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.     

Magnetic field effect on the pseudogap temperature within precursor superconductivity

We determine the magnetic-field dependence of the pseudogap closing temperature T* within a precursor superconductivity scenario. Detailed calculations with an anisotropic lattice model with d-wave superconductivity account for a recently determined experimental relation in BSCCO between the pseudogap closing field and the pseudogap temperature at zero field, as well as for the weak initial dependence of T* at low fields. Our results indicate that the available experimental data are fully compatible with a superconducting origin of the pseudogap in cuprate superconductors.     

Quantum criticality of D-wave quasiparticles and superconducting phase fluctuations

We present finite temperature (T) extension of the (2+1)-dimensional QED (QED3) theory of under-doped cuprates. The theory describes nodal quasiparticles whose interactions with quantum proliferated hc/2e vortex-antivortex pairs are represented by an emergent U(1) gauge field. Finite T introduces a scale beyond which the spatial fluctuations of vorticity are suppressed. As a result, the spin susceptibility of the pseudogap state is bounded by T2 at low T and crosses over to approximately T at higher T, while the low-T specific heat scales as T2, reflecting the thermodynamics of QED3. The Wilson ratio vanishes as T-->0; the pseudogap state is a "thermal (semi)metal" but a "spin-charge dielectric." This non-Fermi liquid behavior originates from two general principles: spin correlations induced by "gauge" interactions of quasiparticles and fluctuating vortices and the "relativistic" scaling of the T=0 fixed point.     

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.     

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).     

Superconducting fluctuations and the pseudogap in the slightly overdoped high- T(c) superconductor TlSr2CaCu2O6.8: high magnetic field NMR studies

From measurements of the 63Cu Knight shift ( K) and the nuclear spin-lattice relaxation rate ( 1/T1) under magnetic fields from zero up to 28 T in the slightly overdoped high- T(c) superconductor TlSr2CaCu2O6.8 ( T(c) = 68 K), we find that the pseudogap behavior, i.e., the reductions of 1/T1T and K above T(c) from the values expected from the normal state at high T, is strongly field dependent and follows a scaling relation. We show that this scaling is consistent with the effects of the Cooper pair density fluctuations. The present finding contrasts sharply with the pseudogap property reported previously in the underdoped regime where no field effect was seen up to 23.2 T. The implications are discussed.     

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.     

High-field interlayer tunnelling transport in layered cuprates: Uncovering the pseudogap state

In high temperature (high T _c ) cuprate superconductors the gap in the electronic density of states is not fully filled at T _c ; it evolves into a partial (pseudo)gap that survives way beyond T _c , challenging the conventional views. We have investigated the pseudogap phenomenon in the field-temperature (H-T) diagram of Bi₂Sr₂CaCu₂O_{8 + y} over a wide range of hole doping ( ). Using interlayer tunneling transport in magnetic fields up to 60 T to probe the density-of states (DOS) depletion at low excitation energies we mapped the pseudogap closing field H _pg . We found that H _pg and the pseudogap onset temperature T ^* are related via a Zeeman relation , irrespective of whether the magnetic field is applied along the c-axis or parallel to CuO₂ planes. In contrast to large anisotropy of the superconducting state, the field anisotropy of H _pg is due solely to the g-factor. Our findings indicate that the pseudogap is of singlet-spin origin, consistent with models based on doped Mott insulator.Received: 2 February 2004, Published online: 10 August 2004PACS: 74.25.Dw Superconductivity phase diagrams - 74.25.Fy Transport properties (electric and thermal conductivity, thermoelectric effects, etc.) - 74.72.Hs Bi-based cuprates     

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.     

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.     

Interlayer tunneling spectroscopy of the field induced CDW state in graphite

Using interlayer tunneling spectroscopy we studied anomalous magnetoresistance state in graphite in pulsed magnetic fields up to 55 T. At low temperatures we found the opening of a pseudogap on tunneling spectra at fields above 17 T. The gap value is saturated above 30 T to 2Δ=70 mV. The gap feature is gradually smearing out with temperature but is still observed up to temperatures of ∼250 K. We discuss possible origin of the pseudogap as being related with the field induced charge density wave (CDW) state in analogy with that recently observed in NbSe₃ above Peierls transition temperature.     

