Correlated insulating states at fractional fillings of moiré superlattices

Yang, Xu; Liu, Song; Rhodes, Daniel; Watanabe, Kenji; Taniguchi, Takashi; Hone, James; Elser, Veit; Mak, Kin Fai; Shan, Jie

doi:10.1038/s41586-020-2868-6

Cited by 421 publications

(344 citation statements)

References 45 publications

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“…Due to the~4% lattice mismatch, the angle-aligned WS 2 /WSe 2 bilayer would form a triangular moiré superlattice with a period of~8 nm. The strong moiré coupling 1,5 will result in mini flatbands 26 , which could host correlated insulating state at half band filling with one carrier localized in one moiré cell (n = ±1) 14,15 , or even at various fractional fillings of the moiré unit cell that have been interpreted as generalized Wigner crystal states 14,18,19 or stripe phases [18][19][20] . The filling patterns for n = 1 and 1/3 are shown schematically in Fig.…”

Section: Resultsmentioning

confidence: 99%

“…In addition, due to the large effective mass [10][11][12] , the kinetic energy is further reduced in twisted bilayer TMDCs 13 . The resulting enhanced Coulomb interaction with respect to the kinetic energy leads to strong interactions that give rise to various exotic correlated insulating states [13][14][15][16][17][18][19][20][21] with high transition temperatures. Very recently, Mott insulator states at fillings n = ±1 (one electron or hole per Moiré cell), generalized Wigner crystal states at filings n = ±1/3, ±2/3, and even more exotic insulating states at other fractional fillings have been reported [14][15][16][17][18][19][20][21] .…”

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confidence: 99%

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Strong interaction between interlayer excitons and correlated electrons in WSe2/WS2 moiré superlattice

et al. 2021

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Heterobilayers of transition metal dichalcogenides (TMDCs) can form a moiré superlattice with flat minibands, which enables strong electron interaction and leads to various fascinating correlated states. These heterobilayers also host interlayer excitons in a type-II band alignment, in which optically excited electrons and holes reside on different layers but remain bound by the Coulomb interaction. Here we explore the unique setting of interlayer excitons interacting with strongly correlated electrons, and we show that the photoluminescence (PL) of interlayer excitons sensitively signals the onset of various correlated insulating states as the band filling is varied. When the system is in one of such states, the PL of interlayer excitons is relatively amplified at increased optical excitation power due to reduced mobility, and the valley polarization of interlayer excitons is enhanced. The moiré superlattice of the TMDC heterobilayer presents an exciting platform to engineer interlayer excitons through the periodic correlated electron states.

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Section: Resultsmentioning

confidence: 99%

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Strong interaction between interlayer excitons and correlated electrons in WSe2/WS2 moiré superlattice

et al. 2021

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“…By varying the twist angle, the relative strength of the bandwidth and electron interaction can be tuned, and a rich quantum phase diagram can potentially be realized [23][24][25][26]. Encouragingly, transport and optical experiments are starting to observe correlated insulating states in the TMD heterobilayer WSe 2 /WS 2 with n 1 holes per moiré unit cell [27][28][29]. In particular, the insulating state at n = 1 is theoretically identified as a charge-transfer insulator with a cation and an anion at different locations in the moiré unit cell, corresponding to localized Wannier orbitals at the primary and secondary energy minimum of the moiré potential, respectively [30,31].…”

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Charge transfer excitations, pair density waves, and superconductivity in moiré materials

Slagle

2020

Phys. Rev. B

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Transition-metal dichalcogenide (TMD) bilayers are a new class of tunable moiré systems attracting interest as quantum simulators of strongly interacting electrons in two dimensions. In particular, recent theory predicts that the correlated insulator observed in WSe 2 /WS 2 at half filling is a charge-transfer insulator similar to cuprates and, upon further hole doping, exhibits a transfer of charge from anionlike to cationlike orbitals at different locations in the moiré unit cell. In this work, we demonstrate that in this doped charge-transfer insulator, tightly bound charge-2e excitations can form to lower the total electrostatic repulsion. This composite excitation, which we dub a trimer, consists of a pair of holes bound to a charge-transfer exciton. When the bandwidth of doped holes is small, trimers crystallize into insulating pair density waves at a sequence of commensurate doping levels. When the bandwidth becomes comparable to the pair binding energy, itinerant holes and charge-2e trimers interact resonantly, leading to unconventional superconductivity similar to superfluidity in an ultracold Fermi gas near Feshbach resonance. Our theory is broadly applicable to strongly interacting charge-transfer insulators, such as WSe 2 /WS 2 or TMD homobilayers under an applied electric field.

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“…It is associated with an occurrence of the Moiré pattern (the triangular lattice with very large supercell). Hetero-bilayer transition metals dichalcogenides system is the other field where this pattern appears [ 97 , 98 ]. This makes further studies of properties of different models on the triangular lattice desirable.…”

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confidence: 99%

Charge-Order on the Triangular Lattice: A Mean-Field Study for the Lattice S = 1/2 Fermionic Gas

Kapcia

2021

Nanomaterials

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The adsorbed atoms exhibit tendency to occupy a triangular lattice formed by periodic potential of the underlying crystal surface. Such a lattice is formed by, e.g., a single layer of graphane or the graphite surfaces as well as (111) surface of face-cubic center crystals. In the present work, an extension of the lattice gas model to S=1/2 fermionic particles on the two-dimensional triangular (hexagonal) lattice is analyzed. In such a model, each lattice site can be occupied not by only one particle, but by two particles, which interact with each other by onsite U and intersite W1 and W2 (nearest and next-nearest-neighbor, respectively) density-density interaction. The investigated hamiltonian has a form of the extended Hubbard model in the atomic limit (i.e., the zero-bandwidth limit). In the analysis of the phase diagrams and thermodynamic properties of this model with repulsive W1>0, the variational approach is used, which treats the onsite interaction term exactly and the intersite interactions within the mean-field approximation. The ground state (T=0) diagram for W2≤0 as well as finite temperature (T>0) phase diagrams for W2=0 are presented. Two different types of charge order within 3×3 unit cell can occur. At T=0, for W2=0 phase separated states are degenerated with homogeneous phases (but T>0 removes this degeneration), whereas attractive W2<0 stabilizes phase separation at incommensurate fillings. For U/W1<0 and U/W1>1/2 only the phase with two different concentrations occurs (together with two different phase separated states occurring), whereas for small repulsive 0<U/W1<1/2 the other ordered phase also appears (with tree different concentrations in sublattices). The qualitative differences with the model considered on hypercubic lattices are also discussed.

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Correlated insulating states at fractional fillings of moiré superlattices

Cited by 421 publications

References 45 publications

Strong interaction between interlayer excitons and correlated electrons in WSe2/WS2 moiré superlattice

Strong interaction between interlayer excitons and correlated electrons in WSe2/WS2 moiré superlattice

Charge transfer excitations, pair density waves, and superconductivity in moiré materials

Charge-Order on the Triangular Lattice: A Mean-Field Study for the Lattice S = 1/2 Fermionic Gas

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