Topology of the Fermi surface and the coexistence of orbital antiferromagnetism and superconductivity in cuprates

It has been shown that the strong coupling model taking into account a rise in the spin antiferromagnetic insulating state explains the doping dependence of the topology and shape of the Fermi contour of superconducting cuprates. Hole pockets with shadow bands in the second Brillouin zone form the Fermi contour with perfect ordinary and mirror nesting, which ensures the coexistence of orbital antiferromagnetism and superconductivity with a large pair momentum for T < T_C. The weak pseudogap region (T_* < T < T*) corresponds to the orbital antiferromagnetic ordering, which coexists with the incoherent state of superconducting pairs with large momenta in the strong pseudogap region (T_C < T < T_*).     

Mott physics, sign structure, ground state wavefunction, and high-T c superconductivity

In this article I give a pedagogical illustration of why the essential problem of high-T _c superconductivity in the cuprates is about how an antiferromagnetically ordered state can be turned into a short-range state by doping. I will start with half-filling where the antiferromagnetic ground state is accurately described by the Liang-Doucot-Anderson (LDA) wavefunction. Here the effect of the Fermi statistics becomes completely irrelevant due to the no double occupancy constraint. Upon doping, the statistical signs reemerge, albeit much reduced as compared to the original Fermi statistical signs. By precisely incorporating this altered statistical sign structure at finite doping, the LDA ground state can be recast into a short-range antiferromagnetic state. Superconducting phase coherence arises after the spin correlations become short-ranged, and the superconducting phase transition is controlled by spin excitations. I will stress that the pseudogap phenomenon naturally emerges as a crossover between the antiferromagnetic and superconducting phases. As a characteristic of non Fermi liquid, the mutual statistical interaction between the spin and charge degrees of freedom will reach a maximum in a high-temperature ??strange metal phase?? of the doped Mott insulator.     

Pseudogap and symmetry of superconducting order parameter in cuprates

The phase diagram, nature of the normal state pseudogap, type of the Fermi surface, and behavior of the superconducting gap in various cuprates are discussed in terms of a correlated state with valence bonds. The variational correlated state, which is a band analogue of the Anderson (RVB) states, is constructed using local unitary transformations. Formation of valence bonds causes attraction between holes in the d-channel and corresponding superconductivity compatible with antiferromagnetic spin order. Our calculations indicate that there is a fairly wide range of doping with antiferromagnetic order in isolated CuO₂ planes. The shape of the Fermi surface and phase transition curve are sensitive to the value and sign of the hopping interaction t′ between diagonal neighboring sites. In underdoped samples, the dielectrization of various sections of the Fermi boundary, depending on the sign of t′, gives rise to a pseudogap detected in photoemission spectra for various quasimomentum directions. In particular, in bismuth-and yttrium-based ceramics (t′>0), the transition from the normal state of overdoped samples to the pseudogap state of underdoped samples corresponds to the onset of dielectrization on the Brillouin zone boundary near k=(0,π) and transition from “large” to “small” Fermi surfaces. The hypothesis about s-wave superconductivity of La-and Nd-based ceramics has been revised: a situation is predicted when, notwithstanding the d-wave symmetry of the superconducting order parameter, the excitation energy on the Fermi surface does not vanish at all points of the phase space owing to the dielectrization of the Fermi boundary at k _x=± k _y. The model with orthorhombic distortions and two peaks on the curve of T _c versus doping is discussed in connection with experimental data for the yttrium-based ceramic. Zh. éksp. Teor. Fiz. 115, 649–674 (February 1999)     

Pseudogap phenomena in ultracold atomic Fermi gases

The pairing and superfluid phenomena in a two-component ultracold atomic Fermi gas is an analogue of Cooper pairing and superconductivity in an electron system, in particular, the high Tc superconductors. Owing to the various tunable parameters that have been made accessible experimentally in recent years, atomic Fermi gases can be explored as a prototype or quantum sinmlator of superconductors. It is hoped that, utilizing such an analogy, the study of atomic Fermi gases may shed light to the mysteries of high Tc superconductivity. One obstacle to the ultimate understand- ing of high Tc superconductivity, from day one of its discovery, is the anomalous yet widespread pseudogap phenomena, for which a consensus is yet to be reached within the physics comnnmity, after over 27 years of intensive research efforts. In this article, we shall review the progress in the study of pseudogap phenomena in atomic Fermi gases in terms of both theoretical understanding and experimental observations. We show that there is strong, unambiguous evidence for the existence of a pseudogap in strongly interacting Fermi gases. In this context, we shall present a pairing fuctuation theory of the pseudogap physics and show that it is indeed a strong candidate theory for high Tc superconductivity.     

Peculiarity of interrelation between electronic and magnetic properties of HTSC cuprates associated with short-range antiferromagnetic order

We report on the results of measurements of anisotropic resistivity of RBa₂Cu₃O_{6 + x} (R = Tm, Lu) high-temperature superconducting single crystals in a wide range of doping levels, indicating a nontrivial effect of magnetic order on the electronic properties of cuprates. In particular, our results visually demonstrate the crossover from the state with moderate anisotropy of resistivity ρ _c /ρ _ab ～ 30 to a strongly anisotropic state with ρ _c /ρ _ab ～ 7 × 10³ upon cooling as well as upon a decrease in the hole concentration in the CuO₂ planes. It is also shown that anisotropy is sensitive to the magnetic state of CuO₂ planes and attains its maximum value after the establishment of the long-range antiferromagnetic order. The results are discussed in the framework of the theory based on the t-t′-t″-J model of CuO₂ layers taking into account strong electron correlations and short-range magnetic order. In this theory, anomalies of spin correlators and Fermi surface topology for a critical hole concentration of p* ≈ 0.24 are demonstrated. The concentration dependence of the charge carrier energy indicates partial suppression of energy due to the emergence of a pseudogap at p < p*. This theory explains both the experimentally observed sensitivity of anisotropy in conductivity to the establishment of the antiferromagnetic order and the absence of anomalies in the temperature dependence of resistivity ρ _ab (T) in the vicinity of the Néel temperature.     

Magnetic ordering in the T* phase La1.2Tb0.8CuO4

We report a muon spin relaxation study of the magnetic properties of the La_1.2Tb_0.8CuO₄ phase with the T^* structure. Random magnetic order is revealed between 280 and 170 K by the zero field data. A spontaneous muon precession then appears below 170 K, arising from antiferromagnetic long range order of the Cu²⁺ spins. Evidence exists below 20 K for ordering of the Tb³⁺ ions. We find that the T^* phase adopts the same magnetic structure as the (T/O) phase La₂CuO₄.     

Pressure-induced magnetic transition in MnRhAs

The magnetic properties of a Fe₂P-type intermetallic compound MnRhAs have been investigated under high pressure up to 8.0 GPa by AC susceptibility measurement. Initially, both the antiferromagnetic (AF(I)) to the canted state magnetic transition temperature T_t and the canted state to another antiferromagnetic one (AF(II)) transition temperature T_C increase with compression. At 4.0 GPa, however, T_t decreases abruptly, while the increasing rate of T_C becomes larger above this pressure. A pressure-induced magnetic phase transition was seen at around this pressure when T_t and T_C are plotted in the pressure–temperature phase diagram. The transition from the antiferromagnetic to the ferromagnetic state observed below 160 K with increasing pressure is not frequently observed.     

Anomalies in the magnetic and magnetoelastic properties of Sm<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Sr<Subscript>x</Subscript>MnO<Subscript>3</Subscript> single crystals (<Emphasis Type="Italic">x</Emphasis> ∼ 0.5) at phase transitions

By studying the magnetic and magnetoelastic properties, it is established that, as the temperature is lowered, Sm_1?xSr_xMnO₃ single crystals (x=0.5, 0.55) undergo spontaneous phase transitions from the paramagnetic to a local charge-ordered state at T_co=220 K and to an A-type antiferromagnetic state at T_N=175 K. It is shown that strong magnetic fields (H_cr ～ 200 kOe) break up the antiferromagnetic order and charge ordering and drive a phase transition to a conducting ferromagnetic state. H-T phase diagrams are constructed for single crystals with x=0.5 and 0.55.     

Theory of high-T c superconductivity based on the fermion-condensation quantum phase transition

A theory of high-temperature superconductivity based on the combination of the fermion-condensation quantum phase transition and the conventional theory of superconductivity is presented. This theory describes maximum values of the superconducting gap, which can be as big as Δ₁～0.1ε _F , with ε _F being the Fermi level. We show that the critical temperature 2T _c ?Δ₁. If the pseudogap exists above T _c , then 2T*?Δ₁ and T* is the temperature at which the pseudogap vanishes. A discontinuity in the specific heat at T _c is calculated. The transition from conventional superconductors to high-T _c ones as a function of the doping level is investigated. The single-particle excitations and their lineshape are also considered     

Remnant Fermi surface in a pseudogap regime of the two-dimensional Hubbard model at finite temperature

A precursor effect on the Fermi surface in the two-dimensional Hubbard model at finite temperatures near the antiferromagnetic instability is studied using three different itinerant approaches: the second order perturbation theory, the paramagnon theory (PT), and the two-particle self-consistent (TPSC) approach. In general, at finite temperature, the Fermi surface of the interacting electron systems is not sharply defined due to the broadening effects of the self-energy. In order to take account of those effects we consider the single-particle spectral function A(, 0) at the Fermi level, to describe the counterpart of the Fermi surface at T = 0. We find that the Fermi surface is destroyed close to the pseudogap regime due to the spin-fluctuation effects in both PT and TPSC approaches. Moreover, the top of the effective valence band is located around = (π/2,π/2) in agreement with earlier investigations on the single-hole motion in the antiferromagnetic background. A crossover behavior from the Fermi-liquid regime to the pseudogap regime is observed in the electron concentration dependence of the spectral function and the self-energy. Received 8 September 2000 and Received in final form 20 December 2000     

The electrodynamic response of heavy-electron materials with magnetic phase transitions

We have investigated the electrodynamic response of the heavy-electron compounds U₂Zn₁₇, UPd₂Al₃, UCu₅ and URu₂Si₂. Particular emphasis has been devoted to the optical evidence of the antiferromagnetic phase transitions at T_N = 9.7 K, 14 K, 15 K and 17 K for U₂Zn₁₇, UPd₂Al₃, UCu₅ and URu₂Si₂, respectively. In the excitation spectrum of UCu₅ and URu₂Si₂, we found an absorption in the far-infrared, which develops below T_N and is ascribed to the excitation across a spin-density-wave type gap, suggesting that the antiferromagnetic phase transition might be itinerant in nature, and invokes a Fermi surface instability. Since this gap-like feature is absent in U₂Zn₁₇ and UPd₂Al₃, we argue that these latter compounds belong to a characteristically different class of antiferromagnets, representative of the heavy-electron compounds with an ordering of essentially localized magnetic moments. The antiferromagnetic ordering then leads to a suppression of the spin-flip mechanism below T_N. At low temperatures, we observe for all compounds the formation of a narrow Drude-like resonance in the optical conductivity, which is ascribed to the electrodynamic response of the heavy-quasiparticles, and is indicative of the progressive development of the manybody coherent Kondo state, coexisting with both types of magnetic ordering. In this review, we also present the evolution of the optical properties due to Ni- and Redoping in UCu₅ and URu₂Si₂, respectively. The optical evidence of the itinerant antiferromagnetic ordering is suppressed in both compounds upon doping and particularly for the URu₂Si₂ compound this is consistent with a crossover to a ferromagnetic ground state upon Re-doping.     

Pseudogap and precursor superconductivity in underdoped cuprate high temperature superconductors: A far-infrared ellipsometry study

With the technique of infrared ellipsometry we performed a detailed study of the temperature- and doping dependence of the c-axis response of a series of YBa₂Cu₃O_7−δ single crystals. In particular, we explored the anomalous electronic properties at temperatures above the macroscopic superconducting transition temperature, T _c, whose conflicting explanations range from a precursor superconducting state to electronic correlations that compete with superconductivity. We show that the c-axis spectra provide evidence that both kinds of correlations are present and that their contributions can be disentangled based on an analysis with a so-called multilayer-model. We find that the onset temperature, T ^*, and the energy scale, Δ_PG, of the competing pseudogap increase rapidly towards the underdoped side whereas they vanish on the overdoped side. In addition, we provide evidence that in a strongly underdoped sample the precursor superconducting correlations develop below an onset temperature, T ^ons, that is considerably lower than T ^* but still much higher than T _c.     

