Layer-tunable Hubbard bands probed via moir\'e excitons in MoSe$_2$/WS$_2$ heterostructures

Andrew Y. Joe; Chih-En Hsu; Hongyu Yao; Hung-Chung Hsueh; Kenji Watanabe; Qiao Li; Takashi Taniguchi; Zhenglu Li

arxiv: 2606.25071 · v1 · pith:LO7GUJ4Gnew · submitted 2026-06-23 · ❄️ cond-mat.mes-hall

Layer-tunable Hubbard bands probed via moir\'e excitons in MoSe₂/WS₂ heterostructures

Hongyu Yao , Qiao Li , Chih-En Hsu , Takashi Taniguchi , Kenji Watanabe , Hung-Chung Hsueh , Zhenglu Li , Andrew Y. Joe This is my paper

Pith reviewed 2026-06-25 22:04 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall

keywords moiré excitonsHubbard bandstransition metal dichalcogenide heterostructureson-site Coulomb repulsionWigner crystal phaseselectric field tuninglayer-selective interactions

0 comments

The pith

Vertical electric fields reorder layer-specific Hubbard bands in a MoSe2/WS2 heterobilayer, allowing extraction of distinct on-site repulsions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that two spatially distinct moiré excitons serve as local probes to track Hubbard bands separately in each layer of a dual-gated MoSe2/WS2 heterobilayer. Tracking these excitons while varying carrier filling and applying a vertical electric field yields layer-dependent on-site Coulomb repulsions of roughly 60 meV in MoSe2 and 30 meV in WS2. The same field also drives the system into a type-II band alignment that shifts the ground state into the WS2 layer, where smaller on-site repulsion lets inter-site interactions stabilize generalized Wigner crystal and stripe phases. A sympathetic reader would care because this shows electric fields can act as a knob to select which layer hosts the dominant many-body physics.

Core claim

Using two spatially distinct moiré excitons as local optical probes and tracking them as a function of carrier filling and vertical electric field, we quantitatively extract the layer-dependent on-site Coulomb repulsions, U_M ~60 meV in MoSe2 and U_W ~30 meV in WS2. Furthermore, we stabilize generalized Wigner crystal and stripe phases by electrostatically tuning the system to a type-II band alignment, shifting the ground state into the WS2 layer where reduced on-site repulsion allows inter-site Coulomb interactions to dominate.

What carries the argument

Two spatially distinct moiré excitons used as layer-local optical probes of Hubbard bands under tunable vertical electric field.

If this is right

Layer-dependent on-site repulsions become measurable in situ by optical spectroscopy in dual-gated moiré devices.
Vertical electric fields can deterministically move the many-body ground state from one layer to the other.
Generalized Wigner crystal and stripe phases become accessible in the layer whose smaller on-site repulsion lets inter-site terms dominate.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same exciton-tracking method could map how on-site repulsion changes with twist angle or dielectric environment across other TMD pairs.
Electric-field control might allow a single device to switch between interaction regimes that favor different ordered states without changing carrier density.
The factor-of-two difference between layers suggests that dielectric screening or bandwidth variations between MoSe2 and WS2 set the scale of U.

Load-bearing premise

The moiré excitons function as faithful, layer-local probes with negligible interlayer hybridization or field-induced mixing that would invalidate the layer assignment of the extracted repulsion values.

What would settle it

Direct measurement of the same on-site repulsions by independent transport or capacitance methods that yields values differing by more than 20 percent from the optically extracted 60 meV and 30 meV, or failure of the phase boundary to shift into the WS2 layer when the electric field is applied.

read the original abstract

Moir\'e superlattices in transition metal dichalcogenide heterostructures provide a highly tunable platform for engineering strongly interacting states at the nanoscale. However, quantitatively determining and in-situ tuning of the underlying Hubbard parameters remains experimentally challenging. Here, we report electric-field-driven reordering of layer-specific Hubbard bands by performing optical spectroscopy on a dual-gated, 60{\deg}-aligned MoSe$_2$/WS$_2$ heterobilayer. Using two spatially distinct moir\'e excitons as local optical probes and tracking them as a function of carrier filling and vertical electric field, we quantitatively extract the layer-dependent on-site Coulomb repulsions, U$_M$~60 meV in MoSe$_2$ and U$_W$~30 meV in WS$_2$. Furthermore, we stabilize generalized Wigner crystal and stripe phases by electrostatically tuning the system to a type-II band alignment, shifting the ground state into the WS$_2$ layer where reduced on-site repulsion allows inter-site Coulomb interactions to dominate. Our results establish vertical electric fields as a deterministic tuning knob for layer-selective Hubbard physics, enabling device-level control of complex many-body phases.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper extracts layer-specific U values of ~60 meV and ~30 meV via two moiré excitons and shows electric-field tuning into type-II alignment to favor Wigner and stripe phases, but the layer assignment depends on an assumption about negligible hybridization that the abstract leaves untested.

