Block excitonic condensate at 
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 in a spin-orbit coupled 
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 multiorbital Hubbard model

Kaushal, Nitin; Nocera, Alberto; Álvarez, Gonzalo; Moreo, Adriana; Dagotto, Elbio

doi:10.1103/physrevb.99.155115

Cited by 10 publications

(8 citation statements)

References 85 publications

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“…We believe that our numerical results related to spin and orbital ordering, using a realistic threeorbital Hubbard model, provide a qualitatively accurate description for the compound Sr 2 CrO 4 . With the evidence provided here and in other related publications that the orbital degree of freedom is active in Cr ox-ides, a plethora of attractive possibilities open up, such as replicating with Cr the wide variety of orbitally ordered states reported in manganites [51,52] and ruthenates [53], the effect of strain [54,55], and the possibility of block states [56][57][58][59] or even spirals [60]. Recent theoretical work has even suggested that superconductivity is possible upon doping a doubly degenerate multiorbital system in chains [61] and, thus, similar results in planes could occur.…”

Section: Discussionmentioning

confidence: 53%

Origin of the Magnetic and Orbital ordering in $α$-Sr$_2$CrO$_4$

Pandey,

Zhang,

Kaushal

et al. 2020

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Motivated by recent experimental progress in transition metal oxides with the K2NiF4 structure, we investigate the magnetic and orbital ordering in α-Sr2CrO4. Using first principles calculations, first we derive a three-orbital Hubbard model, which reproduces the ab initio band structure near the Fermi level. The unique reverse splitting of t2g orbitals in α-Sr2CrO4, with the 3d 2 electronic configuration for the Cr 4+ oxidation state, opens up the possibility of orbital ordering in this material. Using real-space Hartree-Fock for multi-orbital systems, we constructed the ground state phase diagram for the two dimensional compound α-Sr2CrO4. We found stable ferromagnetic, antiferromagnetic, antiferro-orbital, and staggered orbital stripe ordering in robust regions of the phase diagram. Furthermore, using the density matrix renormalization group method for two-leg ladders with the realistic hopping parameters of α-Sr2CrO4, we explore magnetic and orbital ordering for experimentally relevant interaction parameters. Again, we find a clear signature of antiferromagnetic spin ordering along with antiferro-orbital ordering at moderate to large Hubbard interaction strength. We also explore the orbital-resolved density of states with Lanczos, predicting insulating behavior for the compound α-Sr2CrO4, in agreement with experiments. Finally, an intuitive understanding of the results is provided based on a hierarchy between orbitals, with dxy driving the spin order, while electronic repulsion and the effective one dimensionality of the movement within the dxz and dyz orbitals driving the orbital order.

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Section: Discussionmentioning

confidence: 53%

Origin of the Magnetic and Orbital ordering in $α$-Sr$_2$CrO$_4$

Pandey,

Zhang,

Kaushal

et al. 2020

Preprint

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“…On the other hand, in the BEC region we found nearly linearly increasing ∆(q = π) with L, which implies either a very slow power-law decay or even true long-range order. Such a true long-range order in our one-dimensional system is allowed as the U (1) symmetry related to the excitonic condensation is explicitly broken by a finite Hund coupling [13]. The analysis above also clearly implies that as we increase the system size and hence increase the number of excitons, these excitons can condense also at momentum q = π in the BCS limit, whereas in the BEC limit excitons condense only at q = π.…”

Section: B Bcs-bec Crossover and Ic-sdw Metal To Bcs-excitonic Insula...mentioning

confidence: 78%

“…Finally, the P iγ = c i↓γ c i↑γ operator in the fourth term (pair-hopping) is the pair anhilation operator that arises from the matrix elements of the "1/r" Coulomb repulsion as in the early studies of Kanamori. We used the standard relation U = U − 2J H due to rotational invariance, and we fix J H = U/4 for all the calculations as employed widely in previous efforts [12,13,[37][38][39].…”

Section: Model and Methodsmentioning

confidence: 99%

“…The extended Falicov-Kimball model has been used often as a minimal theoretical model to investigate the above discussed physics [7][8][9]. Only recently, the more realistic, but also more difficult, three-orbital Hubbard models were explored to study excitonic condensation [10][11][12][13]. Due to the theoretical progress, on the experimental side there have been some studies showing reliable signatures of the excitonic condensate in real materials such as in a transition metal dichalcogenide [14], Ta 2 NiSe 5 [15], and in bilayer systems [16,17].…”

Section: Introductionmentioning

confidence: 99%

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

Kaushal,

Soni,

Nocera

et al. 2020

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The condensation of spin-orbit-induced excitons in t 4 2g 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 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 (λ) 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 λ vs U phase diagrams for both one-and twodimensional lattices. Our main result is that at the intermediate Hubbard U region of our focus, increasing λ 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 λ, the system eventually crosses over to the BEC limit (with r coh << a).

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“…Our calculations will be extended in future work in various directions. For example, into other chain multiorbital systems with exotic states [33], including spin-orbit coupling [34], into ladder geometries [35], in materials with orbital order [36], ruthenates [37], and into generic t − J models [38].…”

mentioning

confidence: 99%

Excitonic wave-packet evolution in a two-orbital Hubbard model chain: A real-time real-space study

Pandey,

Alvarez,

Dagotto

2021

Preprint

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Motivated by experimental developments introducing the concept of spin-orbit separation, we study the real-space time evolution of an excitonic wave-packet using a two-orbital Hubbard model. The exciton is created by exciting an electron from a lower energy half-filled orbital to a higher energy empty orbital. We carry out the real-time dynamics of the resulting excitonic wave-packet, using the time-dependent density matrix renormalization group method. We find clear evidence of chargespin and spin-orbit separation in real-space, by tracking the time evolution of local observables. We show that the velocity of the orbiton can be tuned by varying the inter-orbital interactions. We also present a comparative study of a hole (in one orbital) and exciton (in two orbitals) dynamics in one-dimensional systems. Moreover, we analyze the dynamics of an exciton with spin-flip excitation, where we observe fractionalized spinons induced by Hund's interaction.

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

Cited by 10 publications

References 85 publications

Origin of the Magnetic and Orbital ordering in $α$-Sr$_2$CrO$_4$

Origin of the Magnetic and Orbital ordering in $α$-Sr$_2$CrO$_4$

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

Excitonic wave-packet evolution in a two-orbital Hubbard model chain: A real-time real-space study

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