Precursor Of Superconductivity Research Articles

Superconducting gap and pseudogap

The discovery of the pseudogap has been a fundamental advance in uncovering the new physics of the high-Tc cuprates, yet its meaning is still far from being clear. In particular, its relation to the superconducting gap remains an object of controversy. While many authors consider that it is a high-temperature precursor of superconductivity, which turns into the superconducting gap at low temperatures, others contend that it is a normal-state property related only indirectly to superconductivity. We review a number of experiments such as single-particle tunneling, Andreev–Saint-James reflections, and others, and conclude that in the underdoped regime there exists considerable evidence for the existence of two distinct energy scales, the superconducting gap and the pseudogap, which appear to merge into one another in overdoped samples.

Nickel Impurity-Induced Enhancement of the Pseudogap of Cuprate High-TcSuperconductors

The influence of magnetic Ni and nonmagnetic Zn impurities on the normal-state pseudogap (PG) in the c-axis optical conductivity of (Sm,Nd)Ba(2){Cu(1-y)(Ni,Zn)(y)}(3)O(7-delta) crystals was studied by spectral ellipsometry. We find that these impurities, which strongly suppress superconductivity, have a profoundly different impact on the PG. Zn gives rise to a gradual and inhomogeneous PG suppression while Ni strongly enhances the PG. Our results challenge theories that relate the PG either to precursor superconductivity or to other phases with exotic order parameters, such as flux phase or d-density wave states, that should be suppressed by potential scattering. The apparent difference between magnetic and nonmagnetic impurities instead points towards an important role of magnetic correlations in the PG state.

Metal-to-insulator crossover and pseudogap in single-layerBi2+xSr2−xCu1+yO6+δsingle crystals in high magnetic fields

The in-plane ${\ensuremath{\rho}}_{ab}(H)$ and the out-of-plane ${\ensuremath{\rho}}_{c}(H)$ magneto-transport in magnetic fields up to $28\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ has been investigated in a series of high quality, single crystal, hole-doped La-free Bi2201 cuprates for a wide doping range and over a wide range of temperatures down to $40\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$. With decreasing hole concentration going from the overdoped $(p=0.2)$ to the underdoped $(p=0.12)$ regimes, a crossover from a metallic to an insulating behavior of ${\ensuremath{\rho}}_{ab}(T)$ is observed in the low temperature normal state, resulting in a disorder induced metal insulator transition. In the zero temperature limit, the normal state ratio ${\ensuremath{\rho}}_{c}(H)∕{\ensuremath{\rho}}_{ab}(H)$ of the heavily underdoped samples in pure Bi2201 shows an anisotropic 3-D behavior, in striking contrast with that observed in La-doped Bi2201 and LSCO systems. Our data strongly support that the negative out-of-plane magnetoresistance is largely governed by interlayer conduction of quasiparticles in the superconducting state, accompanied by a small contribution of normal state transport associated with the field dependent pseudogap. Both in the optimal and overdoped regimes, the semiconducting behavior of ${\ensuremath{\rho}}_{c}(H)$ persists even for magnetic fields above the pseudogap closing field ${H}_{\mathit{pg}}$. The method suggested by [Shibauchi et al. Phys. Rev. Lett. 86, 5763 (2001)] for evaluating ${H}_{\mathit{pg}}$ is unsuccessful for both under- and overdoped Bi2201 samples. Our findings suggest that the normal state pseudogap is not always a precursor of superconductivity.

Single-particle spectra and magnetic field effects within precursor superconductivity

We study the single-particle spectra below the superconducting critical temperature from weak to strong coupling within a precursor superconductivity scenario. The spectral-weight function is obtained from a self-energy that includes pairing-fluctuations within a continuum model representing the hot spots of the Brillouin zone. The effects of strong magnetic fields on the pseudogap temperature are also discussed within the same scenario.

