over from BCS superconductivity to Bose condensation. We point out that the beginning of this cross-over occurs when the gap δ _g becomes comparable to the boson energies Ω_ph. This condition traduces the physical constraint that the distance the paired electron covers during the absorption of the virtual boson, cannot be larger than the coherence length. The frontier region of couplings is of the order of λ ≈ 3, and high-T _c, materials are concerned. A clear qualitative indication of the occurrence of a crossover regime should be a dip structure above the gap in the density of states of excitations, and this is one of the most robust characteristics of the high-T _c, superconducting state. Comparing our results with tunneling and photoemission experiments we conclude that high-T _c materials (cuprates and fullerides) are indeed at the beginning of a cross-over from BCS superconductivity to Bose condensation, even though the fermionic nature still prevails. If the Uemura plot is relevant, then the dip should also be present in the other materials that are close to the cross-over regime like heavy Fermion and organic superconductors. In all these materials Ginzburg Landau equations are irrelevant.     

Effect of strain-induced electronic topological transitions on the superconducting properties of La 2 - x Sr x CuO 4 thin films

We propose a Ginzburg-Landau phenomenological model for the dependence of the critical temperature on microscopic strain in tetragonal high-T _c cuprates. Such a model is in agreement with the experimental results for LSCO under epitaxial strain, as well as with the hydrostatic pressure dependence of T _c in most cuprates. In particular, a nonmonotonic dependence of T _c on hydrostatic pressure, as well as on in-plane or apical microstrain, is derived. From a microscopic point of view, such results can be understood as due to the proximity to an electronic topological transition (ETT). In the case of LSCO, we argue that such an ETT can be driven by a strain-induced modification of the band structure, at constant hole content, at variance with a doping-induced ETT, as is usually assumed. Received 1st October 2001 and Received in final form 5 December 2001     

On field effect studies and superconductor-insulator transition in high-Tc cuprates

We summarize previous field effect studies in high-T _c cuprates and then discuss our method to smoothly tune the carrier concentration of a cuprate film over a wide range using an applied electric field. We synthesized epitaxial one-unit-cell thick films of La_2?x Sr _x CuO₄ and from them fabricated electric double layer transistor devices utilizing various gate electrolytes. We were able to vary the carrier density by about 0.08 carriers per Cu atom, with the resulting change in T _c of 30 K. The superconductor-insulator transition occurred at the critical resistance very close to the quantum resistance for pairs, R _Q = h/(2e)² = 6.5 kΩ. This is suggestive of a quantum phase transition, possibly driven by quantum phase fluctuations, between a “Bose insulator” and a high-T _c superconductor state.     

Spin fluctuations and high temperature superconductivity

Theory of spin fluctuations for itinerant magnetism and its application to high temperature superconductivity are reviewed. After a brief introduction to the whole subject the developments of the self-consistent renormalization theory of spin fluctuations are summarized with particular emphasis on critical properties at the quantum phase transitions. Most of the anomalous properties in the normal state of high-T_c cuprates are understood as due to the critical behaviours for the two dimensional antiferromagnetic metals. By analysing the nuclear magnetic relaxation rate and the T-linear term of resistivity, the set of parameters to specify the spin fluctuations are determined. It is shown that by using the parameters thus obtained one can describe other quantities as well, e.g. optical conductivity. Then we proceed to the theory of superconductivity by the spin fluctuation mechanism. After some discussion on the weak coupling treatments, the strong coupling theory is reviewed. It is shown that the set of parameters determined by the normal state properties of the high-T _c cuprates just give a transition temperature of the right order of magnitude. Among the parameters, the most sensitive one for T _c is the frequency spread of the spin fluctuations. This fact enables us to present a possible unified picture of the antiferromagnetic spin fluctuation-induced superconductors, including heavy fermion superconductors and organic superconductors. This point of view may be confirmed to a certain extent by microscopic calculations based on the fluctuation exchange approximation for the two-dimensional Hubbard models representing not only the cuprates but also organic and trellis lattice compounds. The review is concluded with some discussions on future problems, e.g. the pseudo spin-gap in the under-doped region.     

