Title: 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. 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 $r_{\mathrm{coh}}\ll a$).

Authors:

Kaushal, Nitin ^[1]; Soni, Rahul  ^[1];

• Search DOE PAGES for author "Soni, Rahul"
• Search DOE PAGES for ORCID "0000-0003-1771-4299"

Nocera, Alberto ^[2]; Alvarez, Gonzalo  ^[3];

• Search DOE PAGES for author "Alvarez, Gonzalo"
• Search DOE PAGES for ORCID "0000-0002-1496-8261"

Dagotto, Elbio R. ^[1]

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+ Show Author Affiliations

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)

Publication Date:

Thu Jun 18 00:00:00 EDT 2020

Research Org.:

Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Sponsoring Org.:

USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division

OSTI Identifier:

1649072

Grant/Contract Number:  

AC05-00OR22725

Resource Type:

Accepted Manuscript

Journal Name:

Physical Review B

Additional Journal Information:

Journal Volume: 101; Journal Issue: 24; Journal ID: ISSN 2469-9950

Publisher:

American Physical Society (APS)

Country of Publication:

United States

Language:

English

Subject:

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