C. Di Castro

Singular quasiparticle scattering in the proximity of charge instabilities

We analyze the behavior of the dynamic scattering amplitude between Fermi liquid quasiparticles at the Fermi surface in the proximity of a charge instability, which may occur in the high temperature superconducting cuprates. Within the infinite-U Hubbard-Holstein model in the slave-boson large-N technique we find that, in the absence of long-range Coulomb forces the scattering amplitude is strongly singular at zero momentum transfer close to the phase separation instability and it has the same form provided by gauge-field theories. In the presence of long-range Coulomb forces the charge instability occurs at finite wavevectors and concomitantly the scattering is still singular but anisotropic. Nevertheless it remains strong over extended regions of the momentum space. In both cases we show how normal state properties are largely affected by this scattering.

d-wave superconductivity near charge instabilities.

We investigate the symmetry of the superconducting order parameter in the proximity of a phase separation or of an incommensurate charge-density-wave instability. The attractive effective interaction at small or intermediate transferred momenta is singular near the instability. This strongly {ital q}-dependent interaction, together with a residual local repulsion between the quasiparticles and an enhanced density of states for band structures appropriate for the high-temperature superconducting oxides, strongly favors the formation of {ital d}-wave superconductivity. The relative stability with respect to superconductivity in the {ital s}-wave channel is discussed in detail, finding this latter hardly realized in the above conditions. The superconducting temperature is mostly determined by the closeness to the quantum critical point associated with the charge instability and displays a stronger dependence on doping with respect to a simple proximity to a van Hove singularity. The relevance of this scenario and the generic agreement of the resulting phase diagram with the properties displayed by high-temperature superconducting oxides is discussed. {copyright} {ital 1996 The American Physical Society.}

Gap and pseudogap evolution within the charge-ordering scenario for superconducting cuprates

Abstract:We describe the spectral properties of underdoped cuprates as resulting from a momentum-dependent pseudogap in the normal-state spectrum. Such a model accounts, within a BCS approach, for the doping dependence of the critical temperature and for the two-parameter leading-edge shift observed in the cuprates. By introducing a phenomenological temperature dependence of the pseudogap, which finds a natural interpretation within the stripe quantum-critical-point scenario for high- Tc superconductors, we reproduce also the Tc – T* bifurcation near optimum doping. Finally, we briefly discuss the different role of the gap and the pseudogap in determining the spectral and thermodynamical properties of the model at low temperatures.

Non-Fermi-liquid behavior and d-wave superconductivity near the charge-density-wave quantum critical point

AbstractA scenario is presented, in which the presence of a quantum critical point due to formation of incommensurate charge density waves accounts for the basic features of the high temperature superconducting cuprates, both in the normal and in the superconducting states. Specifically, the singular interaction arising close to this charge-driven quantum critical point gives rise to the non-Fermi liquid behavior universally found at optimal doping. This interaction is also responsible for d-wave Cooper pair formation with a superconducting critical temperature strongly dependent on doping in the overdoped region and with a plateau in the optimally doped region. In the underdoped region a temperature dependent pairing potential favors local pair formation without superconducting coherence, with a peculiar temperature dependence of the pseudogap and a non-trivial relation between the pairing temperature and the gap itself. This last property is in good qualitative agreement with so far unexplained features of the experiments.

Metallic phase and metal-insulator transition in two-dimensional electronic systems

The recent experimental observation of a metal-insulator transition in two dimensions prompts a re-examination of the theory of disordered interacting systems. We argue that the existing theory permits the existence of a metallic phase and propose a number of experiments such as magnetoconductance and tunnelling in the presence of a parallel field, which should provide diagnostic tests as to whether a given experimental system is in fact in this regime. We also comment on a generic flow diagram which predicts a maximum metallic resistivity.

