Magnetic electron-hole asymmetry in cuprates: a computational revisit

TL;DR

This work investigates the longstanding question of electron–hole asymmetry in antiferromagnetism within cuprates by directly solving the three-band Emery model with parameters fitted to La$_2$CuO$_4$ and cross-validating results across VMC, DQMC, CP-AFQMC, DMET, and GA. The study finds that, when stripe or other competing orders are ignored, the AFM response to electron and hole doping is nearly symmetric, with robustness against moderate $U_p$ and Nd$_2$CuO$_4$-style parameter changes. A key insight is that dopant-induced defect potentials can create an extrinsic route to asymmetry: Cu-site defects enhance AFM on the electron-doped side, while O-site defects suppress it on the hole-doped side, highlighting the importance of defect physics in interpreting cuprate phase diagrams. The results imply that observed asymmetries in experiments may owe substantial contributions to dopant-induced effects, guiding future studies to incorporate such extrinsic factors when analyzing competing orders in cuprates.

Abstract

In this work, we revisit the electron-hole asymmetry of antiferromagnetism in cuprates by studying the three-band Emery model. Using parameters relevant to La$_2$CuO$_4$, we benchmark the anti-ferromagnetic response for a large range of dopings with variational Monte Carlo, determinant quantum Monte Carlo, constrained-path auxiliary-field quantum Monte Carlo, density-matrix embedding theory, and the Gutzwiller approximation. Across methods and accessible sizes/temperatures, we find no significant electron-hole asymmetry if we consider only Neel anti-ferronagnetic response and ignore other possible orders such as stripe state. This result is robust to a moderate oxygen-site repulsion $U_p$ and to parameter sets of Nd$_2$CuO$_4$. Incorporating dopant-induced local potentials reveals an extrinsic route to asymmetry: Cu-site defects enhance AFM on the electron-doped side, whereas O-site defects suppress it on the hole-doped side. These results indicate that dopant-driven effects make a non-negligible contribution to apparent electron-hole asymmetry in the general phase diagram of cuprates and should be included when analyzing competing orders in cuprates.

Figures (17)

• Figure 1: Schematic phase diagram of hole-doped and electron-doped cuprates. Only the antiferromagnetism ($T_N$) and superconductivity phase boundaries ($T_c$) are plotted. Experimental data is summarized in Ref. armitage_RevModPhys.82.2421. Right: hole-doped La$_2$CuO$_4$; Left: electron-doped Nd$_2$CuO$_4$. It is noted that both maximum $T_N$ and maximum $T_c$ are comparable in these two materials. But the ending point of AFM phase varies strongly, leading to the electron-hole asymmetry. In the electron-doped side, the AFM ending point is still unclear armitage_RevModPhys.82.2421. In cuprates, doped holes tend to reside on the oxygen sites (the smaller circle in the right), while doped electrons are mainly located on the copper sites (the larger circle in the left).
• Figure 2: (a) Schematic of the three-band Emery model on the CuO$_2$ plane in the hole representation. Orange/blue lobes indicate the orbital phase of Cu $d_{x^2-y^2}$ and O $p_{x/y}$. The signs of $t_{pd}$ and $t_{pp}$ follow the indicated phases. (b) Spin-wave dispersion obtained from DQMC on a $16\times4$ lattice at inverse temperature $\beta=8$. Blue circles denote the DQMC results, and black squares correspond to the experimental dispersion measured by inelastic neutron scattering in Ref. La2CuO4_PhysRevLett.86.5377.
• Figure 3: Undoped $(x=0)$ Anti-ferromagnetic magnetization in the three-band Hubbard model. (a) VMC-based results: peak spin structure factor $S(\pi,\pi)$ versus $1/L$; a quadratic fit in $1/L$ is used to extrapolate to the thermodynamic limit (TL), from which the staggered moment $m=\sqrt{S(\pi,\pi)}$ is obtained. (b) CP-AFQMC: induced staggered magnetization measured at the sites farthest from the pinning centers versus $1/L$. A linear fit with $1/L$ yields the TL estimate.
• Figure 4: Orbital-resolved densities, energies and AFM moments from various methods on $L=12$ clusters. (a) Triangles denote the Cu-site density $n_{\mathrm{Cu}}$; circles denote the oxygen-site density $n_{\mathrm{O}}$ (sum over $p_x$, $p_y$). (b) Ground-state energy per unit cell versus doping $x$. (c) AFM moment from GA and DMET ($2\times2$ impurity cluster with a CCSD solver). All data use the same model parameters; see Appendix for method-specific details.
• Figure 5: (a) The spin correlation function at momentum $Q=(\pi,\pi)$ as a function of doping $x$ estimated by VMC ($L=16,18$) and mVMC ($L=16$, no spin quantum-number projection). (b) DQMC uses $L=8$, $\beta=8,10$ to obtain the staggered spin susceptibility. (c) CP-AFQMC calculated stagger magnetization $m_z$ on $L=16$, using two approaches. For the blue line trial wave-functions are optimized self-consistently while for the red line an optimized AFM trial wave-function is used to force AFM order. When the self-consistent calculation indeed gives AFM state, the two methods agree qualitatively well. For the hole doped side where self-consistent calculation gives stripe state, we only show the results of second approach. All methods show no discernible electron–hole asymmetry; a mild hole-side enhancement is suggested. See Appendix for computational details.