Operator projection theory for electron differentiation in underdoped cuprate superconductors

Metals approaching the Mott insulator generate a new hierarchy in the electronic structure accompanied by an electron differentiation with emergence of strongly momentum dependent structure, beyond the Mott-Hubbard, Brinkman-Rice and Slater pictures of the Mott transition. To consider such nonlinear phenomenon, we develop an analytic nonperturbative theory based on operator projections combined with a self-consistent treatment of the low-energy excitations. This reproduces the Hubbard bands, Mott gap, spin fluctuations, mass divergence, diverging charge compressibility, and strongly renormalized flat and damped dispersion similar to angle-resolved photoemission data in high-T_c cuprates. Electronic spectra show a remarkable similarity to numerical results.     

Mutual Chern-Simons theory and its applications in condensed matter physics

In this paper, the mutual Chern-Simons (MCS) theory is introduced as a new kind of topological gauge theory in 2+1 dimensions. We use the MCS theory in gapped phase as an effective low energy theory to describe the Z ₂ topological order of the Kitaev-Wen model. Our results show that the MCS theory can catch the key properties for the Z ₂ topological order. On the other hand, we use the MCS theory as an effective model to deal with the doped Mott insulator. Based on the phase string theory, the t-J model reduces to a MCS theory for spinons and holons. The related physics in high T _c cuprates is discussed.      

Doping effect on the carrier scattering in iron-pnictide superconductors studied by charge transport

In order to reveal the role of “carrier doping” in the iron-based superconductors, we investigated the transport properties of the oxygen-deficient iron-arsenides LnFeAsO_1−y (Ln=La, Ce, Pr and Nd) over a wide doping range. We found that the effect of “doping” in this system is mainly on the carrier scattering rather than carrier density, quite distinct from that in high-T_c cuprates. In the case of La system with lower T_c, the low temperature resistivity is dominated by T² term and fairly large magnetoresistance is observed. On the other hand, in the Nd system with higher T_c, carriers are subject to stronger scattering showing nearly T-linear resistivity and small magnetoresistance. Such strong scattering appears intimately correlated with high-T_c superconductivity in the iron-based system.     

Superconductivity and electronic liquid-crystal states in twin-free YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>6+x</Subscript> studied by neutron scattering

In this paper, we first give a concise overview of recent experimental and theoretical work dealing with “electronic liquid-crystal states” which spontaneously break different symmetries of the CuO₂ layers of high-T _c cuprates, with an emphasis on evidence in the spin excitation spectrum. Then we describe the importance of using twin-free samples to look for evidence for fourfold symmetry breaking in the spectrum and explain the preparation procedure to obtain such samples. We present inelastic neutron scattering results for moderately underdoped YBa₂Cu₃O_6.6(T _c = 61  K) and nearly optimally doped YBa₂Cu₃O_6.85(T _c = 89  K). In YBa₂Cu₃O_6.6, the dispersion topology changes when heating above T _c from an hourglass shape with constricted, commensurate resonance peak to a “Y”-shape without resonance anomaly. This change, and the fact that the low-energy signal above T _c can be described by an incommensurate, quasi-one-dimensional distribution, indicates a competition of superconductivity with an electronic liquid-crystal state. We then show a striking analogy between the difference signal I(5  K) − I(70  K) and the downward dispersing resonance mode in YBa₂Cu₃O_6.85. We therefore argue that a resonance mode only emerges below T _c, irrespective of the doping level. We finally discuss the implications of our results for the different scenarios invoked to explain the electronic liquid-crystal state in cuprates.     

The evolution mechanism of Fermi arc with increasing of hole-doping in high-Tc cuprates

We have proposed the evolution mechanism of the Fermi arc with increasing of hole-doping in high-T_c cuprates, taking into account the restoration of spontaneous symmetry breaking through the polarization bubble by the hole–electron propagator.     

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.     

Vertex functions as a factor of enhancing electron-electron attraction in d-wave channel of the “Coulomb” superconductivity mechanism

It is shown that many-particle Coulomb correlations described by Coulomb vertex functions Γ_c in layered high-T _c superconducting metal oxide cuprates substantially enhance effective electron-electron attraction in the d-wave Cooper-pairing channel. This attraction is due to the combined action of a strong in-layer anisotropy of the quasi-two-dimensional electronic spectrum and the suppression of a screened Coulomb repulsion for small transferred momenta in small-angle charge-carrier scattering from long-wavelength charge-density fluctuations. Such a “Coulomb” mechanism of anisotropic Cooper pairing may provide high superconducting transition critical temperatures (T _c ≥100 K) for optimum-doped cuprates.     

Condensation energy of the superconducting bilayer cuprates

In the present work, we report the interplay of single particle and Cooper pair tunnelings on the superconducting state of layered high-T _c cuprate superconductors. For this we have considered a model Hamiltonian incorporating the intra-planar interactions and the contributions arising due to the coupling between the planes. The interplanar interactions include the single particle tunneling as well as the Josephson tunneling of Cooper pairs between the two layers. The expression of the out-of-plane correlation parameter which describes the hopping of a particle from one layer to another layer in the superconducting state is obtained within a Bardeen-Cooper-Schriefer (BCS) formalism using the Green’s function technique. This correlation is found to be sensitive to the various parameter of the model Hamiltonian. We have calculated the out-of-plane contribution to the superconducting condensation energy. The calculated values of condensation energy are in agreement with those obtained from the specific heat and the c-axis penetration depth measurements on bilayer cuprates.     

Hole dispersions for antiferromagnetic spin-\hbox{$\frac{1}{2}$}12 two-leg ladders by self-similar continuous unitary transformations

The hole-doped antiferromagnetic spin-\hbox{ \frac12\frac{1}{2}}12 two-leg ladder is an important model system for the high-T _c superconductors based on cuprates. Using the technique of self-similar continuous unitary transformations we derive effective Hamiltonians for the charge motion in these ladders. The key advantage of this technique is that it provides effective models explicitly in the thermodynamic limit. A real space restriction of the generator of the transformation allows us to explore the experimentally relevant parameter space. From the effective Hamiltonians we calculate the dispersions for single holes. Further calculations will enable the calculation of the interaction of two holes so that a handle of Cooper pair formation is within reach.     

Iron pncitide superconductors studied by the functional renormalization group

We review the functional renormalization group (fRG) approach to the superconducting iron pnictides. We start with simple two-pocket models for the basic weak-coupling picture and then build up the complexity of the many-orbital problem in two steps. In this way we discuss what one can learn about the phase diagrams, superconducting pairing mechanism and competing orders in iron arsenides. Special attention is devoted to where this theoretical approach exposes similarities and differences between the physics of the pnictides and that of the high-T _c cuprates. Finally, we describe some challenges for getting a consistent theoretical understanding of the new iron superconductor material class in a combination of ab-initio and functional renormalization group approaches.     

The “pair” Fermi contour and high-temperature superconductivity

Superconducting pairing of holes with a large (on the order of doubled Fermi) total pair momentum and small relative motion momenta is considered taking into account the quasi-two-dimensional electronic structure of high-T _c cuprates with clearly defined nesting of the Fermi contour situated in an extended neighborhood of the saddle point of the electronic dispersion law (the momentum space region with a hyperbolic metric) and the arising of a spatially inhomogeneous (stripe) structure as a result of the redistribution of current carriers (holes) that restores regions with antiferromagnetic ordering. The superconducting energy gap and condensation energy were determined, and their dependences on the doping level were qualitatively studied. The energy gap was shown to exist in some hole concentration region limited on both sides. The superconducting state with a positive condensation energy appears in a narrower range of doping within this region. The reason for the arising of the superconducting state at a repulsive screened Coulomb interaction between holes is largely the redistribution of hole pairs in the momentum space related to the special features of the hyperbolic metric, which is responsible for the formation of the “pair” Fermi contour, and the renormalization of the kinetic energy of holes when the chemical potential changes because of the condensation of pairs. Hole pairs of the type under consideration exist not only in the condensate but also in the form of quasi-stationary states with very weak decay at temperatures substantially exceeding the superconducting transition temperature. The pseudogap region of the phase diagram of high-T _c cuprates is related to such states. The pairing mechanism under consideration allows not only the principal characteristics of the phase diagram but also key experimental data on high-T _c cuprate materials to be qualitatively explained.     

电子型掺杂高温超导体La2-xCexCuO4飞秒时间分辨动力学研究

利用飞秒时间分辨光抽运探测技术研究了电子型掺杂La_2-xCe_xCuO₄(LCCO)高温超导材料的准粒子超快动力学过程.得到低温(T<0.7T_c)、转变温度附近(0.7T_c≤T≤T_c)和高温(T>T_c)三个温区内的动力学行为.研究发 关键词： 电子型掺杂高温超导体 飞秒时间分辨 准粒子 声子瓶颈