BCS-BEC crossover in a $(t_{2g}{)}^4$ Excitonic Magnet

Abstract

The condensation of spin-orbit-induced excitons in $(t_{2g}{)}^4$ electronic systems is attracting considerable attention. In the large Hubbard U limit, antiferromagnetism was proposed to emerge from the Bose-Einstein Condensation (BEC) of triplons ($J_{\text{eff}}=1$). In this publication, we show that even for the weak and intermediate U regimes, the spin-orbit exciton condensation is possible leading also to staggered magnetic order. The canonical electron-hole excitations (excitons) transform into local triplon excitations at large U , and this BEC strong coupling regime is smoothly connected to the intermediate U excitonic insulator region. We solved the degenerate three-orbital Hubbard model with spin-orbit coupling ($\lambda$) in one-dimensional geometry using the Density Matrix Renormalization Group, while in two-dimensional square clusters we use the Hartree-Fock approximation (HFA). Employing these techniques, we provide the full $\lambda$ vs U phase diagrams for both one- and two- dimensional lattices. Our main result is that at the intermediate Hubbard U region of our focus, increasing $\lambda$ at fixed U the system transitions from an incommensurate spin-density-wave metal to a Bardeen-Cooper-Schrieffer (BCS) excitonic insulator, with coherence length r coh of O(a) and O(10a) in 1d and 2d, respectively, with a the lattice spacing. Further increasing $\lambda$, the system eventually crosses over to the BEC limit (with r coh << a).

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• Magnetization dynamics fingerprints of an excitonic condensate $t_{2g}^4$ magnet
• Electronic structure, magnetic properties and pairing tendencies of the copper-based honeycomb lattice Na${}_2$Cu${}_2$TeO${}_6$
• Magnetic phases for two $t_{2g}$ holes with spin-orbit coupling and crystal field
• J = 0 nonmagnetic insulating state in K${}_2$Os$X_6$ (X = F, Cl and Br)
• Collective mode excitations and simulated $L$-edge resonant-inelastic x-ray scattering spectra in antiferromagnetic Ca${}_2$RuO${}_4$