Non-local interactions in moiré Hubbard systems

Morales-Durán, Nicolás; Hu, Nai Chao; Potasz, Pawel; MacDonald, Allan H.

doi:10.48550/arxiv.2108.03313

Cited by 6 publications

(17 citation statements)

References 36 publications

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“…In experiment, the filling can be adjusted, and Van Hove filling can be reached, by tuning the gate voltage, which we model here by varying the chemical potential µ between 1/4 and 1/2 filling. The interaction parameters U , V n also depend on the twist angle, and on the dielectric environment so that the strength and range of interactions can be controlled [43]. First-principles calculations show that the extended interactions V n are sizable in effective models for heterobilayer TMDs [18].…”

mentioning

confidence: 99%

$\mathcal{N}=4$ chiral superconductivity in moiré transition metal dichalcogenides

Scherer,

Kennes,

Classen

2021

Preprint

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mentioning

confidence: 99%

$\mathcal{N}=4$ chiral superconductivity in moiré transition metal dichalcogenides

Scherer,

Kennes,

Classen

2021

Preprint

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“…While electronic triangular lattices occur naturally in Wigner crystals (WC), electrons can also spontaneously organize in honeycomb lattices to form mutually stabilized Mott-Wigner states in twisted homobilayer TMDs. Although super-exchange interactions are expected to generate antiferromagnetic order in bipartite lattices, competition with direct exchange can favor ferromagnetism [30].…”

Section: Umklapp Signatures Of Ferromagnetic and Antiferromagnetic Ho...mentioning

confidence: 99%

Optical signatures of periodic magnetization: the moiré Zeeman effect

Salvador,

Kuhlenkamp,

Ciorciaro

et al. 2021

Preprint

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Detecting magnetic order at the nanoscale is of central interest for the study of quantum magnetism in general, and the emerging field of moiré magnets in particular. Here, we analyze the exciton band structure that arises from a periodic modulation of the valley Zeeman effect. Despite long-range electron-hole exchange interactions, we find a sizable splitting in the energy of the bright circularly-polarized exciton Umklapp resonances, which serves as a direct optical probe of magnetic order. We first analyze quantum moiré magnets realized by periodic ordering of electron spins in Mott-Wigner states of transition metal dichalcogenide (TMD) monolayers or twisted bilayers: we show that spin-valley dependent exciton-electron interactions allow for probing the spin-valley order of electrons and demonstrate that it is possible to observe unique signatures of ferromagnetic order in a triangular lattice and both ferromagnetic and Néel order in a honeycomb lattice. We then focus on semiclassical moiré magnets realized in twisted bilayers of ferromagnetic materials: we propose a detection scheme for moiré magnetism which is based on inter-layer exchange coupling between spins in a moiré magnet and excitons in a TMD monolayer.

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“…On the theory side, a series of sophisticated numerical studies of the triangular-lattice Hubbard model has recently been put forward focusing on the half-filled case [18][19][20][21][22][23] and slightly doping away from it [24,25]. In addition, the important effect of extended Hubbard interactions, which are sizable in moiré TMDs, was investigated [26][27][28]. Away from half filling, several studies have discussed indications for topological superconducting phases, which are facilitated in this system due to the hexagonal lattice structure [29][30][31][32][33][34][35][36][37][38][39][40], and are also strongly affected by the presence of extended Hubbard interactions [37][38][39][40][41][42].…”

Section: Introductionmentioning

confidence: 99%

Competing instabilities of the extended Hubbard model on the triangular lattice: Truncated-unity functional renormalization group and application to moiré materials

Gneist,

Classen,

Scherer

2022

Preprint

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A simple yet paradigmatic model for the interplay of strong electronic correlations and geometric frustration is the triangular lattice Hubbard model. Recently it was proposed that moiré structures of transition metal dichalcogenides can be used to simulate extended versions that include non-local density-density interactions. We study competing instabilities of interacting electrons in such an extended Hubbard model on the triangular lattice near a filling where the density of states has a Van Hove singularity. We employ a truncated-unity functional renormalization group approach to investigate two cases: a paradigmatic minimally extended Hubbard model and a specific model with parameters that are applicable to hetero-bilayers of transition metal dichalcogenides. We unravel rich phase diagrams, including tendencies to spin-density-wave order and unconventional pairing, which can give rise to topological superconductivity. We classify the symmetry of the superconducting instabilities according to their irreducible representations and show that higher lattice harmonics are dominant when the nearest-neighbor interaction is sizable indicating pair formation between second-nearest neighbors. The phenomenological consequences can be enhanced spin and thermal quantum Hall responses in a topological superconductor.

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Non-local interactions in moiré Hubbard systems

Cited by 6 publications

References 36 publications

$\mathcal{N}=4$ chiral superconductivity in moiré transition metal dichalcogenides

$\mathcal{N}=4$ chiral superconductivity in moiré transition metal dichalcogenides

Optical signatures of periodic magnetization: the moiré Zeeman effect

Competing instabilities of the extended Hubbard model on the triangular lattice: Truncated-unity functional renormalization group and application to moiré materials

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