A weak-coupling scenario wherein bosonic preformed electron pairs emerge upon cooling from two-electron correlations can explain the pseudogap phase consisting of segments where a Bogoliubov-like energy-momentum relation gapped spectrum alternates with a normal ungapped one. Bose–Einstein condensation (BEC) of preformed pairs interacting with the background fermions leads to either - or -wave-like superconducting gaps, the result being sensitive to the magnitude of the total number density of pairs at which BEC occurs and becomes possible already for a moderately anisotropic -wave pairing of fermions repelling each other via isotropic coulombic forces. The present model is compatible with the coexistence of pseudogap and of superconductivity phenomena.
The pseudogap state of cuprate high-temperature superconductors has been often viewed as either a yet unknown competing order or a precursor state to superconductivity. While awaiting the resolution of the pseudogap problem in cuprates, we demonstrate that local pairing fluctuations, vortex liquid dynamics, and other precursor phenomena can emerge quite generally whenever fermionic excitations remain gapped across the superconducting transition, regardless of the gap origin. Our choice of a tractable model is a lattice band insulator with short-range attractive interactions between fermions in the
s-wave channel. An effective crossover between Bardeen-Cooper-Schrieffer (BCS) and Bose-Einstein condensate (BEC) regimes can be identified in any band insulator above two dimensions, while in two dimensions only the BEC regime exists. The superconducting transition is ``unconventional'' (non-pair-breaking) in the BEC regime, identified by either the bosonic mean field or
XY universality class. The insulator adjacent to the superconductor in the BEC regime is a bosonic Mott insulator of Cooper pairs, which may be susceptible to charge density wave ordering. We construct a function of the many-body excitation spectrum whose nonanalytic changes define a sharp distinction between band and Mott insulators. The corresponding ``second-order transition'' can be observed out of equilibrium by driving a Cooper pair laser in the Mott insulator. We explicitly show that the gap for charged bosonic excitations lies below the threshold for Cooper pair breakup in any BEC regime, despite quantum fluctuations. Our discussion ends with a view of possible consequences for cuprates, where antinodal pair dynamics has certain features in common with our simple
s-wave picture.
Bosonization of Cooper pairs and novel Bose-liquid superconductivity and superfluidity in high-
Tc cuprates and other systems
The criteria for bosonization of Cooper pairs and novel Bose-liquid superconductivity and superfluidity in high-
Tc cuprates and other pseudogap matters are formulated by using the uncertainty principle and the boson mean field theory. We argue that the BCS-type s- or d-wave superconductivity occurring in the fermionic limit of Cooper pairs (which exist in ordinary metals and heavily overdoped cuprates with large Fermi energies) is not characteristic of underdoped to overdoped cuprates with low Fermi energies. The superconducting order parameter in high-
Tc cuprates and other pseudogap matters cannot be determined as the BCS-like (s- or d-wave) gap. We show that the unconventional superconductivity/superfluidity occurring in the bosonic limit of Cooper pairs exists in low Fermi energy systems where the bosonic Cooper pairs are formed at a pseudogap temperature T* above the uperconducting/superfluid transition temperature
Tc and then such bosons condenses into a Bose superfluid at
Tc. The pair condensation of attracting bosons occurs at
Tc and then their single particle condensation sets in at
Tc∗ lower than
Tc (in three dimensions (3D)) or at T=0 (in two dimensions (2D)). The coherent single particle and pair condensates of bosons exist as two distinct superfluid phases below
Tc. By solving the mean field equations for high-
Tc cuprates, the novel superconducting states (i.e., a vortex-like state existing below the temperature
Tv=Tc2D lower than T* but higher than
Tc=Tc3D and two superconducting phases below
Tc) and their properties characterized by the boson superfluid stiffness are determined and compared with the key experimental findings. The novel Bose-liquid superconductivity and superfluidity exists also in other exotic superconductors/superfluids, including quantum liquids, atomic Fermi gases and low-density nuclear matter.
The quasiparticle excitations and dynamical stability of an atomic Bose-Einstein condensate coupled to a quantum degenerate Fermi gas of atoms at zero temperature is studied. The Fermi gas is assumed to be either in the normal state or to have undergone a phase transition to a superfluid state by forming Cooper pairs. The quasiparticle excitations of the Bose-Einstein condensate exhibit a dynamical instability due to a resonant exchange of energy and momentum with quasiparticle excitations of the Fermi gas. The stability regime for the bosons depends on whether the Fermi gas is in the normal state or in the superfluid state. We show that the energy gap in the quasiparticle spectrum for the superfluid state stabilizes the low-energy excitations of the condensate. In the stable regime, we calculate the boson quasiparticle spectrum, which is modified by the fluctuations in the density of the Fermi gas.
We study the finite temperature-density phase diagram of an attractive fermionic system that supports two-body (dimer) and three-body (trimer) bound states in free space. Using interactions characteristic for nuclear systems, we obtain the critical temperature
Tc2 for the superfluid phase transition and the limiting temperature
Tc3 for the extinction of trimers. The phase diagram features a Cooper-pair condensate in the high-density, low-temperature domain which, with decreasing density, crosses over to a Bose condensate of strongly bound dimers. The high-temperature, low-density domain is populated by trimers whose binding energy decreases toward the density-temperature domain occupied by the superfluid and vanishes at a critical temperature
Tc3>Tc2.
As is known, the
1/q2 theorem of Bogoliubov asserts that the mean density of the fermion pair states with the total momentum q obeys the inequality ${n}_{q}>~{C/q}^{2}(\stackrel{\ensuremath{\rightarrow}}{q}0)$ in the case of the Fermi system taken at nonzero temperature and in the superconducting state provided the interaction term of its Hamiltonian is locally gauge invariant. With the principle of correlation weakening it is proved in this paper that the reason for the mentioned singular behavior of
nq is the presence of the bound states of particle pairs with nonzero total momenta. Thus, below the temperature of the superconducting phase transition there always exist the bound states of the fermion couples beyond the pair condensate. If the pseudogap observed in the normal phase of the high-
Tc superconductors is stipulated by the presence of the electron bound pairs, then the derived result suggests, in a model-independent manner, that the pseudogap survives below
Tc.