We compute the condensation energy in the spin-fermion model using Scalapino-White relation between the condensation energy and the change in the dynamical structure factor in the normal and the superconducting states. We show that for parameters relevant to cuprates, the extra low-frequency spectral weight associated with the resonance peak in the dynamical structure factor in a superconductor is not compensated up to energies $\ensuremath{\sim}J$ which are much larger than the superconducting gap $\ensuremath{\Delta}.$ We argue that in this situation, the condensation energy is large and well accounts for the data for cuprates.
We compute the condensation energy in the spin-fermion model using Scalapino-White relation between the condensation energy and the change in the dynamical structure factor in the normal and the superconducting states. We show that for parameters relevant to cuprates, the extra low-frequency spectral weight associated with the resonance peak in the dynamical structure factor in a superconductor is not compensated up to energies \ensuremath∼J which are much larger than the superconducting gap \ensuremathΔ. We argue that in this situation, the condensation energy is large and well accounts for the data for cuprates.
We present the full analysis of the normal state properties of the spin-fermion model near the antiferromagnetic instability in two dimensions. The model describes low-energy fermions interacting with their own collective spin fluctuations, which soften at the antiferromagnetic transition. We argue that in 2D, the system has two typical energies—an effective spin-fermion interaction g¯ and an energy ωsf below which the system behaves as a Fermi liquid. The ratio of the two determines the dimensionless coupling constant for spin-fermion interaction λ2 ∝ g¯/ωsf. We show that λ scales with the spin correlation length and diverges at criticality. This divergence implies that the conventional perturbative expansion breaks down. We develop a novel approach to the problem—the expansion in either the inverse number of hot spots in the Brillouin zone, or the inverse number of fermionic flavours—which allows us to explicitly account for all terms which diverge as powers of λ, and treat the remaining, O(log λ) terms in the RG formalism. We apply this technique to study the properties of the spin-fermion model in various frequency and temperature regimes. We present the results for the fermionic spectral function, spin susceptibility, optical conductivity and other observables. We compare our results in detail with the normal state data for the cuprates, and argue that the spin-fermion model is capable of explaining the anomalous normal state properties of the high T c materials. We also show that the conventional {4 theory of the quantum-critical behaviour is inapplicable in 2D due to the singularity of the {4 vertex.
Fundamentals of fermion-condensation physics are outlined. Fermion condensation is a phase transition occurring in a strongly correlated Fermi system upon a topological reconstruction of the Landau ground state and leading to the formation of a fermion condensate that possesses the dispersionless single-particle spectrum ϵ(p)=0 in the momentum-space region adjacent to the Fermi surface and, accordingly, an anomalously enhanced density of single-particle states. A original method is developed for solving the set of nonlinear integral equations of fermion-condensation theory. This method makes it possible to analyze the problem of quantum chaos in strongly interacting multifermion systems. The computational technique used is demonstrated by applying it to superdense quark–gluon plasma, where the structure of exchange quark–quark interaction is well known. In electron systems featuring a fermion condensate, the magnitude of the gap appearing in the single-particle spectrum owing to Cooper pairing is shown to be much larger than that in Bardeen–Cooper–Schrieffer (BCS) theory. This explains both a high superconducting-transition temperature Tc and, with allowance for C4 crystal-lattice symmetry, the D -wave pairing-gap structure observed in cuprates. It is found that, in addition to the BCS gap Δ , the spectrum of single-particle excitations of superconducting systems where a fermion condensate is present develops a nonsuperconducting gap Υ that owes its existence to the interaction of condensate particles with normal quasiparticles residing outside the condensate region in momentum space. The question of whether these results are pertinent to the two-gap structure recently unearthed in the excitation spectrum of cuprates upon analyzing ARPES data is addressed.
The cold atomic Fermi gas has become the essential paradigm for understanding the crossover between the weak coupling Bardeen-Schrieffer-Cooper (BCS) and strong coupling Bose-Einstein Condensation (BEC) regimes of paired fermion condensates. On tuning the pairing interactions through the crossover, the superfluid condensate becomes maximally robust between the BCS and BEC regimes at what is referred to as the unitary point, giving rise to a maximally peaked phase transition anomaly in the specific heat. We find here, by tracing the jump \Delta\gamma in the electronic specific heat coefficient \gamma at the transition temperature Tc as a function of the gap ratio 2\Delta/kTc, that this same thermodynamic signature occurs in the high-Tc superconducting cuprates. On taking \Delta as the pairing gap in a cold atomic Fermi gas and as the antinodal pseudogap energy in the cuprates, we find \Delta\gamma to be asymmetrically peaked at the same value 2\Delta/kTc~6.5. We show that the observation of this peak in the cuprates, and its coincidence with a normal state maximum in \gamma, provides a previously overlooked thermodynamic signature of condensation at a unitary point.
The frequency dependence of the superconducting gap function represents the dynamics of the electrons forming the Cooper pairs. Bearing the high-temperature superconducting cuprates in mind, we calculate the superconducting gap function in the two-dimensional Hubbard model by means of a cluster extension of the dynamical mean-field theory. We scrutinize the frequency dependence and its change with temperature, doping concentration and interaction strength. The calculated superconducting gap function shows various different behaviors from the anomalous self-energy, owing to a strong frequency dependence of the normal self-energy. The calculated results also suggest that the superconductivity is stronger when the interaction strength is as large as or slightly smaller than the bare band width and is suppressed for larger interactions.
We consider the slave-fermion Schwinger-boson decomposition of an effective model obtained through a systematic low-energy reduction of the three-band Hubbard Hamiltonian. The model includes a three-site term t ′′ similar to that obtained in the large- U limit of the Hubbard model but of opposite sign for realistic or large O-O hopping. For parameters close to the most realistic ones for the cuprates, the mean-field solution exhibits d + s superconductivity (predominantly d x 2 − y 2 ) with a dependence on doping x very similar to the experimentally observed. We also obtained incommensurate peaks at wave vectors ∼ π(1,1 ± 2 x ) in the spin structure factor, which also agree with experiment.
We construct and analyze a lattice generalization of the Yukawa-Sachdev-Ye-Kitaev model, where spinful fermions experience onsite, random, all-to-all interactions with an Einstein bosonic mode, and random intersite coherent hopping. We obtain the exact self-consistent numerical solution of the model at mean-field level, and analytical approximations, for all values of fermion-boson coupling and hopping, under the spin-singlet ansatz and at particle-hole symmetry, both in the normal and superconducting states, thus tracing the entire phase diagram. In the normal state, the competition between hopping and coupling leads to crossovers between Fermi-liquid and non-Fermi-liquid states, as reflected by the fermionic and bosonic spectral functions and the normal-state entropy. We calculate the finite phase stiffness of the superconducting state through the equilibrium electromagnetic response. Furthermore, we study the critical temperature Tc, as well as the spectral functions, the quasiparticle weight, the gap, and the condensation energy in the superconducting state. At weak coupling, we retrieve a disordered generalization of Bardeen-Cooper-Schrieffer theory. At strong coupling, asymptotically Tc saturates but the stiffness decreases, which suggests strong superconducting fluctuations. Tc is maximum in the single-dot limit, while the stiffness peaks exactly at the crossover between non-Fermi-liquid and Fermi-liquid phases. We discover that the quasiparticle weight, the stiffness, and the condensation energy, are all correlated as a function of coupling, reminiscent of the correlations observed in high-temperature cuprate superconductors.