Electronic phase diagram of La 2− xSr xCuO 4

In this article, we discuss the electronic phase diagram of a high- T c cuprate La 2− x Sr x CuO 4; namely, how the electronic property changes as functions of temperature T and hole-doping level p. In particular, we focus on four crossover lines, which can be seen in the T dependences of uniform magnetic susceptibility and electronic specific heat. One of them is crossover line T a ( p) in the low doping region below p∼0.05 near the margin of the superconducting regime, which is associated with strongly developed antiferromagnetic (AF) spin correlations within the Cu–O planes. The others are crossover lines T max( p), T ∗(p) and T sf( p) in the normal state in the superconducting regime (0.05< p<0.27); T max >T ∗>T sf >T c. It is suggested that crossover lines T max( p), T ∗(p) and T sf( p) will be associated with the gradual developments of AF spin correlations, a kind of precursor of superconductivity and superconducting critical fluctuations, respectively.

A Hidden Pseudogap under the “Dome” of Superconductivity in Electron‐Doped High‐Temperature Superconductors.

AbstractFor Abstract see ChemInform Abstract in Full Text.

Energy Gap Evolution over Wide Temperature and Doping Ranges in Bi2Sr2CaCu2O8+δ

In this article we report the energy gap evolution in Bi 2 Sr 2 CaCu 2 O 8+δ( Bi2212 ) on the basis of recent tunneling and Raman scattering experiments over wide temperature and hole-doping (p) ranges. It has been demonstrated that in the normal-state electronic excitations, there exist two kinds of pseudogaps (LPG and SPG) with different characteristic energies. The LPG, which is 3 to 4 times larger than the superconducting (SC) gap at T ≪ T c , develops below ~ T max , where the magnetic susceptibility starts to decrease because of the gradual development of antiferromagnetic spin fluctuations. On the other hand, the SPG, whose magnitude is comparable to the SC gap, develops progressively, in addition to the LPG, below the mean-field characteristic temperature T co for d-wave superconductors, and then evolves into the SC gap below T c , suggesting that it will be some kind of precursor of superconductivity. It has also been demonstrated that the maximal gap Δ0 or the gap at the positions near (±π, 0) and (0,±π), determined at T ≪ T c by tunneling technique, does not scale with T c , while the gap around (±π/2,±π/2), determined at T ≪ T c from the coherence peak energy in B 2g Raman spectra, scales with T c , suggesting that the latter gap will function as an effective SC gap Δeff in determining T c . Furthermore, we will report that Δeff is given by the product of p and Δ0; Δ eff ~ 5.3pΔ0 in Bi2212, and discuss some scenarios for the SC transition which is consistent with the present result on the effective SC gap.

A hidden pseudogap under the 'dome' of superconductivity in electron-doped high-temperature superconductors.

The ground state of superconductors is characterized by the long-range order of condensed Cooper pairs: this is the only order present in conventional superconductors. The high-transition-temperature (high-T(c)) superconductors, in contrast, exhibit more complex phase behaviour, which might indicate the presence of other competing ground states. For example, the pseudogap--a suppression of the accessible electronic states at the Fermi level in the normal state of high-T(c) superconductors-has been interpreted as either a precursor to superconductivity or as tracer of a nearby ground state that can be separated from the superconducting state by a quantum critical point. Here we report the existence of a second order parameter hidden within the superconducting phase of the underdoped (electron-doped) high-T(c) superconductor Pr2-xCe(x)CuO4-y and the newly synthesized electron-doped material La2-xCe(x)CuO4-y (ref. 8). The existence of a pseudogap when superconductivity is suppressed excludes precursor superconductivity as its origin. Our observation is consistent with the presence of a (quantum) phase transition at T = 0, which may be a key to understanding high-T(c) superconductivity. This supports the picture that the physics of high-T(c) superconductors is determined by the interplay between competing and coexisting ground states.

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.

The origin of the pseudogap phase: precursor superconductivity versus a competing energy gap scenario

In the last few years evidence has been accumulating that there are a multiplicity of energy scales which characterize superconductivity in the underdoped cuprates. In contrast to the situation in BCS superconductors, the phase coherence temperature T c is different from the energy gap onset temperature T ∗. In addition, thermodynamic and tunneling spectroscopies have led to the inference that the order parameter Δ sc is to be distinguished from the excitation gap Δ; in this way, pseudogap effects persist below T c. It has been argued by many in the community that the presence of these distinct energy scales demonstrates that the pseudogap is unrelated to superconductivity. In this paper, we show that this inference is incorrect. We demonstrate that the difference between the order parameter and excitation gap and the contrasting dependences of T ∗ and T c on hole concentration x and magnetic field H follow from a natural generalization of BCS theory. This simple generalized form is based on a BCS-like ground state, but with self-consistently determined chemical potential in the presence of arbitrary attractive coupling g. We have applied this mean field theory with some success to tunneling, transport, thermodynamics, and magnetic field effects. We contrast the present approach with the phase fluctuation scenario and discuss key features which might distinguish our precursor superconductivity picture from that involving a competing order parameter.

