Field-enhanced diamagnetism in the pseudogap state of the cuprate Bi2Sr2CaCu2O(8+delta) superconductor in an intense magnetic field

Evolution from a charge-ordered insulator to a high-temperature superconductor in Bi2Sr2(Ca,Dy)Cu2O8+δ

How Cooper pairs form and condense has been the main challenge in the physics of copper-oxide high-temperature superconductors. Great efforts have been made in the 'underdoped' region of the phase diagram, through doping a Mott insulator or cooling a strange metal. However, there is still no consensus on how superconductivity emerges when electron-electron correlations dominate and the Fermi surface is missing. To address this issue, here we carry out high-resolution resonant inelastic X-ray scattering and scanning tunneling microscopy studies on prototype cuprates Bi2Sr2Ca0.6Dy0.4Cu2O8+δ near the onset of superconductivity, combining bulk and surface, momentum- and real-space information. We show that an incipient charge order exists in the antiferromagnetic regime down to 0.04 holes per CuO2 unit, entangled with a particle-hole asymmetric pseudogap. The charge order induces an intensity anomaly in the bond-buckling phonon branch, which exhibits an abrupt increase once the system enters the superconducting dome. Our results suggest that the Cooper pairs grow out of a charge-ordered insulating state, and then condense accompanied by an enhanced interplay between charge excitations and electron-phonon coupling.

Dissipationless Counterflow Currents above T_{c} in Bilayer Superconductors

We report the existence of dissipationless currents in bilayer superconductors above the critical temperature T_{c}, assuming that the superconducting phase transition is dominated by phase fluctuations. Using a semiclassical U(1) lattice gauge theory, we show that thermal fluctuations cause a transition from the superconducting state at low temperature to a resistive state above T_{c}, accompanied by the proliferation of unbound vortices. Remarkably, while the proliferation of vortex excitations causes dissipation of homogeneous in-plane currents, we find that counterflow currents, flowing in the opposite direction within a bilayer, remain dissipationless. The presence of a dissipationless current channel above T_{c} is attributed to the inhibition of vortex motion by local superconducting coherence within a single bilayer, in the presence of counterflow currents. Our theory presents a possible scenario for the pseudogap phase in bilayer cuprates.

Paramagnons and high-temperature superconductivity in a model family of cuprates

Cuprate superconductors have the highest critical temperatures (T_c) at ambient pressure, yet a consensus on the superconducting mechanism remains to be established. Finding an empirical parameter that limits the highest reachable T_c can provide crucial insight into this outstanding problem. Here, in the first two Ruddlesden-Popper members of the model Hg-family of cuprates, which are chemically nearly identical and have the highest T_c among all cuprate families, we use inelastic photon scattering to reveal that the energy of magnetic fluctuations may play such a role. In particular, we observe the single-paramagnon spectra to be nearly identical between the two compounds, apart from an energy scale difference of ~30% which matches their difference in T_c. The empirical correlation between paramagnon energy and maximal T_c is further found to extend to other cuprate families with relatively high T_c’s, hinting at a fundamental connection between them.

Finding a parameter that limits the critical temperature of cuprate superconductors can provide crucial insight on the superconducting mechanism. Here, the authors use inelastic photon scattering on two Ruddlesden-Popper members of the model Hg-family of cuprates to reveal that the energy of magnetic fluctuations may play such a role, and suggest that the Cooper pairing is mediated by paramagnons.

Unconventional spectral signature of Tc in a pure d-wave superconductor

In conventional superconductors, the phase transition into a zero-resistance and perfectly diamagnetic state is accompanied by a jump in the specific heat and the opening of a spectral gap¹. In the high-transition-temperature (high-T_c) cuprates, although the transport, magnetic and thermodynamic signatures of T_c have been known since the 1980s², the spectroscopic singularity associated with the transition remains unknown. Here we resolve this long-standing puzzle with a high-precision angle-resolved photoemission spectroscopy (ARPES) study on overdoped (Bi,Pb)₂Sr₂CaCu₂O_8+δ (Bi2212). We first probe the momentum-resolved electronic specific heat via spectroscopy and reproduce the specific heat peak at T_c, completing the missing link for a holistic description of superconductivity. Then, by studying the full momentum, energy and temperature evolution of the spectra, we reveal that this thermodynamic anomaly arises from the singular growth of in-gap spectral intensity across T_c. Furthermore, we observe that the temperature evolution of in-gap intensity is highly anisotropic in the momentum space, and the gap itself obeys both the d-wave functional form and particle-hole symmetry. These findings support the scenario that the superconducting transition is driven by phase fluctuations. They also serve as an anchor point for understanding the Fermi arc and pseudogap phenomena in underdoped cuprates.

