We investigate the statistics of the coupled hole pairs in a crystal lattice in high Tc superconductors, following the previously developed approach for the collective charge state (holon). The exact commutation relations for the hole pair operators correspond to a modified parafermi statistics of rank M′ (M′ is the number of sites in a “superlattice” formed by centers of mass for each hole pair), i.e. one state can be occupied by up to M′ pairs. Even in the absence of dynamic interaction, the system of hole pairs is characterized by some immanent interaction (kinematic interaction), which depends on the hole-pairs concentration. In spite of the kinematic interaction, there is no statistical prohibition on the Bose-Einstein condensation of coupled hole pairs.
We discuss certain physical contents of the two-dimensional Luttinger liquid state using the spin and charge current backflow in strongly correlated electron systems. Also we attempt a description of the Luttinger liquid state in the slave boson formalism. Conventional slave boson mean field theory does not possess an important property expected of a Luttinger liquid, namely a pseudo fermi surface for holons. This arises from the bose condensation of holes. We attempt to rectify this by discussing the physics of the fermionic backflow associated with the hole motion. We argue that the fermionic backflow suppresses the Bose condensation. To understand this we introduce the notion of ‘Statistics Transfer’-the medium transfer certain statistics to the slave particle (e's). A variational wave function in which boson condensation is manifestly absent is introduced. The form of the wave function is justified by the concept of statistics transfer. The spinon and holon excitations both exhibiting pseudo fermi surfaces are constructed.
To supplement our recent brief report on the theory of holon-pair boson approach to the t-J Hamiltonian [S.-S. Lee and Sung-Ho Suck Salk, Phys. Rev. B {\bf 64}, 052501(2001)], in this paper we present a full exposure to the theory, detailed physical implications and predicted various physical properties of high
Tc cuprates. We discuss the significance of coupling (interplay) between the spin and charge degrees of freedom in the Heisenberg interaction term of the t-J Hamiltonian. We discuss its importance in causing the arch-shaped superconducting transition temperature
Tc and the pseudogap (spin gap) temperature
T∗ tangential to
Tc in the overdoped region in the observed phase diagram of high
Tc cuprates. A universal parabolic scaling behavior of
T∗/Tc (or
Tc/T∗) with hole doping concentration is predicted in agreement with observations, indicating that there exists correlation between the pseudogap (spin gap) phase and the superconducting phase through antiferromagnetic fluctuations. Our proposed holon-pair boson theory is shown to be self-consistent in that it not only yields the arch (dome) shape structure of
Tc but also reproduces various other physical properties such as superfluid weight, bose condensation energy, spectral function, optical conductivity and spin susceptibility, including their temperature and doping dependence.
We calculate the specific heat of a weakly interacting dilute system of bosons on a lattice and show that it is consistent with the measured electronic specific heat in the superconducting state of underdoped cuprates with boson concentration
ρ∼x/2, where
x is the hole (dopant) concentration. As usual, the
T3 term is due to Goldstone phonons. The zero-point energy, through its dependence on the condensate density
ρ0(T), accounts for the anomalous
T-linear term. These results support the split-pairing mechanism, in which spinons (pure spin) are paired at
T∗ and holons (pure charge) form real-space pairs at
Tp<T∗, creating a gauge-coupled physical pair of charge
+2e and concentration
x/2 which Bose condenses below
Tc, accounting for the observed phases.
We present a bond-operator theory (BOT) for analytical consideration of the
t-
J model and its extensions with longer-rage hopping terms. This technique is based on previously suggested representation of electron operators via localized spins 1/2 and spinless Fermi-operators of mobile holons which requires no constraint between them. We introduce a representation of operators of spins, holons, and electrons in (extended) unit cell containing several lattice sites via a zoo of Bose- and Fermi-operators acting in the Hilbert space of all quantum states of the whole unit cell. BOT provides a regular expansion of physical quantities in powers of
1/n using conventional diagrammatic technique, where
n≥1 is the maximum number of introduced quasiparticles (bosons and fermions) which can occupy a unit cell. The suggested representation reproduces commutation algebra of all operators at any
n>0 and allows to consider both magnetically ordered and disordered phases. Some elementary excitations described in the BOT by separate bosons or fermions appear in common approaches as bound states of conventional quasiparticles. In particular, there are two-hole bound states (Cooper pairs of two holes) which are described within the BOT by separate bosons. We discuss in detail properties of the
t-
J model on the square lattice with no more than two holes (polarons). Although the expansion parameter
1/n is not small in the physically meaningful case of
n=1, we obtain a good quantitative agreement with previous numerical findings at
n=1 even in the first order in
1/n after taking into account a few simple diagrams. Self-consistent calculations in the first order in
1/n bring our results to a very good quantitative agreement with previous numerical findings of the ground state energy, staggered magnetization, and spectra of magnons, polarons, and lowest-energy two-hole bound states.
We explore the universal properties of interacting fermionic lattice systems, mostly focusing on the development of pairing correlations from attractive interactions. Using renormalization group, we identify a large number of fixed points and show that they correspond to resonant scattering in multiple channels. Pairing resonances in finite-density band insulators occur between quasiparticles and quasiholes living at different symmetry-related wave vectors in the Brillouin zone. This allows a BCS-BEC crossover interpretation of both Cooper and particle-hole pairing. We show that, in two dimensions, the runaway flows of relevant attractive interactions lead to charged-boson-dominated low-energy dynamics in the insulating states and superfluid transitions in the bosonic mean-field or
XY universality classes. Analogous phenomena in higher dimensions are restricted to the strong-coupling limit, while, at weak couplings, the transition is in the pair-breaking BCS class. The models discussed here can be realized with ultracold gases of alkali atoms tuned to a broad Feshbach resonance in an optical lattice, enabling experimental studies of pairing correlations in insulators, especially in their universal regimes. In turn, these simple and tractable models capture the emergence of fluctuation-driven superconducting transitions in fermionic systems, which is of interest in the context of high-temperature superconductors.