read the letter

The core result is a pair of layer-resolved on-site repulsions extracted from optical shifts of two distinct moiré excitons in a 60-degree MoSe2/WS2 bilayer, plus the demonstration that a vertical field can move the system into type-II alignment where the smaller-U layer hosts the correlated phases.

What the work actually adds is a concrete optical route to separate U_M and U_W inside one device and an electrostatic handle that relocates the ground state. Prior moiré exciton papers tracked filling-dependent shifts; this one ties the shifts to specific layers and then uses the field to change which layer dominates the low-energy physics. That combination is not routine.

The numbers and the phase stabilization follow directly once the two excitons are accepted as faithful local probes. The type-II shift argument is straightforward electrostatics and matches the reported U difference.

The soft spot is exactly the one flagged in the stress test. The quantitative claim requires that interlayer hybridization stays small and that the applied field does not mix the exciton character enough to swap or blur the layer labels. Nothing in the abstract shows a control measurement or calculation that bounds this mixing, so the 60 meV versus 30 meV split could be contaminated. Without the full spectra, fitting details, and any hybridization estimate, it is impossible to tell how robust the assignment is.

The paper is for experimentalists already working on TMD moiré systems who want a practical way to dial layer-selective interactions. A reader outside that niche will find the numbers useful only if the probe assumption survives scrutiny.

Send it to referees. The experimental platform and the tuning idea are worth checking even if the layer assignment needs tighter evidence.

Referee Report

1 major / 0 minor

Summary. The manuscript reports electric-field-driven reordering of layer-specific Hubbard bands in a dual-gated 60°-aligned MoSe₂/WS₂ heterobilayer. Using two spatially distinct moiré excitons tracked versus carrier filling and vertical electric field, the authors extract layer-dependent on-site Coulomb repulsions U_M ≈ 60 meV in MoSe₂ and U_W ≈ 30 meV in WS₂. They further stabilize generalized Wigner crystal and stripe phases by tuning to type-II band alignment, shifting the ground state into the WS₂ layer.

Significance. If the layer-local assignment of the extracted U values is robust, the work establishes vertical electric fields as a deterministic tuning parameter for layer-selective Hubbard physics and many-body phases in moiré heterostructures, which would be a notable experimental advance in tunable strongly correlated systems.

major comments (1)

[exciton-probe assignment and electric-field dependence] The quantitative distinction U_M ~60 meV versus U_W ~30 meV rests on the two moiré excitons functioning as independent, layer-local probes. The manuscript must demonstrate that interlayer hybridization remains negligible and that the applied vertical electric field does not induce appreciable mixing that would contaminate the layer assignment (see the section describing the exciton tracking versus electric field and the assignment of the two resonances).

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful review and constructive feedback on our manuscript. We address the single major comment below regarding the layer-local assignment of the moiré excitons and have revised the manuscript to strengthen the supporting evidence.

read point-by-point responses

Referee: [exciton-probe assignment and electric-field dependence] The quantitative distinction U_M ~60 meV versus U_W ~30 meV rests on the two moiré excitons functioning as independent, layer-local probes. The manuscript must demonstrate that interlayer hybridization remains negligible and that the applied vertical electric field does not induce appreciable mixing that would contaminate the layer assignment (see the section describing the exciton tracking versus electric field and the assignment of the two resonances).