Signatures of bosonic Landau levels in a finite-momentum superconductor

Charged particles subjected to magnetic fields form Landau levels (LLs). Originally studied in the context of electrons in metals¹, fermionic LLs continue to attract interest as hosts of exotic electronic phenomena^2,3. Bosonic LLs are also expected to realize novel quantum phenomena^4,5, but, apart from recent advances in synthetic systems^6,7, they remain relatively unexplored. Cooper pairs in superconductors-composite bosons formed by electrons-represent a potential condensed-matter platform for bosonic LLs. Under certain conditions, an applied magnetic field is expected to stabilize an unusual superconductor with finite-momentum Cooper pairs^8,9 and exert control over bosonic LLs^10-13. Here we report thermodynamic signatures, observed by torque magnetometry, of bosonic LL transitions in the layered superconductor Ba₆Nb₁₁S₂₈. By applying an in-plane magnetic field, we observe an abrupt, partial suppression of diamagnetism below the upper critical magnetic field, which is suggestive of an emergent phase within the superconducting state. With increasing out-of-plane magnetic field, we observe a series of sharp modulations in the upper critical magnetic field that are indicative of distinct vortex states and with a structure that agrees with predictions for Cooper pair LL transitions in a finite-momentum superconductor^10-14. By applying Onsager's quantization rule¹⁵, we extract the momentum. Furthermore, study of the fermionic LLs shows evidence for a non-zero Berry phase. This suggests opportunities to study bosonic LLs, topological superconductivity, and their interplay via transport¹⁶, scattering¹⁷, scanning probe¹⁸ and exfoliation techniques¹⁹.

Possible Occurrence of Superconductivity by the π-flux Dirac String Formation Due to Spin-Twisting Itinerant Motion of Electrons

We show that the Rashba spin-orbit interaction causes spin-twisting itinerant motion of electrons in metals and realizes the quantized cyclotron orbits of conduction electrons without an external magnetic field. From the view point of the Berry connection, the cause of this quantization is the appearance of a non-trivial Berry connection A fic = − ℏ 2 e ∇ χ ( χ is an angular variable with period 2 π ) that generates π flux (in the units of ℏ = 1 , e = 1 , c = 1 ) inside the nodal singularities of the wave function (a “Dirac string”) along the centers of spin-twisting. Since it has been shown in our previous work that the collective mode of ∇ χ is stabilized by the electron-pairing and generates supercurrent, the π -flux Dirac string created by the spin-twisting itinerant motion will be stabilized by the electron-pairing and produce supercurrent.

Incoherent strange metal sharply bounded by a critical doping in Bi2212

In normal metals, macroscopic properties are understood using the concept of quasiparticles. In the cuprate high-temperature superconductors, the metallic state above the highest transition temperature is anomalous and is known as the "strange metal." We studied this state using angle-resolved photoemission spectroscopy. With increasing doping across a temperature-independent critical value p _c ~ 0.19, we observed that near the Brillouin zone boundary, the strange metal, characterized by an incoherent spectral function, abruptly reconstructs into a more conventional metal with quasiparticles. Above the temperature of superconducting fluctuations, we found that the pseudogap also discontinuously collapses at the very same value of p _c These observations suggest that the incoherent strange metal is a distinct state and a prerequisite for the pseudogap; such findings are incompatible with existing pseudogap quantum critical point scenarios.

Cooper Pair Density of Bi2Sr2CaCu2O8+ x in Atomic scale at 4.2 K

In pursuit of the elusive mechanism of high- T _C superconductors (HTSC), spectroscopic imaging scanning tunneling microscopy (SI-STM) is an indispensable tool for surveying local properties of HTSC. Since a conventional STM utilizes metal tips, which allow the examination of only quasiparticles and not superconducting (SC) pairs, Josephson tunneling using STM has been demonstrated by many authors in the past. An atomically resolved scanning Josephson tunneling microscopy (SJTM), however, was realized only recently on Bi₂Sr₂CaCu₂O_{8+ x} (Bi-2212) below 50 mK and on the Pb(110) surface at 20 mK. Here we report the atomically resolved SJTM on Bi₂Sr₂CaCu₂O_{8+ x} at 4.2 K using Bi-2212 tips created in situ. The I- V characteristics show clear zero bias conductance peaks following Ambegaokar-Baratoff (AB) theory. A gap map was produced for the first time using an atomically resolved Josephson critical current map I _C( r) and AB theory. Surprisingly, we found that this new gap map is anticorrelated to the gap map produced by a conventional method relying on the coherence peaks. Quasiparticle resonance due to a single isolated zinc atom impurity was also observed by SJTM, indicating that atomically resolved SJTM was achieved at 4.2 K. Our result provides a starting point for realizing SJTM at even higher temperatures, rendering possible investigation of the existence of SC pairs in HTSC above the T _C.

