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arXiv:1705.10390

Spin-charge split pairing in underdoped cuprate superconductors: support from low-$T$ specific heat

Sanjoy Kumar Sarker, Timothy Lovorn

Published May 29, 2017• 0 citations
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Abstract

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 $ρ\sim x/2$, where $x$ is the hole (dopant) concentration. As usual, the $T^3$ term is due to Goldstone phonons. The zero-point energy, through its dependence on the condensate density $ρ_0(T)$, 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 $T_p < T^*$, creating a gauge-coupled physical pair of charge $+2e$ and concentration $x/2$ which Bose condenses below $T_c$, accounting for the observed phases.

DOI
10.48550/arxiv.1705.10390

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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.
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.
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.
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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.
We study a system of doped antiferromagnet in three dimensions at finite temperatures using the ttt-JJJ model, a canonical model of strongly correlated electrons. We employ the slave-fermion representation of electrons, in which an electron is described as a composite of a charged spinless holon and a chargeless spinon. We introduce two kinds of U(1) gauge fields on links as auxiliary fields, one describing resonating valence bonds of antiferromagnetic nearest-neighbor spin pairs and the other for nearest-neighbor hopping amplitudes of holons and spinons in the ferromagnetic channel. To perform a numerical study of the system, we integrate out the fermionic holon field by using the hopping expansion in powers of the hopping amplitude, which is legitimate for the region in and near the insulating phase. The resultant effective model is described in terms of bosonic spinons, two U(1) gauge fields, and a collective field for hole pairs. We study this model by means of Monte Carlo simulations, calculating the specific heat, spin correlation functions, and instanton densities. We obtain a phase diagram in the hole concentration-temperature plane, which is in good agreement with that observed recently for clean and homogeneous underdoped samples.
The Chern-Simons bosonization with $\mathrm{U}(1)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ gauge field is applied to the two-dimensional $t\ensuremath{-}J$ model in the limit $t\ensuremath{\gg}J,$ to study the normal-state properties of underdoped cuprate superconductors. We prove the existence of an upper bound on the partition function for holons in a spinon background, and we find the optimal spinon configuration saturating the upper bound on average---a coexisting flux phase and s+ids+ids+id-like resonating-valence-bond state. After neglecting the feedback of holon fluctuations on the U(1) field B and spinon fluctuations on the SU(2) field VVV, the holon field is a fermion and the spinon field is a hard-core boson. Within this approximation we show that the B field produces a \ensuremath{\pi} flux phase for the holons, converting them into Dirac-like fermions, while the VVV field, taking into account the feedback of holons produces a gap for the spinons vanishing in the zero-doping limit. The nonlinear-\ensuremath{\sigma} model with a mass term describes the crossover from the short-ranged antiferromagnetic (AF) state in doped samples to long-range AF order in reference compounds. Moreover, we derive a low-energy effective action in terms of spinons, holons and a self-generated U(1) gauge field. Neglecting the gauge fluctuations, the holons are described by the Fermi-liquid theory with a Fermi surface consisting of four ``half-pockets'' centered at (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2) and one reproduces the results for the electron spectral function obtained in the mean-field approximation, in agreement with the photoemission data on underdoped cuprates. The gauge fluctuations are not confining due to coupling to holons, but nevertheless yield an attractive interaction between spinons and holons leading to a bound state with electron quantum numbers. The renormalization effects due to gauge fluctuations give rise to non-Fermi-liquid behavior for the composite electron, in certain temperature range showing the linear in T resistivity. This formalism provides a new interpretation of the spin gap in the underdoped superconductors (mainly due to the short-ranged AF order) and predicts that the minimal gap for the physical electron is proportional to the square root of the doping concentration. Therefore the gap does not vanish in any direction. All these predictions can be checked explicitly in experiment.