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arXiv:cond-mat/0212436

Universal scaling behavior of pseudogap with doping in high Tc cuprates; temperature and doping dependence of spectral intensity

Sung-Sik Lee, Sung‐Ho Suck Salk

Published Dec 18, 2002• 0 citations
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Abstract

Based on our improved SU(2) slave-boson approach (Phys. Rev. B 64, 052501(2001)) to the t-J Hamiltonian, we report a scaling behavior of pseudogap with doping and the temperature and doping dependence of spectral functions. In addition we discuss the cause of hump and quasi-particle peak in the observed spectral functions of high Tc cuprates. It is demonstrated that the sharpening of the observed quasi-particle peak below Tc is attributed to the bose condensation of holon pair. From the computed ratios of pseudogap $Δ_0$ to both the superconducting temperature Tc and the pseudogap temperature $T^*$ as a function of hole doping concentration x, we find that there exists a universal scaling of these ratios with doping, that is, the hyperbolic scaling behavior of the former, $\frac{2 Δ_0}{k_B T_c} \sim x^{-α}$ with $α\sim 2$ and near doping independence of the latter, $\frac{2 Δ_0}{k_B T^*} \approx 4 \sim 6$ are found.

DOI
10.48550/arxiv.cond-mat/0212436

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cond-mat.supr-conCross-listedarXiv:2606.11056•Jun 10, 2026
Based on our improved SU(2) slave-boson approach (Phys. Rev. B 64, 052501(2001)) to the t-J Hamiltonian, we report a scaling behavior of pseudogap with doping and the temperature and doping dependence of spectral functions. In addition we discuss the cause of hump and quasi-particle peak in the observed spectral functions of high Tc cuprates. It is demonstrated that the sharpening of the observed quasi-particle peak below Tc is attributed to the bose condensation of holon pair. From the computed ratios of pseudogap Δ0Δ_0Δ0​ to both the superconducting temperature Tc and the pseudogap temperature T∗T^*T∗ as a function of hole doping concentration x, we find that there exists a universal scaling of these ratios with doping, that is, the hyperbolic scaling behavior of the former, 2Δ0kBTc∼x−α\frac{2 Δ_0}{k_B T_c} \sim x^{-α}kB​Tc​2Δ0​​∼x−α with α∼2α\sim 2α∼2 and near doping independence of the latter, 2Δ0kBT∗≈4∼6\frac{2 Δ_0}{k_B T^*} \approx 4 \sim 6kB​T∗2Δ0​​≈4∼6 are found.
Using the improved U(1) and SU(2) slave-boson approaches of the $t\ensuremath{-}J$ Hamiltonian [S.-S. Lee and Sung-Ho Suck Salk, Phys. Rev. B 64, 052501 (2001)] that we developed recently, we study the doping and temperature dependence of superfluid weight and spectral function and discuss our finding of the universal scaling behavior of the pseudogap. It is shown that at low hole doping concentrations xxx and at low temperatures TTT, there exists a propensity of linear decrease in the superfluid weight ns∕m∗{n}_{s}∕{m}^{*}ns​∕m∗ with temperature TTT, and a tendency of doping independence in the linearly decreasing slopes of (ns∕m∗)(x,T)({n}_{s}∕{m}^{*})(x,T)(ns​∕m∗)(x,T) with TTT in qualitative agreement with the experimentally observed relation; that is, $({n}_{s}∕{m}^{*})(x,T)=({n}_{s}∕{m}^{*})(x,0)\ensuremath{-}\ensuremath{\alpha}T$, where $\ensuremath{\alpha}$ is a constant. It is also demonstrated that there exists a boomerang behavior; that is, both Tc{T}_{c}Tc​ and ns∕m∗{n}_{s}∕{m}^{*}ns​∕m∗ increase with hole doping concentration xxx in the underdoped region, reach a saturation (maximum) at a hole doping above optimal doping, and decrease beyond the saturation point in the overdoped region, in agreement with $\ensuremath{\mu}\mathrm{SR}$ measurements. Based on our improved SU(2) slave-boson approach to the $t\ensuremath{-}J$ Hamiltonian, we further investigate the doping and temperature dependence of the spectral function and discuss our theoretical finding of a scaling behavior of the pseudogap. In addition, we discuss the cause of the hump and quasiparticle peak in the observed spectral functions of high Tc{T}_{c}Tc​ cuprates. It is demonstrated that the sharpening of the observed quasiparticle peak below Tc{T}_{c}Tc​ is attributed to the bose condensation of holon pair, in agreement with observations. From the predicted ratios of the pseudogap ${\ensuremath{\Delta}}_{0}$ to both the superconducting temperature Tc{T}_{c}Tc​ and the pseudogap temperature T∗{T}^{*}T∗, i.e., $2{\ensuremath{\Delta}}_{0}∕{k}_{B}{T}_{c}$ and $2{\ensuremath{\Delta}}_{0}∕{k}_{B}{T}^{*}$, respectively, as a function of hole doping concentration xxx, we find that there exists a universal scaling behavior (sample independence) of these ratios with doping, by showing a nonlinearly decreasing behavior of the former; that is, $2{\ensuremath{\Delta}}_{0}∕{k}_{B}{T}_{c}\ensuremath{\sim}{x}^{\ensuremath{-}\ensuremath{\alpha}}$ with $\ensuremath{\alpha}\ensuremath{\sim}2$ and a near doping independence of the latter; that is, $2{\ensuremath{\Delta}}_{0}∕{k}_{B}{T}^{*}\ensuremath{\approx}4--6$.
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.
Based on our recent holon-pair boson theory of the t-J Hamiltonian (Phys. Rev. B 64, 052501 (2001)) we report the doping dependence of the bose condensation energy, superfluid weight and spectral peak intensity. We find a universality of doping dependence in these physical quantities, by equally showing an arch shape in the variations of their magnitudes with the hole doping concentration. We find that all of these physical quantities scale well with the positive charge carrier (hole) density x, but not with the electron density 1-x for the entire range of hole doping. It is shown that the doping dependence of the condensation energy U at T = 0 K is given by the relation, U(0)≈αx2∣Δ0∣2U(0) \approx αx^2 |Δ_0|^2U(0)≈αx2∣Δ0​∣2 with Δ0Δ_0Δ0​, the pairing gap at 0 K and ααα, a constant.
The issues of single particle coherence and its interplay with singlet pairing are studied within the slave boson gauge theory of a doped Mott insulator. Prior work by one of us [T. Senthil, Phys. Rev. B 78, 045109 (2008)10.1103/PhysRevB.78.045109] showed that the coherence scale below which Landau quasiparticles emerge is parametrically lower than that identified in the slave boson mean field theory. Here we study the resulting new non-Fermi liquid intermediate temperature regime characterized by a single particle scattering rate that is linear in temperature (T). In the presence of a d-wave pair amplitude, this leads to a pseudogap state with T-dependent Fermi arcs near the nodal direction. Implications for understanding the cuprates are discussed.
We generalize the condition under which a quantum material exhibiting a pseudogap phase is a precursor to a superconducting (SC) dome. The result reveals the non-analytic T* as a function of doping. A well-known example is the high-Tc cuprates. Essentially, the SC dome is generated under two conditions: (1) that the pseudogap T* is a decreasing function of doping, due to the decrease in size of extended pairing of doped holes with doping, and most importantly, (2) that the rate of configurational-ordering parameter is an increasing function of doping as a result of the decrease in extended length of the disordered pairs. The theory behind these hinges on a novel strong entanglement and confinement hole pairing (ECHP) mechanism that unravels the microscopic features of the entire phase diagram of both electron and hole-doped high-Tc cuprates, recently discussed in the by Buot et al. The ECHP configurational ordering (CO) at the underdoped and overdoped regions qualitatively agrees with spin texture experiments, and strongly suggests that strange metal phase can only occur in the overdoped region, in agreement with experiments.