A simple interlayer pair tunneling is solved exactly. We find that in the normal state spin-1/2 particle and hole excitations are gapped. But the state is an unusual metal, characterized by novel fermionic spin zero and charge +2e and -2e excitations that exist about their own Fermi surfaces. The model is consistent with a number of properties of the underdoped cuprates. At finite temperature the Fermi surface appears partially gapped, and at high temperatures the spin gap disappears completely. Superconductivity is induced by an additional intralyer interaction which opens a gap in the charge-fermion spectrum. The symmetry of this charge gap (and hence that of the order parameter) is igenerally different from the symmetry of one-electron or - hole gap. The former can be a d wave, while the latter is more complex.
A simple interlayer pair tunneling is solved exactly. We find that in the normal state spin-1/2 particle and hole excitations are gapped. But the state is an unusual metal, characterized by novel fermionic spin zero and charge +2e and -2e excitations that exist about their own Fermi surfaces. The model is consistent with a number of properties of the underdoped cuprates. At finite temperature the Fermi surface appears partially gapped, and at high temperatures the spin gap disappears completely. Superconductivity is induced by an additional intralyer interaction which opens a gap in the charge-fermion spectrum. The symmetry of this charge gap (and hence that of the order parameter) is igenerally different from the symmetry of one-electron or - hole gap. The former can be a d wave, while the latter is more complex.
We show that a two-dimensional (2D) metal in a superconducting (SC) state with wave-vector-dependent gap behaves as a quantum-spin liquid characterized by a collective mode of resonance type. Formally the mode exists whatever is a form of Fermi surface (FS). However, when the latter is spherical the effect is rather formal: any factor leading to an even weak electron scattering, like finite T, impurity, etc., easily kills the mode. On the contrary, for the type of FS observed in the high-Tc cuprates (characterized by a proximity to the saddle-point wave vectors) the resonance mode exists in a true sense being well separated from the electron-hole continuum and well defined. The effect is due to the effective 1D dimension in a proximity of electronic topological transition quantum critical point. The physical nature of the collective mode varies progressively between two possibilities. In the case of a weak interaction, the resonance mode is a typical effect of a two-particle bound state that appears slightly below the bottom of the two-particle continuum. The effect exists even in the case of infinitesimally weak interaction (of relevant sign). In the case of a strong or intermediate interaction, it is a critical mode existing as a precursor of spin-density wave (SDW) instability. The gap of the collective mode is not related directly to the value of the SC gap (being, however, limited by the latter from above) but rather to a proximity to SDW instability. We predict also a second collective mode lying inside the two-particle continuum. The existence of these two modes and the particular form of their dispersion in the case corresponding to the underdoped cuprates ${(d}_{{x}^{2}\ensuremath{\sim}{y}^{2}}$ symmetry of SC gap, exchange interaction of antiferromagnetic sign, etc.) allows one to understand the main features observed experimentally in the underdoped cuprates, namely the so-called ``41 meV resonance peak'' and ``24 meV incommensurability'' and their two-dimensional wave vector dependences, the doping evolution of the spin dynamics and many other features. The theory also predicts new features to be tested experimentally.
Using continuity, we derive a renormalized Hamiltonian from the parent $t\text{\ensuremath{-}}J$ model to describe the properties of underdoped cuprates. The theory is constrained to agree with the behavior at half filling, which is well described by the Arovas-Auerbach valence bond state in which bosonic spinons are paired into singlets. Spinon states evolve continuously into the doped region preserving their symmetry. We assume that moving holes rapidly destroy magnetic order, which leads to a gap in the spinon spectrum and strongly renormalizes the theory. The spin gap leads to two different types hopping terms for renormalized holes. In one, a fermionic holon hops within the same sublattice accompanied by a singlet backflow, giving rise to a non-Fermi-liquid normal state with novel properties. Spinon singlets condense below a pseudogap temperature ${T}^{\ensuremath{\ast}}$ (< spin gap temperature T0), which allows holons to propagate coherently, forming a spinless Fermi liquid, but without an observable holon Fermi surface. Above ${T}^{\ensuremath{\ast}}$, holons are localized. This is the so-called strange metal phase, which is actually a new type of insulator since its resistivity would be infinite at T=0. In the second term a pair of holons belonging to opposite sublattices hop, accompanied by a singlet backflow. In the presence of the singlet condensate holon pairs condense, leading to d-wave superconductivity; the symmetry is primarily determined by the symmetry of the valence bond state at half filling. The metal and the superconductor preserve the two-sublattice character of the valence bond state. A careful examination of the nuclear magnetic resonance, tunneling, and transport data shows that the predictions of the theory is consistent with experimental results. Remarkably, the existence of the spin gap provides a natural explanation for the phenomenon of two dimensionality of the normal state in the presence of interplane hopping. The marked asymmetry between hole-doped and electron-doped cuprates is also easily explained.