A precursor superconductivity approach to magnetic field effects in the pseudogap phase

We demonstrate that the observed dependences of T c and T ∗ on small magnetic fields can be readily understood in a precursor superconductivity approach to the pseudogap phase. In this approach, the presence of a pseudogap at T c (but not at T ∗) and the associated suppression of the density of states lead to very different sensitivities to pair-breaking perturbations for the two temperatures. Our semi-quantitative results address the puzzling experimental observation that the coherence length ξ is weakly dependent on hole concentration x throughout most of the phase diagram. We present our results in a form which can be compared with the recent experiments of Shibauchi et al. and argue that orbital effects contribute in an important way to the H dependence of T ∗.

Superconducting phase coherence and pairing gap in the three-dimensional attractive Hubbard model

We consider a lattice version of the negative-U Hubbard model in three dimensions, to study the crossover from a superconducting phase transition (dominated by phase fluctuation) to a regime where the amplitude of the superconducting order parameter controls the critical temperature. Starting from a fermionic Hamiltonian, we give a microscopic derivation of the effective action in terms of the relevant physical fields: the modulus and phase of the superconducting order parameter. Furthermore, by employing to the resulting coarse-grained quantum XY model the phase fluctuation algebra between number and phase operators (given by the Euclidean group E 2 ), we map the phase-only action onto a solvable quantum spherical model. We establish the self-consistent theory (involving both fermionic and bosonic degrees of freedom), and calculate the superconducting phase coherence transition temperature T c as a function of the coupling strength U‖, exhibiting a maximum where the behavior crosses over from BCS to Bole-Einstein (BE) condensation. We examine a pseudogap in the normal state which emerges naturally as a precursor of superconductivity at the second characteristic temperature T g due to a state with bound pairs but without long-range phase coherence. Furthermore, we demonstrate that the reduced gaps of the model 2Δ 0 /k B T g ∼4 is almost independent on the pairing strength ‖U‖/t, whereas 2Δ 0 /k B T c increases with increasing ‖U‖ -in striking analogy with the phenomenology of the high-temperature cuprate superconductors when interpreted in terms of the BCS-BC crossover scenario.

Pair and quasiparticle tunneling characteristics of small-sized intrinsic Josephson junctions in Bi 2Sr 2CaCu 2O y

Tunneling properties of small-sized intrinsic Josephson junctions in Bi 2Sr 2CaCu 2O y single crystals have been investigated in order to understand their inherent properties. We have successfully fabricated mesas with lateral dimensions ranging from sub-μm 2 to several tens μm 2 on the same crystal. As a result, a clear gap structure and the normal resistance region could be observed without significant overheating together with typical multiple branches. The gap value, 2 Δ, was about 60 meV at 4.2 K, while the I c R n product was about 2.4 mV. Additionally, we observed that the temperature dependence of I c slightly deviates from the Ambegaoker–Baratoff relation for the s-wave superconductor. This is interpreted as evidence of the d-wave symmetry of the order parameter and coherent interlayer tunneling. We also found that from the simultaneous observation of the superconducting gap and the pseudogap, the pseudogap may be different from the precursor of superconductivity.

A precursor superconductivity approach to magnetic field effects in the pseudogap phase

We study the upper critical field Hc2 (or Tc(H)), and T∗(H) within the pseudogap state, using a mean field scheme which incorporates a strong pairing attraction; for small coupling, g, this approach reduces to BCS theory. However at larger g a pseudogap, Δpg is present at Tc which dramatically changes the behavior of the inferred coherence length ξ, relative to that of BCS theory. Similarly, the quadratic terms in a Ginzburg–Landau description, are modified by Δpg≠0. These pseudogap effects, in accord with experiment, are responsible for the fact that (i) ξ is weakly x-dependent (ii) and Tc is more strongly H dependent than is T∗. Very near the superconductor–insulator transition ξ is predicted to quickly increase.

