Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2002.07351 · Physical review. B./Physical review. B

BCS-BEC crossover in a (t2g)4 excitonic magnet

Nitin Kaushal, Rahul Soni, Alberto Nocera, Gonzalo Álvarez, Elbio R. Dagotto

Published Jun 18, 2020• 13 citations
arXivHTMLPDF

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 (${J}_{\text{eff}}=1$). Here, 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 ($\ensuremath{\lambda}$) 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 $\ensuremath{\lambda}$ versus $U$ phase diagrams for both one- and two-dimensional lattices. Our main result is that at intermediate Hubbard $U$, increasing $\ensuremath{\lambda}$ 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 $\mathcal{O}(a)$ and $\mathcal{O}(10a)$ in $1d$ and $2d$, respectively, with $a$ being the lattice spacing. Further increasing $\ensuremath{\lambda}$, the system eventually crosses over to the BEC limit (with ${r}_{\mathrm{coh}}\ensuremath{\ll}a$).

DOI
10.1103/physrevb.101.245147

Related papers

BCS-BEC crossover in the extended Falicov-Kimball model: Variational cluster approach

Kazuhiro Seki, R. Eder, Y. Ohta

We study the spontaneous symmetry breaking of the excitonic insulator state induced by the Coulomb interaction $U$ in the two-dimensional extended Falicov-Kimball model. Using the variational cluster approximation (VCA) and Hartree-Fock approximation (HFA), we evaluate the order parameter, single-particle excitation gap, momentum distribution functions, coherence length of excitons, and single-particle and anomalous excitation spectra as functions of $U$ at zero temperature. We find that in the weak-to-intermediate coupling regime, the Fermi surface plays an essential role and calculated results can be understood in close correspondence with the BCS theory, whereas in the strong-coupling regime, the Fermi surface plays no role and results are consistent with the picture of a Bose-Einstein condensate (BEC). Moreover, we find that HFA works well in both the weak- and strong-coupling regimes, and that the difference between the results of VCA and HFA mostly appears in the intermediate-coupling regime. The reason for this is discussed from a viewpoint of the self-energy. We thereby clarify the excitonic insulator state that typifies either a BCS condensate of electron-hole pairs (weak-coupling regime) or a BEC of preformed excitons (strong-coupling regime).

arXiv:1110.3150•Physical Review B•Dec 12, 2011•93 citations

Block excitonic condensate at n=3.5 in a spin-orbit coupled t2g multiorbital Hubbard model

Nitin Kaushal, Alberto Nocera, Gonzalo Álvarez +2 more

Theoretical studies recently predicted the condensation of spin-orbit excitons at momentum $q=\ensuremath{\pi}$ in ${t}_{2g}^{4}$ spin-orbit coupled three-orbital Hubbard models at electronic density $n=4$. In parallel, experiments involving iridates with noninteger valence states for the Ir ions are starting to attract considerable attention. In this publication, using the density matrix renormalization group technique we present evidence for the existence of an excitonic condensate at $n=3.5$ in a one-dimensional Hubbard model with a degenerate ${t}_{2g}$ sector, when in the presence of spin-orbit coupling. At intermediate Hubbard $U$ and spin-orbit $\ensuremath{\lambda}$ couplings, we found an excitonic condensate at the unexpected momentum $q=\ensuremath{\pi}/2$ involving ${j}_{\mathrm{eff}}=3/2,m=\ifmmode\pm\else\textpm\fi{}1/2$, and ${j}_{\mathrm{eff}}=1/2,m=\ifmmode\pm\else\textpm\fi{}1/2$ bands in the triplet channel, coexisting with an also unexpected block magnetic order. We also present the entire $\ensuremath{\lambda}$ vs $U$ phase diagram, at a fixed and robust Hund coupling. Interestingly, this new ``block excitonic phase'' is present even at large values of $\ensuremath{\lambda}$, unlike the $n=4$ excitonic phase discussed before. Our computational study helps to understand and predict the possible magnetic phases of materials with ${d}^{3.5}$ valence and robust spin-orbit coupling.