Within the framework of a relativistic non-Abelian gauge theory approach to the physics of spin–charge separation in doped quantum antiferromagnetic planar systems, proposed recently by the authors, we are examining here the effects of constant external magnetic fields on excitations about the superconducting state in the model. The electrically-charged Dirac fermions (holons), describing excitations about specific points on the fermi surface, e.g. those corresponding to the nodes of a d-wave superconducting gap in high-T c cuprates, condense, resulting in the opening of a Kosterlitz–Thouless–like gap (KT) at such nodes. This leads, in general, to a second superconducting phase transition, which occurs at low temperatures[Formula: see text], in addition to the high-T c superconductivity [Formula: see text] due to the bulk of the fermi surface for holons in a (d-wave) spin–charge separated superconductor. In the presence of strong external magnetic fields at the surface regions of the planar superconductor, in the direction perpendicular to the superconducting planes, these KT gaps appear to be enhanced. Our preliminary analysis, based on analytic Schwinger–Dyson treatments, seems to indicate that for an even number of Dirac fermion species, required in our model as a result of gauging a particle–hole SU(2) symmetry, Parity or Time Reversal violation does not necessarily occurs. Based on these considerations, we argue that recent experimental findings, concerning thermal conductivity plateaux of quasiparticles in planar high-T c cuprates in strong external magnetic fields, may indicate the presence of such KT gaps, caused by charged Dirac-fermion excitations in these materials, as suggested in the above model.
The two-dimensional d-p model (or extended Hubbard model) on a square lattice is investigated for fermion pairing by a slave boson method. The inter-site d-fermion interaction is introduced additionally. The momentum space counterpart of this interaction is taken to be separable and expanded in terms of basis functions corresponding to mixed symmetry states. The investigation leads to anomalous pairing of fermion fields only for pure d-wave symmetry. The charge and spin ordering gaps appear in the single- particle spectrum when d(x,y) state is taken into account.The non-Fermi liquid behavior is found to be the prevalent one generally. The study yields a good qualitative account of the nodal-antinodal dichotomy. Two gaps appear in the normal state spectrum; the larger one corresponds to the sum and the smaller to the difference of spin and charge ordering gaps. This two-gap scenario is in qualitative agreement with recent experimental finding.
The interplay between electron-electron and electron-phonon interactions is studied in a one-dimensional lattice model by means of a variational Monte Carlo method based on generalized Jastrow-Slater wave functions. Here, the fermionic part is constructed by a pair-product state, which explicitly depends on the phonon configuration, thus including the electron-phonon coupling in a backflow-inspired way. We report the results for the Hubbard model in the presence of the Su-Schrieffer-Heeger coupling to optical phonons, both at half filling and upon hole doping. At half filling, the ground state is either a translationally invariant Mott insulator, with gapless spin excitations, or a Peierls insulator, which breaks translations and has fully gapped excitations. Away from half filling, the charge gap closes in both Mott and Peierls insulators, turning the former into a conventional Luttinger liquid (gapless in all excitation channels). In the latter case, instead, a finite spin gap remains at small doping. Even though consistent with the general theory of interacting electrons in one dimension, the existence of such a phase (with gapless charge but gapped spin excitations) has never been demonstrated in a model with repulsive interaction and with only two Fermi points. Since the spin-gapped metal represents the one-dimensional counterpart of a superconductor, our results furnish evidence that a true off-diagonal long-range order may exist in the two-dimensional case.
The two-dimensional d-p model (or extended Hubbard model ) on a square lattice is investigated for fermion pairing by a slave boson method. The inter-site d-fermion interaction is introduced additionally. The momentum space counterpart of this interaction is taken to be separable and expanded in terms of basis functions corresponding to mixed symmetry states. The investigation leads to anomalous pairing of fermion fields only for pure d-wave symmetry. The charge and spin ordering gaps appear in the singleparticle spectrum when d(x,y) state is taken into account.The non-Fermi liquid behavior is found to be the prevalent one generally. The study yields a good qualitative account of the nodal-antinodal dichotomy. Two gaps appear in the normal state spectrum; the larger one corresponds to the sum and the smaller to the difference of spin and charge ordering gaps. This two-gap scenario is in qualitative agreement with recent experimental finding.