BCS-BEC crossover in a (t_2g)⁴ excitonic magnet

Journal Article · Thu Jun 18 00:00:00 EDT 2020 · Physical Review B

DOI:https://doi.org/10.1103/physrevb.101.245147· OSTI ID:1649072

Kaushal, Nitin ^[1]; Soni, Rahul  ^[1]; Nocera, Alberto ^[2]; Alvarez, Gonzalo  ^[3]; Dagotto, Elbio R. ^[1]

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1. University of Tennessee, Knoxville, TN (United States); Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
2. University of British Columbia, Vancouver, B.C. (Canada)
3. Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

The condensation of spin-orbit-induced excitons in $t_{2g}^4$ electronic systems is attracting considerable attention. At large Hubbard $U$, antiferromagnetism was proposed to emerge from the Bose-Einstein Condensation (BEC) of triplons ( $J_{\text{eff}}=1$). Furthermore, we show that even at 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 dimension using the density matrix renormalization group, while in two dimensions we use the Hartree-Fock approximation (HFA). Employing these techniques, we provide the full $\lambda$ versus $U$ phase diagrams for both one- and two-dimensional lattices. Our main result is that at intermediate Hubbard $U$, 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 $r_{\mathrm{coh}}$ of $\mathcal{O}\left(a\right)$ and $\mathcal{O}\left(10a\right)$ in $1d$ and $2d$, respectively, with $a$ being the lattice spacing. Further increasing $\lambda$, the system eventually crosses over to the BEC limit (with $r_{\mathrm{coh}}\ll a$).

• Research Organization: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division
• Grant/Contract Number: AC05-00OR22725
• OSTI ID: 1649072
• Journal Information: Physical Review B, Vol. 101, Issue 24; ISSN 2469-9950
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BEC-BCS crossover
Excitons
Magnetism
Phase diagrams
Spin-orbit coupling
1-dimensional systems
2-dimensional systems
Density matrix renormalization group
Hubbard model