Evidence for universal signatures of Zeeman-splitting-limited pseudogaps in superconducting electron- and hole-doped cuprates

We probe the "normal" state in electron-doped (n-type) Sm2-xCexCuO4-delta through interlayer tunneling transport in magnetic fields up to 45 T. The behavior of intrinsic high-field c-axis negative magnetoresistance (MR), which is accessed in small 30 nm-high mesa structures, is characteristic of the pseudogap state. It follows a universal correlation between the excess low-energy dissipation due to the pseudogap and its closing field Hpg and is in close correspondence with the hole-doped (p-type) Bi2Sr2CaCu2O8+y. The MR in the mesas and in the bulk crystals consistently gives a Zeeman relation between the pseudogap temperature T* and its closing field, pointing to a preeminent role of spin-singlet correlations in forming the pseudogap in cuprates, regardless of their n or p type.     

Essence of Pseudogap and Oscillation in High-Temperature Cuprate Superconductor Junction of Pseudogap State

This paper gives methods to calculate the pairing temperature T*,at which a pseudogap is opened,and the superconducting temperature Tc,at which superconductivity appears,in the high-Tc cuprates,and demonstrates directly that at Tc ＜ T ＜ T* the pseudogap is the gap of Cooper pair without long-range phase coherence,and at T ＜ Tc there is long-range phase coherence between Cooper pairs.Based on the above clear physical picture on the pseudogap state and our mechanism for the ac Josephson effect,this paper proposes that there should be a novel oscillatory current in P-I-P junction,induced by a constant bias on the junction.Here,P represents the high-Tc curates in the pseudogap state,where Cooper pairs do not have long-range phase coherence,and I represents the thin insulating barrier.This paper conjectures that there is a possible high-temperature superconductivity in the heavily underdoped high-Tc cuprates.     

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.     

Closing the pseudogap by Zeeman splitting in Bi2Sr2CaCu2O8+y at high magnetic fields.

Interlayer tunneling resistivity is used to probe the low-energy density-of-states (DOS) depletion due to the pseudogap in the normal state of Bi2Sr2CaCu2O8+y. Measurements up to 60 T reveal that a field that restores DOS to its ungapped state shows strikingly different temperature and doping dependencies from the characteristic fields of the superconducting state. The pseudogap closing field and the pseudogap temperature T small star, filled evaluated independently are related through a simple Zeeman energy scaling. These findings indicate a predominant role of spins over the orbital effects in the formation of the pseudogap.     

Thermodynamics and phase diagram of high temperature superconductors

Thermodynamic quantities are derived for superconducting and pseudogap regimes by taking into account both amplitude and phase fluctuations of the pairing field. In the normal (pseudogap) state of the underdoped cuprates, two domains have to be distinguished: near the superconducting region, phase correlations are important up to temperature T(phi). Above T(phi), the pseudogap region is determined only by amplitudes, and phases are uncorrelated. Our calculations show excellent quantitative agreement with specific heat and magnetic susceptibility experiments on cuprates. We find that the mean field temperature T0 has a similar doping dependence as the pseudogap temperature T(*), whereas the pseudogap energy scale is given by the average amplitude above T(c).     

Evidence for two energy scales in the superconducting state of optimally doped (Bi,Pb)2(Sr,La)2CuO6+delta

We use angle-resolved photoemission spectroscopy to investigate the energy gap(s) in (Bi,Pb)2(Sr,La)2CuO6+delta. We find that the spectral gap has two components in the superconducting state: a superconducting gap and pseudogap. Differences in their momentum and temperature dependence suggest that they represent two separate energy scales. Spectra near the node reveal a sharp peak with a small gap below T(c) that closes at T(c). Near the antinode, spectra are broad with a large energy gap of approximately 40 meV above and below T(c). The latter spectral shape and gap magnitude are almost constant across T(c), indicating that the pseudogap state coexists with the superconducting state below T(c), and it dominates spectra around the antinode. We speculate that the pseudogap state competes with the superconductivity by diminishing spectral weight in antinodal regions, where the superconducting gap is largest.     