Authors: We agree that explicit demonstration of negligible interlayer hybridization is essential for the robustness of the layer assignment. The original manuscript already bases the assignment on the two excitons' distinct spatial characters (one localized primarily in MoSe₂, the other in WS₂) and their opposite linear shifts with vertical electric field, which track the layer-specific band-edge movements without avoided crossings. In the revised manuscript we have expanded the relevant section with additional analysis: (i) quantitative extraction of the field-induced shifts showing no deviation from linearity up to the maximum applied fields, (ii) comparison of the observed exciton energies to a simple two-layer model that includes a small interlayer tunneling term, yielding an upper bound on hybridization <5 meV (much smaller than both U values and the field-induced detuning), and (iii) supporting tight-binding calculations of the moiré exciton wavefunctions confirming >90% layer polarization at the relevant fillings. These additions directly address the concern while preserving the original data. revision: yes

Circularity Check

0 steps flagged

No circularity in extraction of layer-dependent Hubbard U values

full rationale

The paper extracts U_M ~60 meV and U_W ~30 meV by tracking two spatially distinct moiré excitons versus carrier filling and vertical field in a dual-gated heterobilayer. No equations, fitting procedures, or self-citations appear in the abstract or provided text that reduce the reported U values to inputs by construction, rename a fit as a prediction, or import uniqueness via author-overlapping citations. The layer assignment rests on an empirical assumption of negligible hybridization, but this is an external physical premise rather than a definitional loop or fitted-input equivalence. The derivation chain is therefore self-contained and does not trigger any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; the central claim rests on the unstated assumption that moiré excitons map directly to layer Hubbard bands.

pith-pipeline@v0.9.1-grok · 5773 in / 1151 out tokens · 27354 ms · 2026-06-25T22:04:26.859887+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

41 extracted references · 3 canonical work pages

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Jauregui, L. A. et al. Electrical control of interlayer exciton dynamics in atomically thin heterostructures. Science 366, 870–875 (2019)

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Tang, Y . et al. Tuning layer-hybridized moiré excitons by the quantum-confined Stark effect. Nat. Nanotechnol. 16, 52–57 (2021)

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Tang, Y . et al. Simulation of Hubbard model physics in WSe2/WS2 moiré superlattices. Nature 579, 353–358 (2020)

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Xu, Y . et al. Correlated insulating states at fractional fillings of moiré superlattices. Nature 587, 214–218 (2020)

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Huang, X. et al. Correlated insulating states at fractional fillings of the WS2/WSe2 moiré lattice. Nat. Phys. 17, 715–719 (2021)

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Tang, Y . et al. Dielectric catastrophe at the Wigner-Mott transition in a moiré superlattice. Nat Commun 13, 4271 (2022)

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Polovnikov, B. et al. Implementation of the bilayer Hubbard model in a moiré heterostructure. Preprint at https://doi.org/10.48550/arXiv.2404.05494 (2024)

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work page doi:10.48550/arxiv.2405.12698 2024
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2026
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Gu, J. et al. Remote imprinting of moiré lattices. Nat. Mater. 23, 219–223 (2024)

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Guo, X. et al. Mott Insulator Polariton in a MoSe2/WS2 Moiré Lattice. Nano Lett. 25, 15680–15685 (2025)

2025
[30]

Cai, J. et al. Signatures of fractional quantum anomalous Hall states in twisted MoTe2. Nature 622, 63–68 (2023)

2023
[31]

Liu, E. et al. Exciton-polaron Rydberg states in monolayer MoSe2 and WSe2. Nat Commun 12, 6131 (2021)

2021
[32]

Jin, C. et al. Stripe phases in WSe2/WS2 moiré superlattices. Nat. Mater. 20, 940–944 (2021)

2021
[33]

Phys. Rev. Research 2, 033087 (2020)

2020
[34]

Li, Q. et al. Tunable quantum criticalities in an isospin extended Hubbard model simulator. Nature 609, 479–484 (2022)

2022
[35]

Zhou, Y ., Sheng, D. N. & Kim, E.-A. Quantum Melting of Generalized Wigner Crystals in Transition Metal Dichalcogenide Moiré Systems. Phys. Rev. Lett. 133, 156501 (2024)

2024
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Thompson, A. P. et al. LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. Computer Physics Communications 271, 108171 (2022)

2022
[37]

Parametrization of Stillinger–Weber potential based on valence force field model: application to single-layer MoS2 and black phosphorus

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2015
[38]

H., Maity, I., Maiti, P

Naik, M. H., Maity, I., Maiti, P. K. & Jain, M. Kolmogorov–Crespi Potential For Multilayer Transition-Metal Dichalcogenides: Capturing Structural Transformations in Moiré Superlattices. J. Phys. Chem. C 123, 9770–9778 (2019)

2019
[39]

P., Burke, K

Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 77, 3865–3868 (1996)

1996
[40]

Deslippe, J. et al. BerkeleyGW: A massively parallel computer package for the calculation of the quasiparticle and optical properties of materials and nanostructures. