We demonstrate how resonant pair scattering of correlated electrons above Tc can give rise to pseudogap behavior. This resonance in the scattering T-matrix appears for superconducting interactions of intermediate strength, within the framework of a simple fermionic model. It is associated with a splitting of the single peak in the spectral function into a pair of peaks separated by an energy gap. Our physical picture is contrasted with that derived from other T-matrix schemes, with superconducting fluctuation effects, and with preformed pair (boson-fermion) models. Implications for photoemission and tunneling experiments in the cuprates are discussed.PACS numbers: 74.20. Mn, 74.25.Fy, 74.25.Nf, It has become clear in recent years that the presence of a pseudogap above the superconducting transition temperature, T c , is a robust feature of the underdoped cuprates. This phenomenon is manifested in thermodynamic [1], magnetic [2], and angle-resolved photoemission spectroscopy (ARPES) data [3]. These ARPES experiments, which have established the presence of a Luttinger volume Fermi surface, place important constraints on any pseudogap scenario: they indicate that the pseudogap appears directly in the spectral function and its magnitude and symmetry [3] seem to evolve smoothly into that of the superconducting state. Furthermore, the minimum gap points in the pseudogap regime retrace the normal state Fermi surface [4].A variety of theoretical scenarios have been proposed, for the origin of the pseudogap. Quantum Monte Carlo simulation studies have been carried out on both positive and negative U Hubbard models [5]. Alternative models relate the pseudogap to either magnetic pairing of spins [6], RVB-like pairing of chargeless spinons [7], or precursor superconductivity effects [8]. The present paper addresses this last scenario, in part because of constraints from ARPES data and in part, because the cuprates are short coherence length, quasi-two dimensional superconductors, with anomalously low plasma frequencies [8,9]. They are, therefore, expected to exhibit important deviations from an abrupt, BCS-like transition.In our physical picture, we associate an important component of the cuprate pseudogap with resonant scattering between electrons of opposite spin and small total momentum. This resonance arises in the presence of intermediate coupling and a sizeable Fermi surface. A depression in the density of states occurs because states near this Fermi surface are unavailable for electrons in the Fermi sea to scatter into; such states are otherwise occupied by relatively long lived (metastable) electron pairs. The related suppression in the spectral weight differs from that derived from conventional low frequency and long wavelength fluctuation effects [10]. In the present case it is the strength of the attractive interaction, rather than the critical slowing down (in proximity to T c ), which leads to the long-lived pair states. It should be noted that our resonant scattering approach is to be distinguished from previo...

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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, Tc, 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 < Tc counterparts. A rich structure is found in Tc which reflects the way in which the superconducting instability at Tc is affected by the pseudogap ∆pg. An important consequence of Cooper-pairinduced pseudogaps is that the magnitude of Tc is sustained, even when ∆pg > Tc.PACS numbers: 74.20. Mn, 74.25.Fy, 74.25.Nf, It is generally agreed that the pseudogap state of the underdoped cuprates represents some type of pairing above T c which is postulated to derive from neutral spinon pairs [1], spin [2] or charge [3] density wave states, or from some form of (2e) Cooper pairing which foreshadows the ultimate superconducting state. Each of these scenarios must not only address the nature of the exotic (ie., pseudogapped) normal state but also the transition from this state to its associated superconducting instability. Indeed, there is an extensive literature on the problem of establishing superconductivity in the presence of gaps in the electronic spectral function [4]. In this paper we investigate this issue under the presumption that the normal state spectral function gap is associated with Cooper pairing above T c . Moreover, by self-consistently coupling the single particle and pair properties we establish the nature and physics of the pseudogap state. In this coupled scheme, we demonstrate how gapping in the electronic spectrum affects T c and argue that this 2e pairing is not particularly deleterious to the superconductivity, despite the relatively large size of the pseudogap (∆ pg > T c ). Our results are consolidated into a phase diagram in which the pseudogap phase occupies a large temperature range in the limit of moderately strong superconducting coupling.An important contribution of this paper is to revisit the BCS -Bose Einstein cross-over problem [5] using a conserving diagrammatic "mode coupling" formulation. Above T c this approach leads to one and two electron Green's functions which are formally continuous with their below T c counterparts obtained in the standard theory of superconductivity. This approach also reproduces the expected limits associated with the extreme weak and strong coupling regimes of previous saddle point schemes [6]. The intermediate coupling regime is of particular importance to the cuprates and Monte Carlo simulations [7] suggest that deviations from Fermi liquid behavior are present there. Our previous diagrammatic calculations [8] indicate that long lived pairs introduce a gap in the electronic spectral function by blocking available single particle states around the Fermi surface. This gap correlates...