Logarithmic Upturn in Low-Temperature Electronic Transport as a Signature of d-Wave Order in Cuprate Superconductors

In cuprate superconductors, high magnetic fields have been used extensively to suppress superconductivity and expose the underlying normal state. Early measurements revealed insulatinglike behavior in underdoped material versus temperature T, in which resistivity increases on cooling with a puzzling log(1/T) form. We instead use microwave measurements of flux-flow resistivity in YBa_{2}Cu_{3}O_{6+y} and Tl_{2}Ba_{2}CuO_{6+δ} to study charge transport deep inside the superconducting phase, in the low-temperature and low-field regime. Here, the transition from metallic low-temperature resistivity (dρ/dT>0) to a log(1/T) upturn persists throughout the superconducting doping range, including a regime at high carrier dopings in which the field-revealed normal-state resistivity is Fermi-liquid-like. The log(1/T) form is thus likely a signature of d-wave superconducting order, and the field-revealed normal state's log(1/T) resistivity may indicate the free-flux-flow regime of a phase-disordered d-wave superconductor.

Emergence of superconductivity in the cuprates via a universal percolation process

A pivotal step toward understanding unconventional superconductors would be to decipher how superconductivity emerges from the unusual normal state. In the cuprates, traces of superconducting pairing appear above the macroscopic transition temperature Tc, yet extensive investigation has led to disparate conclusions. The main difficulty has been to separate superconducting contributions from complex normal-state behaviour. Here we avoid this problem by measuring nonlinear conductivity, an observable that is zero in the normal state. We uncover for several representative cuprates that the nonlinear conductivity vanishes exponentially above Tc, both with temperature and magnetic field, and exhibits temperature-scaling characterized by a universal scale Ξ0. Attempts to model the response with standard Ginzburg-Landau theory are systematically unsuccessful. Instead, our findings are captured by a simple percolation model that also explains other properties of the cuprates. We thus resolve a long-standing conundrum by showing that the superconducting precursor in the cuprates is strongly affected by intrinsic inhomogeneity.

Resonant torsion magnetometry in anisotropic quantum materials

Unusual behavior in quantum materials commonly arises from their effective low-dimensional physics, reflecting the underlying anisotropy in the spin and charge degrees of freedom. Here we introduce the magnetotropic coefficient k = ∂²F/∂θ², the second derivative of the free energy F with respect to the magnetic field orientation θ in the crystal. We show that the magnetotropic coefficient can be quantitatively determined from a shift in the resonant frequency of a commercially available atomic force microscopy cantilever under magnetic field. This detection method enables part per 100 million sensitivity and the ability to measure magnetic anisotropy in nanogram-scale samples, as demonstrated on the Weyl semimetal NbP. Measurement of the magnetotropic coefficient in the spin-liquid candidate RuCl₃ highlights its sensitivity to anisotropic phase transitions and allows a quantitative comparison to other thermodynamic coefficients via the Ehrenfest relations.

Superconducting fluctuation effect in CaFe0.88Co0.12AsF

Out-of-plane angular dependent torque measurements were performed on CaFe0.88Co0.12AsF single crystals. Superconducting fluctuations, featured by magnetic field enhanced and exponential temperature dependent diamagnetism, are observed above the superconducting transition temperature T c, which is similar to that of cuprate superconductors, but less pronounced. In addition, the ratio of T c versus superfluid density follows well the Uemura line of high-T c cuprates, which suggests the exotic nature of the superconductivity in CaFe0.88Co0.12AsF.

Magnetic phase diagram of underdoped YBa2Cu3O y inferred from torque magnetization and thermal conductivity

Strong evidence for charge-density correlation in the underdoped phase of the cuprate YBa₂Cu₃O _y was obtained by NMR and resonant X-ray scattering. The fluctuations were found to be enhanced in strong magnetic fields. Recently, 3D charge-density-wave (CDW) formation with long-range order (LRO) was observed by X-ray diffraction in [Formula: see text] 15 T. To elucidate how the CDW transition impacts the pair condensate, we have used torque magnetization to 45 T and thermal conductivity [Formula: see text] to construct the magnetic phase diagram in untwinned crystals with hole density p = 0.11. We show that the 3D CDW transitions appear as sharp features in the susceptibility and [Formula: see text] at the fields [Formula: see text] and [Formula: see text], which define phase boundaries in agreement with spectroscopic techniques. From measurements of the melting field [Formula: see text] of the vortex solid, we obtain evidence for two vortex solid states below 8 K. At 0.5 K, the pair condensate appears to adjust to the 3D CDW by a sharp transition at 24 T between two vortex solids with very different shear moduli. At even higher H (41 T), the second vortex solid melts to a vortex liquid which survives to fields well above 41 T. de Haas-van Alphen oscillations appear at fields 24-28 T, below the lower bound for the upper critical field [Formula: see text].

Andreev-Bragg Reflection from an Amperian Superconductor

We show how an electrical measurement can detect the pairing of electrons on the same side of the Fermi surface (Amperian pairing), recently proposed by Patrick Lee for the pseudogap phase of high-Tc cuprate superconductors. Bragg scattering from the pair-density wave introduces odd multiples of 2k(F) momentum shifts when an electron incident from a normal metal is Andreev reflected as a hole. These Andreev-Bragg reflections can be detected in a three-terminal device, containing a ballistic Y junction between normal leads (1, 2) and the superconductor. The cross-conductance dI1/dV2 has the opposite sign for Amperian pairing than it has either in the normal state or for the usual BCS pairing.

Point nodes persisting far beyond Tc in Bi2212

In contrast to a complex feature of antinodal state, suffering from competing orders, the pairing gap of cuprates is obtained in the nodal region, which therefore holds the key to the superconducting mechanism. One of the biggest question is whether the point nodal state as a hallmark of d-wave pairing collapses at T_c like the BCS-type superconductors, or it instead survives above T_c turning into the preformed pair state. A difficulty in this issue comes from the small magnitude of the nodal gap, which has been preventing experimentalists from solving it. Here we use a laser ARPES capable of ultrahigh-energy resolution, and detect the point nodes surviving far beyond T_c in Bi2212. By tracking the temperature evolution of spectra, we reveal that the superconductivity occurs when the pair-breaking rate is suppressed smaller than the single-particle scattering rate on cooling, which governs the value of T_c in cuprates.

The pairing gap of the high-T_c cuprates has been expected to close at the transition temperature, similarly to the case of conventional superconductors. Here the authors perform ARPES measurements on Bi2212, and reveal a point nodal gap formation beyond T_c, characterized in terms of three parameters.

Ultrafast dynamics of fluctuations in high-temperature superconductors far from equilibrium

Despite extensive work on high-temperature superconductors, the critical behavior of an incipient condensate has so far been studied exclusively under equilibrium conditions. Here, we excite Bi(2)Sr(2)CaCu(2)O(8+δ) with a femtosecond laser pulse and monitor the subsequent nonequilibrium dynamics of the midinfrared conductivity. Our data allow us to discriminate temperature regimes where superconductivity is either coherent, fluctuating or vanishingly small. Above the transition temperature T(c), we make the striking observation that the relaxation to equilibrium exhibits power-law dynamics and scaling behavior, both for optimally and underdoped superconductors. Our findings can in part be modeled using time-dependent Ginzburg-Landau theory, and they provide strong indication of universality in systems far from equilibrium.

Charge segregation model for superconducting correlations in cuprates above T(c)

We present a theoretical framework for understanding recent transverse field muon spin rotation (TF-µSR) experiments on cuprate superconductors in terms of localized regions of phase-coherent pairing correlations above the bulk superconducting transition temperature Tc. The local regions of phase coherence are associated with a tendency toward charge ordering, a phenomenon found recently in hole-doped cuprates. We use the Cahn-Hilliard equation as a means to phenomenologically model the inhomogeneous charge distribution of the electron system observed experimentally. For this system we perform self-consistent superconducting calculations using the Bogoliubov-deGennes method. Within this context we explore two possible scenarios: (i) the magnetic field is diamagnetically screened by the sum of varying shielding currents of isolated small-sized superconducting domains. (ii) These domains become increasingly correlated by Josephson coupling as the temperature is lowered and the main response to the applied magnetic field is from the sum of all varying tunneling currents. The results indicate that these two approaches may be used to simulate the TF-µSR data but case (ii) yields better agreement.

Separating pairing from quantum phase coherence dynamics above the superconducting transition by femtosecond spectroscopy

In classical superconductors an energy gap and phase coherence appear simultaneously with pairing at the transition to the superconducting state. In high-temperature superconductors, the possibility that pairing and phase coherence are distinct and independent processes has led to intense experimental search of their separate manifestations. Using femtosecond spectroscopy methods we now show that it is possible to clearly separate fluctuation dynamics of the superconducting pairing amplitude from the phase relaxation above the critical transition temperature. Empirically establishing a close correspondence between the superfluid density measured by THz spectroscopy and superconducting optical pump-probe response over a wide region of temperature, we find that in differently doped Bi₂Sr₂CaCu₂O_8+δ crystals the pairing gap amplitude monotonically extends well beyond T_c, while the phase coherence shows a pronounced power-law divergence as T → T_c, thus showing that phase coherence and gap formation are distinct processes which occur on different timescales.