Magnetic phase transitions in Nd7Rh3 single crystal

Magnetic phase transitions in rare earth intermetallic compound Nd₇Rh₃ have been investigated using a single crystal. Measurement results of magnetization, magnetic susceptibility, specific heat, and electrical resistivity reveal that Nd₇Rh₃ has two magnetic phase transitions at T_N=34 K, T_t2=9.1 K and a change of the magnetic feature at T_t1=6.8 K in the absence of an external magnetic field. Antiferromagnetic orderings exist in all the three magnetic states; a large magnetic anisotropy between the c-axis and the c-plane is observed. In the magnetic phase below T_t2, an irreversible field-induced magnetic phase transition takes place in the c-plane; after removing external magnetic field, a coexistence state of ferro- and antiferromagnetic ordering or a ferrimagnetic state having a remanent magnetization M_R is stabilized. The M_R decays to a certain value for several hours after the first process; a magnetic field cooling effect was also observed in the c-plane below T_t2. In the antiferromagentic state above T_t2, the irreversibility disappears and an ordinary antiferromagnetic state takes place. As the origin of this phenomenon, a kind of martensitic structural transition that is observed in Gd₅Ge₄ can be considered.     

First-order phase transition from an antiferromagnetic ferroelectric to a cycloidal multiferroic with weak ferromagnetism during the joint action of applied magnetic and electric fields

The thermodynamics of the phase transition in a perovskite-like multiferroic, in which an antiferromagnetic ferroelectric transforms into a new magnetic state where a spiral spin structure and weak ferromagnetism can coexist in applied magnetic field H, is described. This state forms as a result of a first-order phase transition at a certain temperature (below Néel temperature T _N ), where a helicoidal magnetic structure appears due to the Dzyaloshinskii-Moriya effect. In this case, the axes of electric polarization and the helicoid of magnetic moments are mutually perpendicular and lie in the ab plane, which is normal to principal axis c. Additional electric polarization p, which decreases the total polarization of the ferroelectric P, appears in the ab plane. The effect of applied magnetic and electric fields on the properties of a multiferroic with a helicoidal magnetic structure is described. An alternating electric field is shown to cause a field-linear change in magnetic moment m, whose sign is opposite to the sign of the change of electric field E. The detected hysteretic phenomena that determine the temperature ranges of overheating and supercooling of each phase are explained. A comparison with the experimental data is performed.     

Superconductivity in a simple model of the pseudogap state

An analysis is made of characteristics of the superconducting state (s-and d-pairing) using a simple, exactly solvable model of the pseudogap state produced by fluctuations of the short-range order (such as antiferromagnetic) based on a Fermi surface model with “hot” sections. It is shown that the superconducting gap averaged over these fluctuations is nonzero at temperatures higher than the mean-field superconducting transition temperature T _c over the entire sample. At temperatures T > T _c superconductivity evidently exists in isolated sections (“ drops”). Studies are made of the spectral density and the density of states in which superconducting characteristics exist in the range T > T _c however, in this sense the temperature T = T _c itself is no different in any way. These anomalies show qualitative agreement with various experiments using underdoped high-temperature superconducting cuprates.     

ARPES spectral functions and Fermi surface for La<Subscript>1.86</Subscript>Sr<Subscript>0.14</Subscript>CuO<Subscript>4</Subscript> compared with LDA + DMFT + Σ<Subscript>k</Subscript> calculations

The slightly underdoped high-temperature system La_1.86Sr_0.14CuO₄ (LSCO) is studied by means of high-energy high-resolution angular resolved photoemission spectroscopy (ARPES) and the combined LDA + DMFT + Σ _k computational scheme. The corresponding one-band Hubbard model is solved via dynamical mean field theory (DMFT), and the model parameters needed are obtained from first principles in the local density approximation (LDA). An “external” k-dependent self-energy Σ _k describes the interaction of correlated electrons with antiferromagnetic (AFM) pseudogap fluctuations. Experimental and theoretical data clearly show a “destruction” of the LSCO Fermi surface in the vicinity of the (π, 0) point and formation of “Fermi arcs” in the nodal directions. ARPES energy distribution curves as well as momentum distribution curves demonstrate a deviation of the quasiparticle band from the Fermi level around the (π, 0) point. The same behavior of spectral functions follows from theoretical calculations suggesting the AFM origin of the pseudogap state.     

