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arXiv:1012.1058 · Physical Review B

Charge pair hopping and Bose-Einstein condensation in underdoped Mott insulators

Sanjoy Kumar Sarker, Timothy Lovorn

Published Apr 2, 2012• 2 citations
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Abstract

Recently, a renormalized Hamiltonian has been derived by continuing spin states from the Mott limit of the $t$-$J$ model to the underdoped region. We show that it naturally leads to a pairing mechanism in which the pair has a dual character. Its spin part is a spinon singlet that condenses at ${T}^{*}$. The charge part is a real-space holon pair formed at ${T}_{p}<{T}^{*}$, which undergoes a Bose-Einstein condensation at ${T}_{c}<{T}_{p}$. While neither is observable separately, the combination is predicted to be observable as a sharp excitation above and below ${T}_{c}$. The mechanism is consistent with the small superfluid density, the decline of ${T}_{c}$ at small doping, and the existence of pairs above ${T}_{c}$ in cuprates, indicated by the observation of diamagnetism and Nernst effect.

DOI
10.1103/physrevb.85.144502

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Recently, a renormalized Hamiltonian has been derived by continuing spin states from the Mott limit of the ttt-JJJ model to the underdoped region. We show that it naturally leads to a pairing mechanism in which the pair has a dual character. Its spin part is a spinon singlet that condenses at T∗{T}^{*}T∗. The charge part is a real-space holon pair formed at Tp<T∗{T}_{p}<{T}^{*}Tp​<T∗, which undergoes a Bose-Einstein condensation at Tc<Tp{T}_{c}<{T}_{p}Tc​<Tp​. While neither is observable separately, the combination is predicted to be observable as a sharp excitation above and below Tc{T}_{c}Tc​. The mechanism is consistent with the small superfluid density, the decline of Tc{T}_{c}Tc​ at small doping, and the existence of pairs above Tc{T}_{c}Tc​ in cuprates, indicated by the observation of diamagnetism and Nernst effect.
Spin-charge split pairing in underdoped cuprate superconductors: support from low-TTT specific heat
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/2ρ\sim x/2ρ∼x/2, where xxx is the hole (dopant) concentration. As usual, the T3T^3T3 term is due to Goldstone phonons. The zero-point energy, through its dependence on the condensate density ρ0(T)ρ_0(T)ρ0​(T), accounts for the anomalous TTT-linear term. These results support the split-pairing mechanism, in which spinons (pure spin) are paired at T∗T^*T∗ and holons (pure charge) form real-space pairs at Tp<T∗T_p < T^*Tp​<T∗, creating a gauge-coupled physical pair of charge +2e+2e+2e and concentration x/2x/2x/2 which Bose condenses below TcT_cTc​, accounting for the observed phases.
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{T}^{0}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=0T=0T=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 ddd-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.
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{T}_{c}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.
We demonstrate the existence of an unconventional pairing state in photodoped Mott insulators on ladder and quasi-two-dimensional geometries, characterized by quasi-long-range doublon-holon correlations that signal Mott exciton condensation. The doublon-holon pairing exhibits correlations of ddd-wave-like symmetry, reminiscent of superconducting pairing in chemically doped Mott insulators. By constructing the phase diagram, using density matrix renormalization group, we reveal that the doublon-holon pairing state in the photodoped ladder emerges between the spin-singlet, charge-density-wave, and ηηη-pairing phases. Our study suggests that the interplay of charge, spin, and ηηη-spin degrees of freedom can give rise to exotic quantum many-body states in photodoped Mott insulators.
We improve a previous theory of doped Mott insulators with duality between pairing and magnetism by a further duality transform. As the result we obtained a quantum Ginzburg-Landau theory describing the Cooper pair condensate and the dual of spin condensate. We address the superconductivity by doping a Mott insulator, which we call the Mott superconductivity. Some fingerprints of such novelty in cuprates are the scaling between neutron resonance energy and superfluid density, and the induced quantized spin moment by vortices or Zn impurity (together with circulating charge super-current to be checked by experiments).
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 TcT_cTc​ 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 TcT_cTc​ and the pseudogap (spin gap) temperature T∗T^*T∗ tangential to TcT_cTc​ in the overdoped region in the observed phase diagram of high TcT_cTc​ cuprates. A universal parabolic scaling behavior of T∗/TcT^*/T_cT∗/Tc​ (or Tc/T∗T_c/T^*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 TcT_cTc​ 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.