Pairing mechanism for the high-TC superconductivity: symmetries and thermodynamic properties

The pairing mechanism for the high-Tc superconductors based on the electron-phonon (EPH) and electron-electron-phonon (EEPH) interactions has been presented. On the fold mean-field level, it has been proven, that the obtained s-wave model supplements the predictions based on the BCS van Hove scenario. In particular: (i) For strong EEPH coupling and T < T(C) the energy gap (Δtot) is very weak temperature dependent; up to the critical temperature Δtot extends into the anomalous normal state to the Nernst temperature. (ii) The model explains well the experimental dependence of the ratio R(1) ≡ 2Δ(tot)(0)/k(B)T(C) on doping for the reported superconductors in the terms of the few fundamental parameters. In the presented paper, the properties of the d-wave superconducting state in the two-dimensional system have been also studied. The obtained results, like for s-wave, have shown the energy gap amplitude crossover from the BCS to non-BCS behavior, as the value of the EEPH potential increases. However, for T > T(C) the energy gap amplitude extends into the anomalous normal state to the pseudogap temperature. Finally, it has been presented that the anisotropic model explains the dependence of the ratio R(1) on doping for the considered superconductors.

Energy gaps in Bi(2)Sr(2)CaCu(2)O(8+δ) cuprate superconductors

The relationship between the cuprate pseudogap (Δ(p)) and superconducting gap (Δ(s)) remains an unsolved mystery. Here, we present a temperature- and doping-dependent tunneling study of submicron Bi(2)Sr(2)CaCu(2)O(8+δ) intrinsic Josephson junctions, which provides a clear evidence that Δ(s) closes at a temperature T(c) (0) well above the superconducting transition temperature T(c) but far below the pseudogap opening temperature T*. We show that the superconducting pairing first occurs predominantly on a limited Fermi surface near the node below T(c) (0), accompanied by a Fermi arc due to the lifetime effects of quasiparticles and Cooper pairs. The arc length has a linear temperature dependence, and as temperature decreases below T(c) it reduces to zero while pairing spreads to the antinodal region of the pseudogap leading to a d-wave superconducting gap on the entire Fermi surface at lower temperatures.

Insensitivity of the superconducting gap to variations in the critical temperature of Zn-substituted Bi2Sr2CaCu2O(8+δ) superconductors

The phase diagram of the superconducting high-T(c) cuprates is governed by two energy scales: T*, the temperature below which a gap is opened in the excitation spectrum, and T(c), the superconducting transition temperature. The way these two energy scales are reflected in the low-temperature energy gap is being intensively debated. Using Zn substitution and carefully controlled annealing we prepared a set of samples having the same T* but different T(c)'s, and measured their gap using angle-resolved photoemission spectroscopy (ARPES). We show that T(c) is not related to the gap shape or size, but it controls the size of the coherence peak at the gap edge.

Diamagnetism of real-space pairs above T(c) in hole doped cuprates

The nonlinear normal state diamagnetism reported by Li et al (2010 Phys. Rev. B 81 054510) is shown to be incompatible with a claimed Cooper pairing and vortex liquid above the resistive critical temperature. However, it is perfectly compatible with the normal state Landau diamagnetism of real-space composed bosons, which provides a description of the nonlinear magnetization curves of the less anisotropic cuprates La-Sr-Cu-O (LSCO) and Y-Ba-Cu-O (YBCO) as well as for strongly anisotropic bismuth-based cuprates over the whole range of available magnetic fields.

Effects of thermal phase fluctuations in a two-dimensional superconductor: an exact result for the spectral function

We consider the single particle spectral function for a two-dimensional clean superconductor in a regime of strong critical thermal phase fluctuations. In the limit where the maximum of the superconducting gap is much smaller than the Fermi energy we obtain an exact expression for the spectral function integrated over the momentum component perpendicular to the Fermi surface.

High-field μSR studies of superconducting and magnetic correlations in cuprates above T(c)

The advent of high transverse field muon spin rotation (TF-μSR) has led to recent μSR investigations of the magnetic field response of cuprates above the superconducting transition temperature T(c). Here the results of such experiments on hole-doped cuprates are reviewed. Although these investigations are currently ongoing, it is clear that the effects of high field on the internal magnetic field distribution of these materials is dependent upon competition between superconductivity and magnetism. In La(2 - x)Sr(x)CuO(4) the response to the external field above T(c) is dominated by heterogeneous spin magnetism. However, the magnetism that dominates the observed inhomogeneous line broadening below x ∼ 0.19 is overwhelmed by the emergence of a completely different kind of magnetism in the heavily overdoped regime. The origin of the magnetism above x ∼ 0.19 is probably related to intrinsic disorder, but the systematic evolution of the magnetism with doping changes in the doping range beyond the superconducting 'dome'. In contrast, the width of the internal field distribution of underdoped Y Ba(2)Cu(3)O(y) above T(c) is observed to track T(c) and the density of superconducting carriers. This observation suggests that the magnetic response above T(c) is not dominated by electronic moments, but rather inhomogeneous fluctuating superconductivity. The spatially inhomogeneous response of Y Ba(2)Cu(3)O(y) to the applied field may be a means of minimizing energy, rather than being caused by intrinsic disorder.