We study the order parameter symmetry in bi-layer cuprates such as YBaCuO, where interesting π phase shifts have been observed in Josephson junctions. Taking models which represent the measured spin fluctuation spectra of this cuprate, as well as more general models of Coulomb correlation effects, we classify the allowed symmetries and determine their associated physical properties. π phase shifts are shown to be a general consequence of repulsive interactions, independent of whether a magnetic mechanism is operative. While it is known to occur in d-states, this behavior can also be associated with (orthorhombic) s-symmetry when the two sub-band gaps have opposite phase. Implications for the magnitude of Tc are discussed.PACS numbers: 74.20.Mn, 74.50.+r, The observation in YBCO of unusual Josephson junction behavior 1-4 is one of the most important experimental results to emerge from the cuprate literature in recent years. Here in a Josephson SQUID experiment the two junctions are configured so that their normals lie along the a and b axes of the CuO 2 plane. This measurement has been widely interpreted as support for a d-symmetry of the order parameter, as well as for a magnetic mechanism for superconductivity. In this paper we show that both of these inferences may be inappropriate. For notational precision, throughout this paper we use the terms s-( or d-) symmetry to correspond to states which have the same (or opposite) sign under a π/2 rotation. Thus the d-states under consideration are not necessarily of the specific d x 2 −y 2 form.The gap equation for bi-layer systems has been studied earlier in the context of a magnetic mechanism for superconductivity 5,6 . There it was observed that the d-symmetric state of the single layer problem, is transformed to a pair of in-phase d states on each of the two sub-bands, and that these compete with a pair of outof-phase s-states. Here we take the problem to a greater level of generality, establishing that this situation persists for a wide class of repulsive interactions, which are unrelated to the antiferromagnetic spin fluctuation picture. Alternate classes of the order parameter symmetry are also generated. These correspond to in-phase s-states and out-of-phase d-states. We establish how the relative stability of the two competing states is affected by changes in bandstructure, orthorhombicity, and hole filling.It should not be surprising that d-states have a more general origin beyond the antiferromagnetic spin exchange models. In a one layer cuprate, the lattice symmetry requires that all gap states are either even (s-) or odd (d-) under a π/2 rotation. In bi-layer systems, these one layer states generalize naturally to a pair of even or odd, in-phase or out-of-phase states, associated with each of the two sub-bands. Thus, as one of two allowed states, d-symmetry should be widespread, and independent of the microscopic details of the model.In the presence of both intra-and inter-layer interactions (V and V ⊥ ), the weak coupling BCS gap equation becomes a set...