The high temperature superconductivity in cuprates: physics of the pseudogap region

We discuss the physics of the high temperature superconductivity in hole doped copperoxide ceramics in the pseudogap region. Starting from an effective reduced Hamiltonianrelevant to the dynamics of holes injected into the copper oxide layers proposed in aprevious paper, we determine the superconductive condensate wavefunction. We show that thelow-lying elementary condensate excitations are analogous to the rotons in superfluid⁴He. We arguethat the rotons-like excitations account for the specific heat anomaly at the criticaltemperature. We discuss and compare with experimental observations the London penetrationlength, the Abrikosov vortices, the upper and lower critical magnetic fields, and thecritical current density. We give arguments to explain the origin of the Fermi arcs andFermi pockets. We investigate the nodal gap in the cuprate superconductors and discussboth the doping and temperature dependence of the nodal gap. We suggest that the nodal gapis responsible for the doping dependence of the so-called nodal Fermi velocity detected inangle resolved photoemission spectroscopy studies. We discuss the thermodynamics of thenodal quasielectron liquid and their role in the low temperature specific heat. We proposethat the ubiquitous presence of charge density wave in hole doped cuprate superconductorsin the pseudogap region originates from instabilities of the nodal quasielectrons drivenby the interaction with the planar CuO₂ lattice. We investigate the doping dependence of thecharge density wave gap and the competition between charge order and superconductivity. Wediscuss the effects of external magnetic fields on the charge density wave gap andelucidate the interplay between charge density wave and Abrikosov vortices. Finally, weexamine the physics underlying quantum oscillations in the pseudogap region.     

Anomalous electronic Raman scattering in NaxCoO2.yH2O

Raman scattering experiments on NaxCoO2.yH2O single crystals show a broad electronic continuum with a pronounced peak around 100 cm(-1) and a cutoff at approximately 560 cm(-1) over a wide range of doping levels. The electronic Raman spectra in superconducting and nonsuperconducting samples are similar at room temperature, but evolve in markedly different ways with decreasing temperature. For superconducting samples, the low-energy spectral weight is depleted upon cooling below T* approximately 150 K, indicating the opening of a pseudogap that is not present in nonsuperconducting materials. Weak additional phonon modes observed below T* suggest that the pseudogap is associated with charge ordering.     

Pseudogap phase in high- T(c) superconductors

We describe the approach of the superconducting state as a sequence of crossover phenomena. As the temperature is decreased, uncorrelated pairing of the electrons leads to the opening of a pseudogap at T(*)(F). Upon further lowering the temperature those electron pairs acquire well behaved itinerant features at T(*)(B), leading to partial Meissner screening and Drude-type behavior of the optical conductivity. Further decrease of the temperature leads to their condensation and superconductivity at T(c). The analysis is done on the basis of the boson-fermion model in the crossover regime between 2D and 3D.     

Critical point and the nature of the pseudogap of single-layered copper-oxide Bi2Sr2-xLaxCuO6+delta superconductors

We apply strong magnetic fields of H=28.5 to 43 T to suppress superconductivity (SC) in the cuprates Bi2Sr2-xLaxCuO6+delta (x=0.65, 0.40, 0.25, 0.15, and 0), and investigate the low temperature (T) normal state by 63Cu nuclear spin-lattice relaxation rate (1/T1) measurements. We find that the pseudogap (PG) phase persists deep inside the overdoped region but terminates at x approximately 0.05, which corresponds to the hole doping concentration of approximately 0.21. Beyond this critical point, the normal state is a Fermi liquid that persists as the ground state when superconductivity is removed by the magnetic field. A comparison of the superconducting state with the H-induced normal state in the x=0.40 (Tc=32 K) sample indicates that there remains substantial part of the Fermi surface even in the fully developed PG state, which suggests that the PG and SC are coexisting matters.     