Chirality induced tilted-hill giant Nernst signal

We reveal a novel source of a giant Nernst response exhibiting strong nonlinear temperature and magnetic field dependence, including the mysterious tilted-hill temperature profile observed in a pleiad of materials. The phenomenon results directly from the formation of a chiral ground state, e.g., a chiral d-density wave, which is compatible with the eventual observation of diamagnetism and is distinctly different from the usual quasiparticle and vortex Nernst mechanisms. Our picture provides a unified understanding of the anomalous thermoelectricity observed in materials as diverse as the hole-doped cuprates and heavy-fermion compounds like URu(2)Si(2).

Specific-heat measurement of a residual superconducting state in the normal state of underdoped Bi_{2}Sr_{2-x}La_{x}CuO_{6+delta} cuprate superconductors

We have measured the magnetic field and temperature dependence of specific heat on Bi_{2}Sr_{2-x}La_{x}CuO_{6+delta} single crystals in wide doping and temperature regions. The superconductivity related specific-heat coefficient gamma_{sc} and entropy S_{sc} are determined. It is found that gamma_{sc} has a humplike anomaly at T_{c} and behaves as a long tail which persists far into the normal state for the underdoped samples, but for the heavily overdoped samples the anomaly ends sharply just near T_{c}. Interestingly, we found that the entropy associated with superconductivity is roughly conserved when and only when the long tail part in the normal state is taken into account for the underdoped samples, indicating the residual superconductivity above T_{c}.

Elucidation of the origins of transport behaviour and quantum oscillations in high temperature superconducting cuprates

A detailed exposition is given of recent transport and 'quantum oscillation' results from high temperature superconducting (HTSC) systems covering the full carrier range from overdoped to underdoped material. This now very extensive and high quality data set is here interpreted within the framework developed by the author of local pairs and boson-fermion resonance, arising in the context of negative- U behaviour within an inhomogeneous electronic environment. The strong inhomogeneity comes with the mixed-valence condition of these materials, which when underdoped lie in close proximity to the Mott-Anderson transition. The observed intense scattering is presented as resulting from pair formation and from electron-boson collisions in the resonant crossover circumstance. The high level of scattering carries the systems to incoherence in the pseudogapped state, p<p(c)(= 0.183). In a high magnetic field the striped partition of the inhomogeneous charge distribution becomes much strengthened and regularized. Magnetization and resistance oscillations, of period dictated by the favoured positioning of the fluxon array within the real space environment of the diagonal 2D charge striping array, are demonstrated to be responsible for the recently reported behaviour hitherto widely attributed to the quantum oscillation response of a much more standard Fermi liquid condition. A detailed analysis embracing all the experimental data serves to reveal that in the given conditions of very high field, low temperature, 2D-striped, underdoped, d-wave superconducting, HTSC material the flux quantum becomes doubled to h/e.

Spin vortices in cuprate superconductors: fictitious magnetic field, fictitious electric field, and persistent current

We theoretically investigate loop currents generated by a Berry phase that arises from spin vortices and argue that a coherent collection of them forms a supercurrent in cuprate superconductors. First, we explain enhanced Nernst signals in cuprates using a fictitious electric field that arises from flow of spin vortices with their centers at sites where lattice-distortion-clad holes (small polaronic holes) reside. Assuming the coexistence of holes in large and small polaron forms, the magnitude of the Nernst signal is shown to be proportional to density and mobility of small polarons, and expressed as e(N) = c(3)T(-1)e(-0.5W(p)/k(B)T)/(1 + (2pim*k(B)T)/(n(s)h(2))e(-W(p)/k(B)T)), where c(3) is a constant, W(p) is the small polaron formation energy, n(s) is the surface density of sites, and m* is the effective mass of the large polaron; by treating unknown parameters as fitting parameters, this formula follows the experimental temperature dependence very well. From the obtained W(p) value, it is indicated that superconductivity occurs at temperatures where almost all of the holes become small polarons; thus, the conventional current generation mechanism is ineffective at temperatures around T(c); however, loop current generation by the spin Berry phase is effective. We calculate the superconducting transition temperature as an order-disorder transition temperature of the loop currents. The doped hole concentration, x, dependence of the transition temperature is obtained as T(c) = T(0) ln x/x(0) and agrees with experimental data, where T(0) and x(0) are treated as fitting parameters. Lastly, we briefly mention an artificial nanostructure that generates a persistent current by utilizing the spin Berry phase.