Electronic and magnetic structure of the undoped two and three-leg ladder cuprates in an itinerant electrons model

We study the electronic and magnetic structure of the undoped ideal two and three-leg ladder cuprates by assuming a moderate on site coulombic repulsion. This analysis is an extension of the Fermi liquids studies proposed for the CuO₂ plane in view to explain the high T_c superconductivity and the competition with the antiferromagnetic phase. At zero doping, the quasi-one-dimensionality of the structure results in SDW correlations with different (commensurate) vectors according to the number of legs, which contrasts with the predictions made from the Heisenberg model. At mean field, and for n = 3 (Sr₂Cu₃O₅), we predict a magnetic ordered state, detected by μSr and NMR measurements with critical temperatures consistent with our assumptions on the physical parameters, the modulation vector being .The presence of several bands at the Fermi level explains why there is no observable gap in the static susceptibility measurements. For n = 2, we predict a gap consistent with experimental Curie susceptibility. But the expected magnetic instability is detected only in La₂Cu₂O₅, where the interladder coupling is stronger. In every case the one-dimensional van Hove singularities are far from the Fermi level, making difficult the obtaining of high T_c superconductivity. Received 3 June 1998     

Pseudogap behavior in Pr0.5Sr0.5MnO3: A photoemission study

The valence band electronic structure of Pr_0.5Sr_0.5MnO₃ has been investigated across its paramagnetic metallic (PMM)–ferromagnetic metallic (FMM)–antiferromagnetic insulator (AFMI) transition. Using surface sensitive high resolution photoemission we have conclusively demonstrated the presence of a pseudogap of magnitude 80 meV in the near Fermi level electronic spectrum in the PMM and FMM phases and finite intensity at the Fermi level in the charge ordering (CO)-AFMI phase. The pseudogap behavior is explained in terms of the strong electron–phonon interaction and the formation of Jahn Teller (JT) polarons, indicating the charge localizations. The finite intensity at the Fermi level in the insulating phase showed a lack of charge ordering in the surface of the Pr_0.5Sr_0.5MnO₃ samples.     

Zeeman and orbital limiting magnetic fields in cuprates: The pseudogap connection

In cuprates, in a view where pairing correlations set in at the pseudogap energy scale T* and acquire global coherence at a lower temperature T_c, the regionT _c⪯ T ⪯ T* is a vast fluctuation regime.T _c andT* vary differently with doping and the question remains about the doping trends of the relevant magnetic field scales: the field H_c2 bounding the superconducting response and the pseudogap closing field H_pg. In-plane thermal (Nernst) and our interlayer (tunneling) transport experiments in Bi₂Sr₂CaCu₂O_8+y report hugely different limiting magnetic fields. Here, based on pairing (and the uncertainty principle) combined with the definitions of the Zeeman energy and the magnetic length, we show that both fields convert to the same pseudogap scaleT* upon transformation as orbital and Zeeman critical fields, respectively. The region of superconducting coherence is confined to the ‘dome’ that coincides with the usual unique upper critical field H_c2 on the strongly overdoped side. We argue that the distinctly different orbital and the Zeeman limiting fields can co-exist owing to charge and spin degrees of freedom separated to different parts of the strongly anisotropic Fermi surface.     

Superconductivity close to the Mott state: From condensed-matter systems to superfluidity in optical lattices

Since the discovery of high-temperature superconductivity in 1986 by Bednorz and Müller, great efforts have been devoted to finding out how and why it works. From the d-wave symmetry of the order parameter, the importance of antiferromagnetic fluctuations, and the presence of a mysterious pseudogap phase close to the Mott state, one can conclude that high-T_c superconductors are clearly distinguishable from the well-understood BCS superconductors. The d-wave superconducting state can be understood through a Gutzwiller-type projected BCS wavefunction. In this review article, we revisit the Hubbard model at half-filling and focus on the emergence of exotic superconductivity with d-wave symmetry in the vicinity of the Mott state, starting from ladder systems and then studying the dimensional crossovers to higher dimensions. This allows to confirm that short-range antiferromagnetic fluctuations can mediate superconductivity with d-wave symmetry. Ladders are also nice prototype systems allowing to demonstrate the truncation of the Fermi surface and the emergence of a Resonating Valence Bond (RVB) state with preformed pairs in the vicinity of the Mott state. In two dimensions, a similar scenario emerges from renormalization group arguments. We also discuss theoretical predictions for the d-wave superconducting phase as well as the pseudogap phase, and address the crossover to the overdoped regime. Finally, cold atomic systems with tunable parameters also provide a complementary insight into this outstanding problem.