Implications of tunneling studies on high- Tc cuprates: superconducting gap and pseudogap

Tunneling spectra have been measured on high- T c cuprates including single crystals Bi 2Sr 2− x La x CuO 6+ δ (Bi2201) and Bi 2Sr 2CaCu 2O 8+ δ (Bi2212) using superconductor–insulator–normal metal point contact or superconductor–insulator–superconductor break junction methods. The doping dependence of the energy gap parameter is similar in both Bi2212 and Bi2201, increasing monotonically to very large values in the underdoped regime even as T c decreases. This doping dependence of superconducting gap is similar to that of pseudogap temperature, T *, indicating this is consistent with the scenario whereby the low-energy pseudogap is due to some type of precursor of superconductivity. The high-energy feature observed as the hump structure may be another kind of pseudogap whose energy scale is much larger than superconducting gap, and it may be magnetic in origin.

Magnetic-field effects in the pseudogap phase: A competing energy gap scenario for precursor superconductivity

We study the sensitivity of T_c and T^* to low fields, H, within the pseudogap state using a BCS-based approach extended to arbitrary coupling. We find that T^* and T_c, which are of the same superconducting origin, have very different H dependences. This is due to the pseudogap, \Delta_{pg}, which is present at the latter, but not former temperature. Our results for the coherence length \xi fit well with existing experiments.We predict that very near the insulator \xi will rapidly increase.

Intrinsic tunneling in high- Tc Bi2212 crystals supports a coexistence of superconducting and pseudo-gaps

From intrinsic tunneling spectroscopy, superconducting- and pseudo-gaps could be separated within a wide range of temperatures. We have found that the two gaps have different temperature ( T) and magnetic field ( H) dependencies. The superconducting gap closes both as T→ T c and H→ H c2, while the pseudo-gap does not change neither with T, or H. This would speak in favor of two coexisting phenomena and against the precursor superconductivity scenario of the pseudo-gap.

Superconducting gap and pseudogap from tunneling conductance on Bi 2Sr 2CaCu 2O 8+δ with various oxygen concentration

The evolution of tunneling spectra on Bi 2Sr 2CaCu 2O 8+δ measured by SIN point contacts, SIS break junctions and STM/STS has been studied as a function of doping and temperature. The detailed examinations of the spectra show that the energy gap measured at low temperature appear to be due to superconducting pairing. The doping dependence of the superconducting gap at low temperature suggests a strong connection to the pseudogap temperature, T*, and this indicates that the pseudogap region is at least partly a consequence of some form of precursor superconductivity. In addition, dip/hump structures observed at high bias scale approximately with not only Δ but also superexchange interaction J over the entire doping range examined, indicating these features are linked to the underlying interaction responsible for superconductivity. We suggest that the hump structure may originate from short-range magnetic correlations.

Superconductivity from a pseudogapped normal state: A mode-coupling approach to precursor superconductivity

We derive a phase diagram for the pseudogap onset temperature $T^*$ (associated with the breakdown of the Fermi liquid state, due to strong pairing correlations) and the superconducting instability, $T_c$, as a function of variable pairing strength. Our diagrammatic approach to the BCS - Bose-Einstein cross-over problem self consistently treats the coupling between the single particle and pair propagators, and leads to a continuous evolution of these propagators into the standard $T<T_c$ counterparts. A rich structure is found in $T_c$ which reflects the way in which the superconducting instability at $T_c$ is affected by the pseudogap $\Delta_{pg}$. An important consequence of Cooper-pair- induced pseudogaps is that the magnitude of $T_c$ is sustained, even when $\Delta_{pg}>T_c$.

Preparation of high-temperature superconductor oxide powders by electrodeposition

Superconducting precursor powders have been prepared using an electrodeposition process. The electrodeposition technique deposits all of the precursor components, including Tl, at the same time providing mixing on an atomic scale that reduces the reaction time to the order of minutes to obtain the desired phase development. The magnetization measurements of the annealed powder showed an intrinsic J c of about 10 5 A⧸cm 2 at 77 K in zero field. A current density near 10 4 A⧸cm 2 at 77 K in zero field was obtained for powder-in-tube (PIT) tape processed using electrodeposited precursor. This PIT tape showed the promising single-layer 1223 phase formation.