Anomalous Isotopic Effect Near the Charge-Ordering Quantum Criticality

Within the Hubbard-Holstein model, we evaluate the crossover lines marking the opening of pseudogaps in the cuprates, which, in our scenario, are ruled by the proximity to a charge-ordering quantum criticality (stripe formation). We find that their isotopic dependence, due to critical fluctuations, implies a substantial positive shift of the pseudogap-formation temperature T(*). We infer that the isotopic shift of the superconducting T(c) is nearly absent in the optimally and overdoped regimes and is negative and increasing upon underdoping. The dynamical nature of the charge-ordering transition may explain the spread of the experimental values of T(*).

Two-gap model for underdoped cuprate superconductors

Various properties of underdoped superconducting cuprates, including the momentum-dependent pseudogap opening, indicate a behavior which is neither BCS- nor Bose-Einstein condensation (BEC)\char21{} like. To explain this issue we introduce a two-gap model. This model assumes an anisotropic pairing interaction among two kinds of fermions with small and large Fermi velocities representing the quasiparticles near the M and the nodal points of the Fermi surface, respectively. We find that a gap forms near the M points resulting in incoherent pairing due to strong fluctuations. Instead, the pairing near the nodal points sets in with phase coherence at lower temperature. By tuning the momentum-dependent interaction, the model allows for a continuous evolution from a pure BCS pairing (in the overdoped and optimally doped regime) to a mixed boson-fermion picture (in the strongly underdoped regime).

STRIPE FORMATION: A QUANTUM CRITICAL POINT FOR CUPRATE SUPERCONDUCTORS

Abstract We discuss the effects of a quantum critical point located nearby optimum doping and related to local charge segregation (stripe phase). The fluctuations in the critical region produce at the same time a strong pairing mechanism and a non-Fermi liquid behavior in the normal phase above the superconducting critical temperature. Superconductivity is a stabilizing mechanism against charge ordering, i.e. the incommensurate charge density wave quantum critical point is unstable with respect to superconductivity. A complete scenario for the cuprates is presented.

Phase separation frustrated by the long-range Coulomb interaction. I. Theory

first-order density-driven phase transitions between two phases in the presence of a compensating rigid background. In the coexistence region we study mixed states formed by regions of one phase surrounded by the other in the case in which the scale of the inhomogeneities is much larger than the interparticle distance. Two geometries are studied in detail: spherical drops of one phase into the other and a layered structure of one phase alternating with the other. In the latter case we find the optimum density profile in an approximation in which the free energy is a function of the local density @local density approximation ~LDA!#. It is shown that an approximation in which the density is assumed to be uniform @uniform density approximation ~UDA!# within each phase region gives results very similar to those of the more involved LDA approach. Within the UDA we derive the general equations for the chemical potential and the pressures of each phase which generalize the Maxwell construction to this situation. The equations are valid for a rather arbitrary geometry. We find that the transition to the mixed state is quite abrupt; i.e., inhomogeneities of the first phase appear with a finite value of the radius and of the phase volume fraction. The maximum size of the inhomogeneities is found to be on the scale of a few electric field screening lengths. Contrary to the ordinary Maxwell construction, the inverse specific volume of each phase depends here on the global density in the coexistence region and can decrease as the global density increases. The range of densities in which coexistence is observed shrinks as the LRC interaction increases until it reduces to a singular point. We argue that close to this singular point the system undergoes a lattice instability as long as the inverse lattice compressibility is finite.

Charge-density waves and superconductivity as an alternative to phase separation in the infinite- U Hubbard-Holstein model

We investigate the density instabilities present in the infinite-U Hubbard-Holstein model both at zero and finite momenta as well as the occurrence of Cooper instabilities with a specific emphasis on the role of long-range Coulomb forces. In carrying out this analysis special attention is devoted to the effects of the strong local e-e interaction on the e-ph coupling and particularly to both the static and dynamic screening processes dressing this coupling. We also clarify under which conditions in strongly correlated electron systems a weak additional interaction, e.g., a phonon-mediated attraction, can give rise to a charge instability. In the presence of long-range Coulomb forces, the frustrated phase separation leads to the formation of incommensurate charge density waves. These instabilities, in turn, lead to strong residual scattering processes between quasiparticles and to superconductivity, thus providing an interesting clue to the interpretation of the physics of the copper oxides. \textcopyright{} 1996 The American Physical Society.