Visualizing pair formation on the atomic scale and the search for the mechanism of superconductivity in high-T(c) cuprates

We have developed several new experimental techniques, based on the scanning tunneling microscope, to visualize the process of pair formation on the atomic scale and to probe with high precision what controls the strength of pairing in high-T(c) cuprate superconductor compounds. These new experiments provide evidence that pairing in these exotic superconductors occurs above the bulk transition temperature and in nanoscale regions with sizes of 1-3 nm. The high temperature nucleation and proliferation of these nanoscale puddles have a strong connection to the temperature-doping phase diagram of these superconductors. On average we have found that the pairing gap Δ and the temperature at which they first nucleate T(p) follow the simple relation: 2Δ/k(B)T(p)∼8. Moreover, the variations of the pairing strength on the nanoscale can be examined to find microscopic clues to the mechanism of pairing. Specifically, we have found evidence that suggests that strong electronic correlation, as opposed to coupling of electrons to bosons, is responsible for the pairing mechanism in the cuprates. Surprisingly, we have found that nanoscale measurements of electronic correlations in the normal state (at temperatures as high as twice T(c)) can be used to predict the strength of the local pairing interaction at low temperatures.

Emergence of preformed Cooper pairs from the doped Mott insulating state in Bi2Sr2CaCu2O8+delta

Superconductors are characterized by an energy gap that represents the energy needed to break the pairs of electrons (Cooper pairs) apart. At temperatures considerably above those associated with superconductivity, the high-transition-temperature copper oxides have an additional 'pseudogap'. It has been unclear whether this represents preformed pairs of electrons that have not achieved the coherence necessary for superconductivity, or whether it reflects some alternative ground state that competes with superconductivity. Paired electrons should display particle-hole symmetry with respect to the Fermi level (the energy of the highest occupied level in the electronic system), but competing states need not show such symmetry. Here we report a photoemission study of the underdoped copper oxide Bi(2)Sr(2)CaCu(2)O(8+delta) that shows the opening of a symmetric gap only in the anti-nodal region, contrary to the expectation that pairing would take place in the nodal region. It is therefore evident that the pseudogap does reflect the formation of preformed pairs of electrons and that the pairing occurs only in well-defined directions of the underlying lattice.

Evidence for pairing above the transition temperature of cuprate superconductors from the electronic dispersion in the pseudogap phase

In the underdoped high temperature superconductors, instead of a complete Fermi surface above Tc, only disconnected Fermi arcs appear, separated by regions that still exhibit an energy gap. We show that in this pseudogap phase, the energy-momentum relation of electronic excitations near EF behaves like the dispersion of a normal metal on the Fermi arcs, but like that of a superconductor in the gapped regions. We argue that this dichotomy in the dispersion is difficult to reconcile with a competing order parameter, but is consistent with pairing without condensation.

Giant proximity effect in a phase-fluctuating superconductor

When a tunneling barrier between two superconductors is formed by a normal material that would be a superconductor in the absence of phase fluctuations, the resulting Josephson effect can undergo an enormous enhancement. We establish this novel proximity effect by a general argument as well as a numerical simulation and argue that it may underlie recent experimental observations of the giant proximity effect between two cuprate superconductors separated by a barrier made of the same material rendered normal by severe underdoping.

Evidence for two separate energy gaps in underdoped high-temperature cuprate superconductors from broadband infrared ellipsometry

We present broadband infrared ellipsometry measurements of the c-axis conductivity of underdoped RBa_{2}Cu_{3}O_{7-delta} (R=Y, Nd, and La) single crystals. Our data show that separate energy scales are underlying the redistributions of spectral weight due to the normal state pseudogap and the superconducting gap. Furthermore, they provide evidence that these gaps do not share the same electronic states and do not merge on the overdoped side. Accordingly, our data are suggestive of a two gap scenario with a pseudogap that is likely extrinsic with respect to superconductivity.

Nernst effect and diamagnetism in phase fluctuating superconductors

We study superconducting systems in the regime where superconductivity is destroyed by phase fluctuations. We find that the Nernst effect has a much sharper temperature decay than predicted by Gaussian fluctuations, with an onset temperature that tracks Tc rather than the pairing temperature. We find a close quantitative connection with diamagnetism--the ratio of magnetization to transverse thermoelectric conductivity reaches a fixed value at high temperatures. We interpret measurements on underdoped cuprates in terms of a dilute vortex liquid over a wide temperature range above Tc.