arXiv:1901.05578•Physical review. B./Physical review. B•Apr 8, 2019•6 citations

BCS–BEC Crossover of Triplet Exciton Condensation in Bilayer Systems

Hidemaro Suwa, Shang-Shun Zhang, Cristian D. Batista

We study the BCS-BEC crossover phenomenon of triplet exciton condensation using a half-filled bilayer Hubbard model.We calculate the dynamical spin structure factor and the exciton wave function on the phase boundary between the antiferromagnetically ordered and disordered phases.In the BCS regime, the formation and condensation of particle-hole bound states, namely excitons, occur simultaneously at the phase transition point, and the exciton wave function is extended in real space.In the BEC regime, on the other hand, bound states are well defined over the whole Brillouin zone also in the disordered phase, and the size of particle-hole pairs is smaller than a lattice space.Quantum criticality of charge-spin-orbital entangled states can emerge from intermediate coupling materials in the crossover regime.

arXiv:2209.07178•International Conference on Low Temperature Physics (LT)•May 22, 2023•0 citations

Excitonic BCS-BEC crossover at finite temperature: Effects of repulsion and electron-hole mass difference

Yuh Tomio, Kotaro Honda, Tetsuo Ogawa

The BCS to Bose-Einstein condensation (BEC) crossover of electron-hole $(e\text{\ensuremath{-}}h)$ pairs in optically excited semiconductors is studied using the two-band Hubbard model with both repulsive and attractive interactions. Applying the self-consistent $t$-matrix approximation combined with a local approximation, we examine the properties of a normal phase and an excitonic instability. The transition temperature from the normal phase to an $e\text{\ensuremath{-}}h$ pair condensed one is studied to clarify the crossover from an $e\text{\ensuremath{-}}h$ BCS-like state to an excitonic Bose-Einstein condensation, which takes place on increasing the $e\text{\ensuremath{-}}h$ attraction strength. To investigate effects of the repulsive interaction and the $e\text{\ensuremath{-}}h$ mass difference, we calculate the transition temperature for various parameters of the interaction strengths, the $e\text{\ensuremath{-}}h$ particle density, and the mass difference. While the transition temperature in the $e\text{\ensuremath{-}}h$ BCS regime is sufficiently suppressed by the repulsive interaction, that of the excitonic BEC is largely insensitive to it. We also show quantitatively that in the whole regime the mass difference leads to large suppression of the transition temperature.

arXiv:cond-mat/0606100•Physical Review B•Jun 12, 2006•28 citations

Order, Criticality, and Excitations in the Extended Falicov-Kimball Model

Satoshi Ejima, Tatsuya Kaneko, Y. Ohta +1 more

Using exact numerical techniques, we investigate the nature of excitonic (electron-hole) bound states and the development of exciton coherence in the one-dimensional half-filled extended Falicov-Kimball model. The ground-state phase diagram of the model exhibits, besides band-insulator and staggered orbital ordered phases, an excitonic insulator (EI) with power-law correlations. The criticality of the EI state shows up in the von Neumann entropy. The anomalous spectral function and condensation amplitude provide the binding energy and coherence length of the electron-hole pairs which, on their part, point towards a Coulomb interaction driven crossover from BCS-like electron-hole pairing fluctuations to tightly bound excitons. We show that while a mass imbalance between electrons and holes does not affect the location of the BCS-BEC crossover regime, it favors staggered orbital ordering to the disadvantage of the EI. Within the Bose-Einstein condensation (BEC) regime, the quasiparticle dispersion develops a flat valence-band top, in accord with the experimental finding for Ta2NiSe5.

arXiv:1308.0361•Physical Review Letters•Jan 13, 2014•58 citations

Density matrix renormalization group study of a three-orbital Hubbard model with spin-orbit coupling in one dimension

Nitin Kaushal, J. Herbrych, Alberto Nocera +4 more

Using the density matrix renormalization group technique we study the effect of spin-orbit coupling on a three-orbital Hubbard model in the ${({t}_{2g})}^{4}$ sector and in one dimension. Fixing the Hund coupling to a robust value compatible with some multiorbital materials, we present the phase diagram varying the Hubbard $U$ and spin-orbit coupling $\ensuremath{\lambda}$, at zero temperature. Our results are shown to be qualitatively similar to those recently reported using the dynamical mean-field theory in higher dimensions, providing a robust basis to approximate many-body techniques. Among many results, we observe an interesting transition from an orbital-selective Mott phase to an excitonic insulator with increasing $\ensuremath{\lambda}$ at intermediate $U$. In the strong $U$ coupling limit, we find a nonmagnetic insulator with an effective angular momentum $\ensuremath{\langle}{({\mathbf{J}}^{\mathrm{eff}})}^{2}\ensuremath{\rangle}\ensuremath{\ne}0$ near the excitonic phase, smoothly connected to the $\ensuremath{\langle}{({\mathbf{J}}^{\mathrm{eff}})}^{2}\ensuremath{\rangle}=0$ regime. We also provide a list of quasi-one-dimensional materials where the physics discussed in this paper could be realized.