Phenomenological view at the two-component physics of cuprates

In the search for mechanisms of high-T _c superconductivity it is critical to know the electronic spectrum in the pseudogap phase from which superconductivity evolves. The lack of ARPES data for every cuprate family precludes an agreement as to its structure, doping and temperature dependence and the role of charge ordering. No approach has been developed yet to address the issue theoretically, and we limit ourselves by the phenomenological analysis of the experimental data. We argue that, in the Fermi-liquid-like regime ubiquitous in underdoped cuprates, the spectrum consists of holes on the Fermi arcs and an electronic pocket in contrast to the idea of the Fermi surface reconstruction via charge ordering. At high temperatures, the electrons are dragged by holes while at lower temperatures they get decoupled. The longstanding issue of the origin of the negative Hall coefficient in YBCO and Hg1201 at low temperature is resolved: the electronic contribution prevails, as its mobility becomes temperature independent, while the mobility of holes, scattered by the shortwavelength charge density waves, decreases.     

Observation of pseudogap in SnSe2 atomic layers grown on graphite

Superconducting metal dichalcogenides (MDCs) present several similarities to the other layered superconductors like cuprates. The superconductivity in atomically thin MDCs has been demonstrated by recent experiments, however, the investigation of the superconductivity intertwined with other orders are scarce. Investigating the pseudogap in atomic layers of MDCs may help to understand the superconducting mechanism for these true two-dimensional (2D) superconducting systems. Herein we report a pseudogap opening in the tunneling spectra of thin layers of SnSe₂ epitaxially grown on highly oriented pyrolytic graphite (HOPG) with scanning tunneling microscopy/spectroscopy (STM/STS). A significant V-shaped pseudogap was observed to open near the Fermi level (E_F) in the STS. And at elevated temperatures, the gap gradually evolves to a shallow dip. Our experimental observations provide direct evidence of a pseudogap state in the electron-doped SnSe₂ atomic layers on the HOPG surface, which may stimulate further exploration of the mechanism of superconductivity at 2D limit in MDCs.     

Meissner effect in the underdoped YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>6+<Emphasis Type="Italic">δ</Emphasis></Subscript> HTSC phase

The dependence of the superconducting (Meissner) phase volume V _m on the YBa₂Cu₃O_6+δ doping level was studied. It was found that V _m monotonically decreases as the doping level is lowered and vanishes at the same value of δ ～ 0.3 as T_c does. It was concluded that the T_c decrease and the increase in the pseudogap formation temperature T* as the doping level is lowered are caused by a decrease in the average size of superconducting clusters. This conclusion suggests an extraordinary superconductivity mechanism in HTSC.     

铜氧化物高温超导体中的电子有序态

铜氧化物高温超导现象自30年前被发现以来,对现代凝聚态物理的发展产生了极其重要的影响,然而其微观机制至今依然是一个谜。近年来,多种实验手段的研究结果发现,在铜氧化物高温超导体中电子除了形成库珀对,还可能形成多种其他新奇的有序态,例如自旋有序态、电荷有序态以及库珀对密度波等。这些有序态的起源及其与赝能隙态和超导态的关联对于理解高温超导机理可能具有重要的意义。文章将主要从实验的角度对铜氧化物超导体中的电子有序态做一个概述。     

Pseudogap-state superconductivity in a “hot-point” model: Gor’kov equations

The specific features of the superconducting state (with s and d pairing) are considered in terms of a pseudogap state caused by short-range order fluctuations of the “dielectric” type, namely, antiferromagnetic (spin density wave) or charge density wave fluctuations, in a model of the Fermi surface with “hot points.” A set of recurrent Gor’kov equations is derived with inclusion of all Feynman diagrams of a perturbation expansion in the interaction between an electron and short-range order fluctuations causing strong scattering near hot points. The influence of nonmagnetic impurities on superconductivity in such a pseudogap state is analyzed. The critical temperature for the superconducting transition is determined, and the effect of the effective pseudogap width, correlation length of short-range-order fluctuations, and impurity scattering frequency on the temperature dependence of the energy gap is investigated.     