Two crossovers in the Pseudogap regime of YBa 2Cu 3O (7-delta) superconductors observed by ultrafast spectroscopy

We have investigated the temperature dependence of the optical reflectivity on a femtosecond scale in a near optimally doped YBa 2Cu 3O (7-delta) superconductor. The combined study of the lattice and carrier dynamics at temperatures above T(c) allows us to identify two crossover temperatures in the normal state, giving evidence for an inhomogeneity of the pseudogap regime. These crossovers exhibit a clear hysteresis behavior depending on the direction of temperature change. The carrier and lattice dynamics within the crossover regimes show distinct differences from and similarities to the superconducting state, which may help in choosing between the competing theories for the pseudogap state.     

Protected nodes and the collapse of Fermi arcs in high-T{c} cuprate superconductors

Angle resolved photoemission on underdoped Bi2Sr2CaCu2O8 reveals that the magnitude and d-wave anisotropy of the superconducting state energy gap are independent of temperature all the way up to T{c}. This lack of T variation of the entire k-dependent gap is in marked contrast to mean field theory. At T{c} the point nodes of the d-wave gap abruptly expand into finite length "Fermi arcs." This change occurs within the width of the resistive transition, and thus the Fermi arcs are not simply thermally broadened nodes but rather a unique signature of the pseudogap phase.     

Antiferromagnetic vortex core in Tl(2)Ba(2)CuO(6+delta) studied by nuclear magnetic resonance

Spatially resolved NMR is used to probe the magnetism in and around vortex cores of nearly optimally doped Tl(2)Ba(2)CuO(6+delta) (T(c)=85 K). The NMR relaxation rate T(-1)1 at the 205Tl site provides direct evidence that the antiferromagnetic (AF) spin correlation is significantly enhanced in the vortex core region. In the core region Cu spins show a local AF ordering with moments parallel to the layers at T(N)=20 K. Above T(N) the core region is in the paramagnetic state which is a reminiscence of the state above the pseudogap temperature (T(*) approximately 120 K), indicating that the pseudogap disappears within cores.     

Nearly antiferromagnetic Fermi liquids: a progress report

I describe recent theoretical and experimental progress in understanding the physical properties of the two dimensional nearly antiferromagnetic Fermi liquids (NAFL's) found in the normal state of the cuprate superconductors. In such NAFL's, the magnetic interaction between planar quasiparticles is strong and peaked at or near the commensurate wave vector, Q ≡ (fy fy). For the optimally doped and underdoped systems, the resulting strong antiferromagnetic correlations produce three distinct magnetic phases in the normal state: mean field above T_cr, pseudoscaling between T_cr and T_*, and pseudogap below T_*. I present arguments which suggest that the physical origin of the pseudogap found in the quasiparticle spectrum below Tcr is the formation of a precursor to a spin-densitywave- state, describe the calculations based on this scenario of the dynamical spin susceptibility, Fermi surface evolution, transport, and Hall effect, and summarize the experimental evidence in its support.     

Magnetic field dependence of the superconducting gap and the pseudogap in Bi2212 and HgBr2-Bi2212, studied by intrinsic tunneling spectroscopy

Intrinsic tunneling spectroscopy in high magnetic field (H) is used for a direct test of superconducting features in the quasiparticle density of states of pure Bi2212 and intercalated HgBr2-Bi2212 high- T(c) superconductors. We were able to distinguish with great clarity two coexisting gaps: (i) the superconducting gap, which closes as H-->H(c2)(T), and (ii) the c-axis pseudogap, which does not change either with H or with T. Strikingly different H dependencies, together with previously observed different temperature dependencies of the two gaps, speak against a superconducting origin of the pseudogap.     

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.     

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.     

ab plane ac conductivity in the cuprates: pseudogap effects below Tc

Building on our understanding of the superfluid density rho(s)(T), we show how the pseudogap enters the in-plane optical conductivity sigma(omega,T) for temperatures T相似文献