arXiv:1707.04313•Physical review. B./Physical review. B•Oct 9, 2017•24 citations
The condensation of spin-orbit-induced excitons in t2g4{t}_{2g}^{4}t2g4​ electronic systems is attracting considerable attention. At large Hubbard UUU, antiferromagnetism was proposed to emerge from the Bose-Einstein Condensation (BEC) of triplons (Jeff=1{J}_{\text{eff}}=1Jeff​=1). Here, we show that even at intermediate UUU 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 UUU, and this BEC strong coupling regime is smoothly connected to the intermediate UUU excitonic insulator region. We solved the degenerate three-orbital Hubbard model with spin-orbit coupling (\ensuremathλ\ensuremath{\lambda}\ensuremathλ) 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 \ensuremathλ\ensuremath{\lambda}\ensuremathλ versus UUU phase diagrams for both one- and two-dimensional lattices. Our main result is that at intermediate Hubbard UUU, increasing \ensuremathλ\ensuremath{\lambda}\ensuremathλ at fixed UUU the system transitions from an incommensurate spin-density-wave metal to a Bardeen-Cooper-Schrieffer (BCS) excitonic insulator, with coherence length rcoh{r}_{\mathrm{coh}}rcoh​ of O(a)\mathcal{O}(a)O(a) and O(10a)\mathcal{O}(10a)O(10a) in 1d1d1d and 2d2d2d, respectively, with aaa being the lattice spacing. Further increasing \ensuremathλ\ensuremath{\lambda}\ensuremathλ, the system eventually crosses over to the BEC limit (with rcoh\ensuremath≪a{r}_{\mathrm{coh}}\ensuremath{\ll}arcoh​\ensuremath≪a).
We study the spontaneous symmetry breaking of the excitonic insulator state induced by the Coulomb interaction UUU in the two-dimensional extended Falicov-Kimball model. Using the variational cluster approximation (VCA) and Hartree-Fock approximation (HFA), we evaluate the order parameter, single-particle excitation gap, momentum distribution functions, coherence length of excitons, and single-particle and anomalous excitation spectra as functions of UUU at zero temperature. We find that in the weak-to-intermediate coupling regime, the Fermi surface plays an essential role and calculated results can be understood in close correspondence with the BCS theory, whereas in the strong-coupling regime, the Fermi surface plays no role and results are consistent with the picture of a Bose-Einstein condensate (BEC). Moreover, we find that HFA works well in both the weak- and strong-coupling regimes, and that the difference between the results of VCA and HFA mostly appears in the intermediate-coupling regime. The reason for this is discussed from a viewpoint of the self-energy. We thereby clarify the excitonic insulator state that typifies either a BCS condensate of electron-hole pairs (weak-coupling regime) or a BEC of preformed excitons (strong-coupling regime).
Theoretical studies recently predicted the condensation of spin-orbit excitons at momentum $q=\ensuremath{\pi}$ in t2g4{t}_{2g}^{4}t2g4​ spin-orbit coupled three-orbital Hubbard models at electronic density n=4n=4n=4. In parallel, experiments involving iridates with noninteger valence states for the Ir ions are starting to attract considerable attention. In this publication, using the density matrix renormalization group technique we present evidence for the existence of an excitonic condensate at n=3.5n=3.5n=3.5 in a one-dimensional Hubbard model with a degenerate t2g{t}_{2g}t2g​ sector, when in the presence of spin-orbit coupling. At intermediate Hubbard UUU and spin-orbit $\ensuremath{\lambda}$ couplings, we found an excitonic condensate at the unexpected momentum $q=\ensuremath{\pi}/2$ involving ${j}_{\mathrm{eff}}=3/2,m=\ifmmode\pm\else\textpm\fi{}1/2$, and ${j}_{\mathrm{eff}}=1/2,m=\ifmmode\pm\else\textpm\fi{}1/2$ bands in the triplet channel, coexisting with an also unexpected block magnetic order. We also present the entire $\ensuremath{\lambda}$ vs UUU phase diagram, at a fixed and robust Hund coupling. Interestingly, this new ``block excitonic phase'' is present even at large values of $\ensuremath{\lambda}$, unlike the n=4n=4n=4 excitonic phase discussed before. Our computational study helps to understand and predict the possible magnetic phases of materials with d3.5{d}^{3.5}d3.5 valence and robust spin-orbit coupling.
