Phase fluctuations and single-fermion spectral density in 2d systems with attraction (original) (raw)
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Pseudogap and spectral function from superconducting fluctuations to the bosonic limit
2002
The crossover from weak to strong coupling for a three dimensional continuum model of fermions interacting via an attractive contact potential is studied above the superconducting critical temperature Tc. The pair-fluctuation propagator, the one-loop self-energy, and the spectral function are investigated in a systematic way from the superconducting fluctuation regime (weak coupling) to the bosonic regime (strong coupling). Analytic and numerical results are reported. In the strongcoupling regime, where the pair fluctuation propagator has bosonic character, two quite different peaks appear in the spectral function at a given wave vector, a broad one at negative frequencies and a narrow one at positive frequencies. The broad peak of the spectral function at negative frequencies is asymmetric about its maximum, with its spectral weight decreasing by increasing coupling and temperature. In this regime, two crossover temperatures T * 1 (at which the two peaks in the spectral function merge in one peak) and T * 0 (at which the maximum of the lower peak crosses zero frequency) can be identified, with Tc ≪ T * 0 < T * 1. By decreasing coupling, the two-peak structure evolves smoothly. In the weak-coupling regime, where the fluctuation propagator has diffusive Ginzburg-Landau character, the overall line-shape of the spectral function is more symmetric and the two crossover temperatures approach Tc. The systematic analysis of the spectral function identifies specific features which allow one to distinguish by ARPES whether a system is in the weak-or strong-coupling regime. Connection of the results of our analysis with the phenomenology of cuprate superconductors is also attempted and rests on the recently introduced two-gap model , according to which a crossover from weak to strong coupling is realized when moving in the Brillouin zone away from the nodal points toward the M points where the d-wave gap acquires its maximum value.
Pseudogap phenomena in the superconducting phase of the cuprates
1999
The presence of a normal state spectral (pseudo) gap at the superconducting transition temperature in the underdoped cuprates has important implications for the associated superconducting phase. We argue that this normal state pseudogap derives from pairing fluctuations, which necessarily persist below ¢ ¡ and which have important implications on the superconducting state. Our Greens function approach, based on the equation of motion method, can be viewed as a a natural extension of BCS theory for sufficiently strong pairing interaction, suggested by the short coherence length of the cuprates. In addition to the usual fermionic excitations, there are also incoherent (but not pre-formed) pairs of finite center of mass momentum which must be self consistently incorporated in computing ¢ ¡ and other superconducting properties, such as the superfluid density and the Josephson critical current. Finally, we discuss some of the experimental implications of our theory for the cuprates.
Phase fluctuations and pseudogap phenomena
Physics Reports, 2001
This article reviews the current status of precursor superconducting phase fluctuations as a possible mechanism for pseudogap formation in high-temperature superconductors. In particular we compare this approach which relies on the twodimensional nature of the superconductivity to the often used T -matrix approach. Starting from simple pairing Hamiltonians we present a broad pedagogical introduction to the BCS-Bose crossover problem. The finite temperature extension of these models naturally leads to a discussion of the Berezinskii-Kosterlitz-Thouless superconducting transition and the related phase diagram including the effects of quantum phase fluctuations and impurities. We stress the differences between simple Bose-BCS crossover theories and the current approach where one can have a large pseudogap region even at high carrier density where the Fermi surface is welldefined. The Green's function and its associated spectral function, which explicitly show non-Fermi liquid behaviour, is constructed in the presence of vortices. Finally different mechanisms including quasi-particle-vortex and vortex-vortex interactions for the filling of the gap above T c are considered. 6.1 The modulus-phase representation for the fermion Green function 87 6.2 The correlation function for the phase fluctuations 88 6.3 The Fourier transform of D(r) 92 6.4 The derivation of the fermion Green's function in Matsubara representation and its analytical continuation 93 6.5 The branch cut structure of G(ω, k) and non-Fermi liquid behaviour 97 7 The spectral function in the modulus-phase representation and filling of the gap 99 7.1 Absence of gap filling for the Green's function calculated for the static phase fluctuations in the absence of spin-charge coupling 99 7.2 Gap filling by static phase fluctuations due to quasi-particle vortex interactions. The phenomenology of ARPES 103 7.3 Gap filling due to dynamical phase fluctuations without quasi-particle vortex interactions 106 8 Concluding remarks 109 A Calculation of the effective potential 111 B Another representation for the retarded Green's function 113 References 114
Pair phase fluctuations and the pseudogap
Physical Review B, 2002
The single-particle density of states and the tunneling conductance are studied for a twodimensional BCS-like Hamiltonian with a d x 2 −y 2-gap and phase fluctuations. The latter are treated by a classical Monte Carlo simulation of an XY model. Comparison of our results with recent scanning tunneling spectra of Bi-based high-Tc cuprates supports the idea that the pseudogap behavior observed in these experiments can be understood as arising from phase fluctuations of a d x 2 −y 2 pairing gap whose amplitude forms on an energy scale set by T M F c well above the actual superconducting transition.