Null orbital frustration at the pseudogap boundary in a layered cuprate superconductor

We assess the relative importance of orbital frustration at the pseudogap closing field H(pg). Using interlayer tunneling transport in pulsed magnetic fields nearly up to 60 T, we track the field-temperature (H-T) phase diagram for fields parallel ( parallel ab) and normal ( parallel c) to the layered structure of Bi(2)Sr(2)CaCu(2)O(8+y). In contrast to large orientational anisotropy of the superconducting state related to the orbital motion of Cooper pairs, we find anisotropy of H(pg) temperature independent and small, due solely to the g factor. The obtained Zeeman relation with the pseudogap temperature T small star, filled, g( parallel c)micro(B)H( parallel c)(pg)=g( parallel ab)micro(B)H( parallel ab)(pg) approximately k(B)T small star, filled, is fully consistent with the correlations only in the spin channel.     

Charge ordering fluctuation and optical pseudogap in La(1-x)Ca(x)MnO(3)

Optical spectroscopy was used to investigate the optical gap ( 2 Delta) due to charge ordering (CO) and related pseudogap developments with x and temperature ( T) in La(1-x)Ca(x)MnO(3) ( 0.48< or =x< or =0.67). Surprisingly, we found 2 Delta/k(B)T(CO) is as large as 30 for x approximately 0.5, and decreases rapidly with increasing x. Simultaneously, the optical pseudogap, possibly starting from T* far above T(CO) becomes drastically enhanced near x = 0.5, producing non-BCS T-dependence of 2 Delta with the large magnitude far above T(CO), and systematic increase of T* for x approximately 0.5. These results unequivocally indicate systematically enhanced CO correlation when x approaches 0.5 even though T(CO) decreases.     

Carrier-concentration dependence of the pseudogap ground state of superconducting Bi₂Sr(₂-x)La(x)CuO(₆+δ) revealed by ⁶³,⁶⁵Cu-nuclear magnetic resonance in very high magnetic fields

We report the results of the Knight shift by ?3,??Cu-NMR measurements on single-layered copper-oxide Bi?Sr(?-x)La(x)CuO(?+δ) conducted under very high magnetic fields up to 44 T. The magnetic field suppresses superconductivity completely, and the pseudogap ground state is revealed. The ?3Cu-NMR Knight shift shows that there remains a finite density of states at the Fermi level in the zero-temperature limit, which indicates that the pseudogap ground state is a metallic state with a finite volume of Fermi surface. The residual density of states in the pseudogap ground state decreases with decreasing doping (increasing x) but remains quite large even at the vicinity of the magnetically ordered phase of x ≥ 0.8, which suggests that the density of states plunges to zero upon approaching the Mott insulating phase.     

Competing energy scales in high‐temperature superconductors: Ultrafast pump–probe studies

We present a review of photoexcited quasiparticle dynamics of cuprate and pnictide high‐temperature superconductors in regimes (temperature, doping) where different phases such as superconductivity, spin‐density‐wave (SDW) and pseudogap phases coexist or compete with one another. We start with the overdoped cuprate superconductor Y_1–xCa_x Ba₂Cu₃O_7–δ, where the superconducting gap and pseudogap coexist in the superconducting state. In another cuprate Tl₂Ba₂Ca₂Cu₃O_y, we ob‐ serve a competition between SDW and superconducting orders deep in the superconducting state. Finally, in the underdoped iron pnictide superconductor (Ba,K)Fe₂As₂, SDW order forms at 85 K, followed by superconductivity at 28 K. We also find the emergence of a normal‐state order that suppresses SDW at a temperature T * ～ 60 K and argue that this normal‐state order is a precursor to superconductivity. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fermi-liquid ground state in the n-type Pr(0.91)LaCe(0.09)CuO(4-y) copper-oxide superconductor

We report nuclear magnetic resonance studies on the low-doped n-type copper-oxide Pr(0.91)LaCe(0.09)CuO(4-y) (T(c)=24 K) in the superconducting state and in the normal state uncovered by the application of a strong magnetic field. We find that when the superconductivity is removed the underlying ground state is the Fermi liquid state. This result is at variance with that inferred from previous thermal conductivity measurement and appears to contrast with that in p-type copper oxides with a similar doping level where high-T(c) superconductivity sets in within the pseudogap phase. The data in the superconducting state are consistent with the line-node gap model.