We study the BCS-BEC crossover phenomenon of triplet exciton condensation using a half-filled bilayer Hubbard model.We calculate the dynamical spin structure factor and the exciton wave function on the phase boundary between the antiferromagnetically ordered and disordered phases.In the BCS regime, the formation and condensation of particle-hole bound states, namely excitons, occur simultaneously at the phase transition point, and the exciton wave function is extended in real space.In the BEC regime, on the other hand, bound states are well defined over the whole Brillouin zone also in the disordered phase, and the size of particle-hole pairs is smaller than a lattice space.Quantum criticality of charge-spin-orbital entangled states can emerge from intermediate coupling materials in the crossover regime.
The BCS to Bose-Einstein condensation (BEC) crossover of electron-hole $(e\text{\ensuremath{-}}h)$ pairs in optically excited semiconductors is studied using the two-band Hubbard model with both repulsive and attractive interactions. Applying the self-consistent ttt-matrix approximation combined with a local approximation, we examine the properties of a normal phase and an excitonic instability. The transition temperature from the normal phase to an $e\text{\ensuremath{-}}h$ pair condensed one is studied to clarify the crossover from an $e\text{\ensuremath{-}}h$ BCS-like state to an excitonic Bose-Einstein condensation, which takes place on increasing the $e\text{\ensuremath{-}}h$ attraction strength. To investigate effects of the repulsive interaction and the $e\text{\ensuremath{-}}h$ mass difference, we calculate the transition temperature for various parameters of the interaction strengths, the $e\text{\ensuremath{-}}h$ particle density, and the mass difference. While the transition temperature in the $e\text{\ensuremath{-}}h$ BCS regime is sufficiently suppressed by the repulsive interaction, that of the excitonic BEC is largely insensitive to it. We also show quantitatively that in the whole regime the mass difference leads to large suppression of the transition temperature.
Using exact numerical techniques, we investigate the nature of excitonic (electron-hole) bound states and the development of exciton coherence in the one-dimensional half-filled extended Falicov-Kimball model. The ground-state phase diagram of the model exhibits, besides band-insulator and staggered orbital ordered phases, an excitonic insulator (EI) with power-law correlations. The criticality of the EI state shows up in the von Neumann entropy. The anomalous spectral function and condensation amplitude provide the binding energy and coherence length of the electron-hole pairs which, on their part, point towards a Coulomb interaction driven crossover from BCS-like electron-hole pairing fluctuations to tightly bound excitons. We show that while a mass imbalance between electrons and holes does not affect the location of the BCS-BEC crossover regime, it favors staggered orbital ordering to the disadvantage of the EI. Within the Bose-Einstein condensation (BEC) regime, the quasiparticle dispersion develops a flat valence-band top, in accord with the experimental finding for Ta2NiSe5.
Using the density matrix renormalization group technique we study the effect of spin-orbit coupling on a three-orbital Hubbard model in the (t2g)4{({t}_{2g})}^{4}(t2g​)4 sector and in one dimension. Fixing the Hund coupling to a robust value compatible with some multiorbital materials, we present the phase diagram varying the Hubbard UUU and spin-orbit coupling $\ensuremath{\lambda}$, at zero temperature. Our results are shown to be qualitatively similar to those recently reported using the dynamical mean-field theory in higher dimensions, providing a robust basis to approximate many-body techniques. Among many results, we observe an interesting transition from an orbital-selective Mott phase to an excitonic insulator with increasing $\ensuremath{\lambda}$ at intermediate UUU. In the strong UUU coupling limit, we find a nonmagnetic insulator with an effective angular momentum $\ensuremath{\langle}{({\mathbf{J}}^{\mathrm{eff}})}^{2}\ensuremath{\rangle}\ensuremath{\ne}0$ near the excitonic phase, smoothly connected to the $\ensuremath{\langle}{({\mathbf{J}}^{\mathrm{eff}})}^{2}\ensuremath{\rangle}=0$ regime. We also provide a list of quasi-one-dimensional materials where the physics discussed in this paper could be realized.