[Paper Review] Dichotomy in underdoped high $T_c$ superconductors and spinon-dopon approach to $t$-$t'$-$t''$-$J$ model

Ying Ran, Xiao-Gang Wen|arXiv (Cornell University)|Nov 2, 2006

Physics of Superconductivity and Magnetism3 citations

TL;DR

This paper proposes a spinon-dopon approach to the $t$-$t'$-$t''$-$J$ model to explain the dichotomy in underdoped high-$T_c$ superconductors, where non-uniform mixing of spinons and dopons in momentum space lowers $t'$ and $t''$ hopping energy, leading to momentum-dependent quasiparticle spectral weight $Z_k$. The model reproduces the observed suppression of $Z_k$ in anti-nodal regions for hole-doped systems and enhancement in electron-doped systems, consistent with ARPES and tunneling data.

ABSTRACT

We studied underdoped high $T_c$ superconductors using a spinon-dopon approach (or doped-carrier approach) to $t$-$t'$-$t''$-$J$ model, where spinon carries spin and dopon carries both spin and charge. In this approach, the mixing of spinon and dopon describes superconductivity. We found that a nonuniform mixing in $k$-space is most effective in lowering the $t'$ and $t''$ hopping energy. We showed that at mean-field level, the mixing is proportional to quasiparticle spectral weight $Z_-$. We also found a simple monte-carlo algorithm to calculate $Z_{-}$ from the projected spinon-dopon wavefunction, which confirms the mean-field result. Thus the non-uniform mixing caused by $t'$ and $t"$ explains the different electron spectral weights near the nodal and anti-nodal points ({\it i.e.} the dichotomy) observed in underdoped high $T_c$ superconductors. For hole-doped sample, we found that $Z$ is enhanced in the nodal region and suppressed in the anti-nodal region. For electron doped sample, the same approach leads to a suppressed $Z$ in the nodal region and enhanced in the anti-nodal region, in agreement with experimental observations.

Motivation & Objective

• To resolve the long-standing puzzle of spectral weight dichotomy in underdoped high-$T_c$ superconductors, where quasiparticle peaks are strong in nodal directions but suppressed in anti-nodal directions.
• To address the failure of conventional slave-boson approaches in explaining momentum-dependent quasiparticle spectral weight $Z_k$.
• To develop a unified theoretical framework that explains both hole-doped and electron-doped systems using a spinon-dopon approach.
• To provide a mean-field theory and a practical Monte Carlo algorithm for calculating $Z_k$ from projected spinon-dopon wavefunctions.
• To predict a non-uniform quasiparticle current distribution that correlates with $Z_k$, offering a testable signature for future experiments.

Proposed method

• Introduces a spinon-dopon approach where spinons carry spin and dopons carry both spin and charge, with superconductivity arising from their coherent mixing.
• Uses a mean-field theory to show that the mixing amplitude is proportional to the quasiparticle spectral weight $Z_k$, particularly $Z_{-}$ for hole-doped systems.
• Develops a simple Monte Carlo algorithm to compute $Z_k$ from the projected spinon-dopon wavefunction, confirming the mean-field prediction.
• Applies the method to the $t$-$t'$-$t''$-$J$ model with realistic parameters ($t'=-0.3t$, $t''=0.2t$, $J=0.3t$) to simulate real materials like Sr$_2$CuO$_2$Cl$_2$.
• Uses local projection operators $P_i$ to enforce physical constraints (no double occupancy, local singlets), enabling energy calculations via fermionic two-point correlation functions.
• Applies Wick’s theorem to reduce projected expectation values (e.g., $\langle \vec{S}_i \cdot \vec{S}_j \rangle_{\text{prj}}$) to products of known two-point functions.

Experimental results

Research questions

• RQ1 Can the spinon-dopon approach explain the momentum-space dichotomy in quasiparticle spectral weight observed in ARPES experiments on underdoped high-$T_c$ superconductors?
• RQ2 How does the inclusion of next-nearest-neighbor ($t'$) and next-next-nearest-neighbor ($t''$) hopping terms lead to non-uniform $Z_k$ in the $k$-space?
• RQ3 Why does the conventional slave-boson approach fail to capture the $k$-dependence of $Z_k$, and can the spinon-dopon framework overcome this limitation?
• RQ4 Does the spinon-dopon model predict distinct $Z_k$ behavior in hole-doped versus electron-doped systems, consistent with experimental observations?
• RQ5 Can the quasiparticle current distribution derived from this model differ significantly from BCS predictions and provide a testable signature for superfluid density anomalies?

Key findings

• Non-uniform mixing of spinons and dopons in $k$-space is most effective in lowering the $t'$ and $t''$ hopping energy, explaining the origin of spectral weight dichotomy.
• At the mean-field level, the mixing amplitude is proportional to the quasiparticle spectral weight $Z_{-}$, which is enhanced in the nodal region and suppressed in the anti-nodal region for hole-doped systems.
• For electron-doped systems, the same approach predicts $Z_{+}$ suppressed in the nodal region and enhanced in the anti-nodal region, matching experimental observations.
• The Monte Carlo algorithm successfully computes $Z_k$ from the projected spinon-dopon wavefunction and confirms the mean-field result, validating the theoretical framework.
• The model predicts a quasiparticle current distribution strongly correlated with $Z_k$, with large current near nodal points and small current near anti-nodal points, differing from BCS predictions.
• The results are consistent with exact diagonalization studies on 32-site clusters, showing strong $Z_k$ anisotropy when $t'$ and $t''$ are non-zero, particularly $Z_{-} \approx 0.029$ at $(\pi,0)$ and $Z_{-} \approx 0.353$ at $(\pi/2,\pi/2)$.