Physical Review B, 1999
We investigate the behavior of the superconducting transition temperature within a previously developed BCS-Bose Einstein crossover picture. This picture, based on a decoupling scheme of Kadanoff and Martin, further extended by Patton, can be used to derive a simple form for the superconducting transition temperature in the presence of a pseudogap. We extend previous work which addressed the case of s-wave pairing in jellium, to explore the solutions for Tc as a function of variable coupling in more physically relevant situations. We thereby ascertain the effects of reduced dimensionality, periodic lattices and a d-wave pairing interaction. Implications for the cuprate superconductors are discussed.
Quantum phase fluctuations responsible for pseudogap
Physica C: Superconductivity, 2002
The effect of ordering field phase fluctuations on the normal and superconducting properties of a simple 2D model with a local four-fermion attraction is studied. Neglecting the coupling between the spin and charge degrees of freedom an analytical expression has been obtained for the fermion spectral function as a single integral over a simple function. From this we show that, as the temperature increases through the 2D critical temperature and a nontrivial damping for a phase correlator develops, quantum fluctuations fill the gap in the quasiparticle spectrum. Simultaneously the quasiparticle peaks broaden significantly above the critical temperature, resembling the observed pseudogap behavior in high-Tc superconductors.
Pseudogap transition within the superconducting phase in the three-band Hubbard model
2019
The onset of the pseudogap in high-T_c superconducting cuprates (HTSC) is marked by the T^* line in the doping-temperature phase diagram, which ends at a point p^* at zero temperature within the superconducting dome. There is no general consensus on how the pseudogap manifests itself within the superconducting phase. We use cluster dynamical mean field theory on a three-band Hubbard model for the HTSC to study the superconducting phase at T=0 K, obtained when doping the correlated insulator, for two different sets of band parameters and for several values of U. We observe a first-order transition within the superconducting phase, which we believe, marks the onset of the pseudogap. Further, we also observe that the d-wave node vanishes within the superconducting phase at low values of hole doping, lower than that at which the first-order transition occurs. Various aspects of the results and their implications are discussed.
Reports on Progress in Physics, 2016
The anomalous transport and thermodynamic properties in the quantum-critical region, in the cuprates, and in the quasi-two dimensional Fe-based superconductors and heavy-fermion compounds, have the same temperature dependences. This can occur only if, despite their vast microscopic differences, a common statistical mechanical model describes their phase transitions. The antiferromagnetic (AFM)-ic models for the latter two, just as the loop-current model for the cuprates, map to the dissipative XY model. The solution of this model in 2+1 D reveals that the critical fluctuations are determined by topological excitations, vortices and a variety of instantons, and not by renormalized spin-wave theories of the Landau-Ginzburg-Wilson type, adapted by Moriya, Hertz and others for quantum-criticality. The absorptive part of the fluctuations is a separable function of momentum q, measured from the ordering vector, and of the frequency ω and the temperature T which scale as tanh(ω/2T) at criticality. Direct measurements of the fluctuations by neutron scattering in the quasi-two-dimensional heavy fermion and Fe-based compounds, near their antiferromagnetic quantum critical point, are consistent with this form. Such fluctuations, together with the vertex coupling them to fermions, lead to a marginal fermi-liquid, with the imaginary part of the self-energy ∝ max(ω, T) for all momenta, a resistivity ∝ T , a T ln T contribution to the specific heat, and other singular fermi-liquid properties common to these diverse compounds, as well as to d-wave superconductivity. This is explicitly verified, in the cuprates, by analysis of the pairing and the normal self-energy directly extracted from the recent high resolution angle resolved photoemission measurements. This reveals, in agreement with the theory, that the frequency dependence of the attractive irreducible particle-particle vertex in the d-wave channel is the same as the irreducible particle-hole vertex in the full symmetry of the lattice.
Effect of pairing fluctuations on low-energy electronic spectra in cuprate superconductors
Physical Review B, 2011
High-temperature superconductivity in holedoped cuprates, accompanied by a 'pseudogap phase' as well as other strange phenomena, continues to be an outstanding question in condensed matter physics for a quarter of a century now 1 . Over the years, Angle Resolved Photo Emission Spectroscopy (ARPES) 2 has uncovered a number of unusual spectral properties of electrons with definite in-plane momenta near the Fermi energy. We describe here a minimal theory of tight binding electrons moving on the square planar Cu lattice of the cuprates, mixed quantum mechanically with pairs of them (Cooper pairs). Superconductivity occurring at the transition temperature T c is the long-range phase coherence of Cooper pairs with d-wave symmetry. Fluctuations necessarily associated with incipient long-range superconducting order have a generic large-distance behaviour near T c . We calculate the spectral density of electrons coupled to such Cooper pair fluctuations and show that many features observed in ARPES experiments on different cuprates above T c as a function of doping and temperature emerge naturally in this description. These features include 'Fermi arcs' with temperature-dependent length and an antinodal pseudogap which fills up linearly as the temperature increases towards the pseudogap temperature. Below T c , the effects of nonzero superfluid density and thermal fluctuations are calculated and compared successfully with experiment.