Total suppression of superconductivity by high magnetic fields in YBa(2)Cu(3)O(6.6)

We have studied the variation of transverse magnetoresistance of underdoped YBCO(6.6) crystals, either pure or with reduced T(c) down to 3.5 K by electron irradiation, in fields up to 60 T. We find evidence that the superconducting fluctuation contribution to the conductivity is suppressed only above a threshold field H(c)'(T), which is found to vanish at T(c)' > T(c). In the pure YBCO(6.6) sample, H(c)' is already 50 T at T(c). We find that increasing disorder weakly depresses H(c)'(0), T(c)', and T(nu), the onset of the Nernst signal. Thus, these energy scales appear more characteristic of the 2D local pairing than the pseudogap temperature which is not modified by disorder.

Visualizing pair formation on the atomic scale in the high-Tc superconductor Bi2Sr2CaCu2O8+δ

Pairing of electrons in conventional superconductors occurs at the superconducting transition temperature T(c), creating an energy gap Delta in the electronic density of states (DOS). In the high-T(c) superconductors, a partial gap in the DOS exists for a range of temperatures above T(c) (ref. 2). A key question is whether the gap in the DOS above T(c) is associated with pairing, and what determines the temperature at which incoherent pairs form. Here we report the first spatially resolved measurements of gap formation in a high-T(c) superconductor, measured on Bi2Sr2CaCu2O8+delta samples with different T(c) values (hole concentration of 0.12 to 0.22) using scanning tunnelling microscopy. Over a wide range of doping from 0.16 to 0.22 we find that pairing gaps nucleate in nanoscale regions above T(c). These regions proliferate as the temperature is lowered, resulting in a spatial distribution of gap sizes in the superconducting state. Despite the inhomogeneity, we find that every pairing gap develops locally at a temperature T(p), following the relation 2Delta/k(B)T(p) = 7.9 +/- 0.5. At very low doping (< or =0.14), systematic changes in the DOS indicate the presence of another phenomenon, which is unrelated and perhaps competes with electron pairing. Our observation of nanometre-sized pairing regions provides the missing microscopic basis for understanding recent reports of fluctuating superconducting response above T(c) in hole-doped high-T(c) copper oxide superconductors.

Magnetothermoelectric response at a superfluid-Mott-insulator transition

We investigate the finite temperature magnetothermoelectric response in the vicinity of a superfluid-Mott-insulator quantum phase transition. We focus on the particle-hole symmetric transitions of the Bose-Hubbard model, and combine Lorentz invariance arguments with quantum Boltzmann calculations. By means of an epsilon expansion, we find that a nonvanishing thermoelectric tensor and a finite thermal transport coefficient are supported in this quantum critical regime. We comment on the singular Nernst effect in this problem.

Normal-state diamagnetism of charged bosons in cuprate superconductors

Normal-state orbital diamagnetism of charged bosons quantitatively accounts for recent high-resolution magnetometery results near and above the resistive critical temperature T(c) of superconducting cuprates. The parameter-free descriptions of normal-state diamagnetism, T(c), upper critical fields, and specific heat anomalies support the 3D Bose-Einstein condensation of preformed real-space pairs with a zero off-diagonal order parameter above T(c) at variance with phase fluctuation scenarios of cuprates.

Nernst effect and disorder in the normal state of high-T(c) cuprates

We have studied the influence of disorder induced by electron irradiation on the Nernst effect in optimally and underdoped YBa2Cu3O(7-delta) single crystals. The fluctuation regime above T(c) expands significantly with disorder, indicating that the T(c) decrease is partly due to the induced loss of phase coherence. In pure crystals the temperature extension of the Nernst signal is found to be narrow whatever the hole doping, contrary to data reported in the low-T(c) cuprate families. Our results show that the presence of intrinsic disorder can explain the enhanced range of the Nernst signal found in the pseudogap phase of the latter compounds.

Weak magnetic order in the normal state of the high-Tc superconductor La2-xSrxCuO4

We report magnetization measurements in the normal state of the high transition temperature (high-Tc) superconductor La2-xSrxCuO4. A magnetic order in the form of hysteresis in the low-field magnetization is observed at temperatures well above Tc. The doping (x) dependence of the onset and strength of this order follows Tc(x) and falls within the pseudogap regime.

Superfluid density of strongly underdoped cuprate superconductors from a four-dimensional XY model

A new phenomenology is proposed for the superfluid density rhos of strongly underdoped cuprate superconductors based on recent data for ultraclean single crystals of YBa2Cu3O7-x. We show that the puzzling departure from Uemura scaling and the decline of the slope as the Tc=0 quantum critical point is approached can be understood in terms of the renormalization of quasiparticle effective charge by quantum fluctuations of the superconducting phase. We then employ a (3+1)-dimensional XY model to calculate, within particular approximations, the renormalization of rhos and its slope, explain the new phenomenology, and predict its eventual demise close to the quantum critical point.