We extend previous work on pre-formed pair models of superconductivity to incorporate Coulomb correlation effects. For neutral systems, these models have provided a useful scheme which interpolates between BCS and Bose Einstein condensation with increasing coupling and thereby describes some aspects of pseudo-gap phenomena. However, charge fluctuations (via the plasmon, ωp) significantly modify the collective modes and therefore the interpolation behavior. We discuss the resulting behavior of the pseudo-gap and thermodynamic quantities such as Tc, χ and Cv as a function of ωp.The role of the pseudo-gap 1 in the high T c cuprates is emerging as an important indicator of the nature of the superconductivity as well as the normal state. There are two widely discussed but competing explanations for pseudo-gap effects but no clear and decisive experiments to support one scenario over the other. Early observations associated the pseudo-gap with magnetic pairing 2 above T c (often called the "spin gap"). It is now clear, however, that some form of normal state pairing is seen in photoemission as well as charge transport data. Moreover, at least in the photoemission data the pseudo-gap appears to have the d-wave symmetry 1 of the ordered state and this leads naturally to the association of this "gap" with precursor superconductivity. 3-5 This second scenario is further supported by the observation of low dimensionality and short coherence lengths in high T c superconductors, which suggests important deviations from ideal mean field or BCS transitions. Indeed, the approach of the present paper assumes the precursor superconductivity scenario, in large part because it is important to establish, at least as a base-line, the extent to which such superconducting "fluctuation" effects may be responsible for pseudo-gap behavior.Among those models which subscribe to a precursor superconductivity scenario there are additionally two rather distinct viewpoints. Emery and Kivelson 5 have argued that the pseudo-gap state of the cuprates is similar to that observed in granular films where phase coherence is not fully established, although large regions of the material have a well established superconducting amplitude. Because it is small, in some sense, in the cuprates their approach focuses on n/m * or alternatively on the plasma frequency ω p as the key "phase stiffness" parameter. Alternatively, others 3,4,6,7 have focused on the observed small size of the superconducting correlation length ξ to argue for important corrections to BCS theory associated with pre-formed or nearly-formed pairs 8 which exist well above T c and therefore give rise to significant pseudo-gap effects. The present paper is based on the viewpoint that in the cuprates the characteristic parameter of the charge degrees of freedom, n/m * or equivalently ω p , should be treated on a relatively equal footing with the correlation length, ξ.To study the role of Coulomb interactions on pseudogap phenomena, we adopt a natural microscopic framework which incoporates ch...

In this paper we classify the allowed order parameter symmetries in multilayer cuprates and discuss their physical consequences, with emphasis on Josephson tunneling and impurity scattering. Our solutions to the gap equation are based on highly non-specific forms for the inter-and intra-plane pairing interactions in order to arrive at the most general conclusions. Within this framework, the bi-layer (N = 2) case is discussed in detail with reference to YBCO and BSCCO and the related Landau-Ginzburg free energy functional. Particular attention is paid to the role of small orthorhombic distortions as would derive from the chains in YBCO and from superlattice effects in BSCCO, which give rise to a rich and complex behavior of the multilayer order parameter. This order parameter has N components associated with each of the N bands or layers. Moreover, these components have specific phase relationships. In the orthorhombic bi-layer case the (s, −s) state is of special interest, since for a wide range of phase space, this state exhibits π phase shifts in corner Josephson junction experiments. In addition, its transition temperature is found to be insensitive to non-magnetic inter-plane disorder, as would be present at the rare earth site in YBCO, for example. Of particular interest, also, are the role of van Hove singularities which are seen to stabilize states with d x 2 −y 2 -like symmetry, (as well as nodeless s-states) and to elongate the gap functions along the four van Hove points, thereby leading to a substantial region of gaplessness. We find that d x 2 −y 2 -like states are general solutions for repulsive interactions; they possess the fewest number of nodes and therefore the highest transition temperatures. In this way, they should not be specifically associated with a spin fluctuation driven pairing mechanism.

␦͑Si͒-doped GaAs samples grown by metalorganic vapor phase epitaxy are studied by capacitancevoltage and deep level transient spectroscopy ͑DLTS͒ techniques. A detailed analysis of the DLTS signal ͑including spatial profiles͒ is performed. DLTS spectra exhibit a clear development depending on the sheet dopant concentration ranging from 5ϫ10 14 to 2ϫ10 16 m Ϫ2 . Two observed peaks do not change its activation energy with the doping level while their amplitude increases rapidly when the doping rises. We assign them to defects generated by high silicon concentration, probably related to gallium vacancy. Another peak in the most densely doped sample seems to correspond to the DX level which is occupied near the ␦ layer. Peculiar features of the EL2 level are observed in ␦-doped GaAs and explained by the band bending due to the dopant sheet. No indication of the emission from the quantum confinement states is found in DLTS spectra taken at temperatures 80-400 K.

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