Pairing occurs in conventional superconductors through a reduction of the electronic potential energy accompanied by an increase in kinetic energy, indicating that the transition is driven by a pairing potential. In the underdoped cuprates, optical experiments show that pairing is driven by a reduction of the electronic kinetic energy. Using the Dynamical Cluster Approximation we study the nature of superconductivity in a microscopic model of the cuprates, the two-dimensional Hubbard model. We find that pairing is indeed driven by the kinetic energy and that superconductivity evolves from an unconventional, spin-charge separated state, consistent with the RVB model of high-temperature superconductors.
Pairing occurs in conventional superconductors through a reduction of the electronic potential energy accompanied by an increase in kinetic energy. In the underdoped cuprates, optical experiments show that pairing is driven by a reduction of the electronic kinetic energy. Using the dynamical cluster approximation we study superconductivity in the two-dimensional Hubbard model. We find that pairing is indeed driven by the kinetic energy and that superconductivity evolves from an unconventional state with partial spin-charge separation, to a superconducting state with quasiparticle excitations.
Superconductivity is usually assumed to arise from attractive interaction. In this work we show that strong pairing is possible soley from kinetic energy even without a net attraction. We demonstrate a high-temperature kinetic superconductor in a simple lattice model with nearest-neighbor hopping (
t) projected onto a constrained Hilbert space, analogous to the
t-
J model with
J=0, where kinetic magnetism has been previously studied. Using density matrix renormalization group (DMRG) on cylinders up to width
Ly=8, we find a superconducting ground state exhibiting a key difference from high-
Tc cuprates: both the pairing gap and phase stiffness \textit{increase} with doping (
x). We find pairing gaps, determined from spin and single-electron charge gaps, exceeding
1.5t. This model can be realized within the double Kondo lattice model, relevant to bilayer nickelates, in the limit of strong inter-layer spin coupling (
J⊥/t→+∞) and a balancing inter-layer repulsion (
V). Importantly, the double Kondo model does not fundamentally restrict
J⊥/t, suggesting the potential for high critical temperatures (
Tc) approaching
0.5t. While this idealized limit predicts large pairing gaps, we show a smooth connection to the more realistic regime with
J⊥∼t, albeit with a reduced pairing gap of approximately
0.1t. Assuming
t∼103 K in typical solid state systems, our model suggests the exciting possibility of achieving
Tc of hundreds of Kelvin. We propose searching for bilayer materials with reduced out-of-plane lattice constants to better approximate the conditions of our ideal model.
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.
This thesis deals with different aspects of high temperature superconductivity in hole-doped cuprates. We assume the t - J model to describe the CuO2 planes of cuprates and we use a spin-charge gauge approach with spin-charge separation to describe holes in terms of a spinless fermion carrying the charge (holon) and a neutral boson carrying spin 1/2 (spinon), coupled by a slave-particle gauge field. In this framework we consider the effects of the presence of a finite density of incoherent holon pairs in the normal state as a precursor of superconductivity. We show that it is possible to take such pairs into account through a strongly direction dependent spectral weight for holons, which suppresses quasi-particles starting from the anti-nodal directions, and a wave function renormalization for the slave particle gauge field. In this way we prove that, when temperature is reduced, the formation of holon pairs causes both the deviation from linearity of the resistivity and the deviation from the constant value of the Knight shift. Moreover we point out the need for a negative next-nearest-neighbor hopping term ((t - t' - J model) to get a good continuum limit and to evaluate the Knight shift. These results are obtained through a Green's function, which follows naturally from the formalism and analytically interpolates between a Fermi liquid-like behavior and a d-wave superconductor when the coherence length of the holon pair order parameter is increased. The system preserves a finite Fermi surface until the superconducting transition, where it reduces to four nodes. Finally when, at lower temperatures, both the holon pairs and the RVB spinon pairs condense we enter the superconducting phase. In this phase we study the magnetic excitations showing how to extend to spin waves the hourglass-shape dispersion, found for spinons near the antiferromagnetic vector, if a suitable local mechanism of attraction between spinon and anti-spinon is assumed. The resulting spin wave Green's function, whose imaginary part is directly comparable with experiments, generates the hourglass with a finite gap between the two branches. Since the U(1) slave-particle gauge field gains mass in the superconducting phase via Anderson-Higgs mechanism, we propose the necessary mechanism of attraction comes from the unbroken Z2 subgroup of the U(1) gauge group.
A spin-charge binding mechanism is analyzed using the Schwinger boson representation of the two-dimensional $t\ensuremath{-}J$ model. In the normal state spinons are paired into singlets which evolve out of the antiferromagnetic phase at half-filling. The singlets induce, via the hopping term, a pairing of holons and bind with the latter. The ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ symmetry of the order parameter and the shape of the
Tc vs doping curve, observed in cuprate superconductors, emerge naturally as a consequence of the symmetry of the spinon pairs, thus connecting superconductivity with quantum spin fluctuations in the insulator.