The description of heteropairs like 40 K- 6 Li near and in the superconducting state requires a fully self-consistent theory (see H anai R. and O hashi Y., Phys. Rev. A , 90 (2014) 043622). We derive analytic pseudogap Green's functions for the “normal” and superconducting states from the Luttinger-Ward theory with the T -matrix in the static separable approximation. The self-consistency in the closing loop of self-energy has two pronounced effects on the single-particle spectrum. First, the single-particle excitations decay before the asymptotic quasiparticle propagation is established, therefore the normal state is not a Fermi liquid. Second, the pseudogap has a V shape even for s -wave pairing. The V-shaped pseudogap and the U-shaped BCS gap interfere resulting in slope breaks of the gap walls and the in-gap states in the density of states. Various consequences of an incomplete self-consistency are demonstrated.
The description of heteropairs like 40 K- 6 Li near and in the superconducting state requires a fully self-consistent theory (see H anai R. and O hashi Y., Phys. Rev. A , 90 (2014) 043622). We derive analytic pseudogap Green's functions for the “normal” and superconducting states from the Luttinger-Ward theory with the T -matrix in the static separable approximation. The self-consistency in the closing loop of self-energy has two pronounced effects on the single-particle spectrum. First, the single-particle excitations decay before the asymptotic quasiparticle propagation is established, therefore the normal state is not a Fermi liquid. Second, the pseudogap has a V shape even for s -wave pairing. The V-shaped pseudogap and the U-shaped BCS gap interfere resulting in slope breaks of the gap walls and the in-gap states in the density of states. Various consequences of an incomplete self-consistency are demonstrated.
Abstract In the normal state of a superfluid condensate, like the Bardeen–Cooper–Schrieffer (BCS) superconducting state, we do not expect a gapped feature in the single-particle spectral function. Here we calculate the spectral function and single-particle density of states (DOS) of ultracold Fermi gases at different temperatures in the normal state. The calculation is conducted based on the non-self-consistent T -matrix approximation (nTMA) with particle–hole fluctuation. It is found that a dip structure emerges in the DOS above the superfluid phase-transition temperature T c . We attribute this dip structure to the pseudogap, and its temperature is determined. From the temperature dependence of the spectral function, we also find another characteristic temperature where a two-peak structure disappears. The results provide deep insight into the superfluid condensate formed by ultracold fermions.
Starting from the Friedberg-TD Lee Hamiltonian describing a coexisting and dynamically interacting many-particle binary boson-fermion gas mixture with a coupling $(\ensuremath{\lambda})$-dependent gap $2\ensuremath{\Delta}(\ensuremath{\lambda})$ in the boson dispersion relation for the s-wave Cooper or BCS model interaction, we deduce several observed characteristic features of high-temperature superconductors at the simplest level. Analytic expressions for both the unpaired-fermion and boson number densities, as well for the fermion chemical potential $\ensuremath{\mu}(\ensuremath{\lambda},T)$, all of which vary with the degree of bosonization and with temperature T, are derived in detail using two-time, finite-temperature Green function techniques. Simple implicit formulas are then obtained for both two and three dimensions for the pseudogap T∗ and Bose-Einstein condensation Tc temperatures in terms of $\ensuremath{\mu}(\ensuremath{\lambda},T)$ and $2\ensuremath{\Delta}(\ensuremath{\lambda})$. In particular, even at the s-wave level we find a self-consistent description of the generic phase diagram observed in cuprates, including the appearance of a pseudogap and a dome-shaped Tc vs doping behavior both of which hinge on the gapped boson spectrum.
We investigate the pseudogap onset temperature T∗, the superconducting transition temperature Tc and the general nature of the pseudogap phase using a diagrammatic BCS-Bose Einstein crossover theory. This decoupling scheme is based on the pairing approximation of Kadanoff and Martin, further extended by Patton (KMP). Our consideration of the KMP pairing approximation is driven by the objective to obtain BCS like behavior at weak coupling, (which does not necessarily follow for other diagrammatic schemes). The breakdown of the Fermi liquid state at T∗ is investigated within the lowest order theory and is associated with intermediate values of the coupling. The superconducting instability Tc is evaluated by introducing mode coupling effects, in which the long lived pairs are affected by the single particle pseudogap states and vice versa. Our Tc equations, which turn out to be rather simple as a result of the KMP scheme, reveal a rich structure as a function of g in which the pseudogap is found to compete with superconductivity. Our results are compared with alternate theories in the literature.
The quasiparticle and spin excitation spectra in the 2D Hubbard model are calculated self-consistently as functions of momentum on the real frequency axis. Near half filling we obtain in the normal state a pseudogap in the density of states. The pairing state has ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ symmetry. Below Tc, gaps open rapidly in the frequency spectra of the gap function, the quasiparticle scattering rate, and the density of states. The scattering rate and spin-lattice relaxation rate drop abruptly below Tc. Our results are consistent with experiments on ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Cu}{\mathrm{O}}_{4}$.
We investigate strong-coupling properties of a unitary Fermi gas consisting of two different species with different masses. Including pairing fluctuations within the self-consistent T -matrix approximation, we calculate the single-particle density of states in the normal state. We show that the pseudogap phenomenon, which is characterized by a dip structure in the density of states around ω = 0, appears more remarkably in the light mass component than in the heavy mass component. As a result, the pseudogap temperature, which is determined as the temperature at which the pseudogap disappears in the density of states, is higher in the former than in the latter. We also find that this different pseudogap temperatures lead to the existence of two kinds of pseudogap regions. That is, one is the ordinary pseudogap regime where the pseudogap appears in both the component, and the other case is that the light mass component only exhibits the pseudogap phenomenon. As the origin of these component- dependent pseudogap phenomena, we point out the importance of different Fermi temperatures between the two components. Since the formation of hetero-Cooper pairs and their condensation are expected in various systems, such as a 6 Li- 40 K Fermi gas mixture, an exciton (polariton) gas, as well as color superconductivity, our results would be useful for the understanding of strong-coupling properties of these novel Fermi condensates.
We have studied the pseudogap formation in the single-particle spectra of the half-filling two-dimensional Hubbard model. Using a Green's function with the one-loop self-energy correction of the spin and charge fluctuations, we have numerically calculated the self-energy, the spectral function, and the density of states in the weak-coupling regime at finite temperature. Pseudogap formations have been observed in both the density of states and the spectral function at the Fermi level. The pseudogap in the spectral function is explained by the non-Fermi-liquid-like nature of the self-energy. The anomalous behavior in the self-energy is caused by both the strong antiferromagnetic spin fluctuation and the nesting condition on the non-interacting Fermi surface. In the present approximation, we find a logarithmic singularity in the integrand of the imaginary part of the self-energy. Concerning the energy dependence of the spectral function and the self-energy, two theorems are proved. They give a necessary condition in the self-energy to produce the pseudogap at the Fermi level. The pseudogap in the spectral function is highly momentum dependent on the Fermi surface. It opens initially in the (±π,0), (0,±π) regions as the normal state pseudogap observed in the high-Tc superconductors and if the interaction is increased, it spreads to other Fermi surface sectors. The anisotropy of the pseudogap is produced by the low-energy enhancement of the spin excitation around Q=(π,π) and the flatness of the band dispersion around the saddle point.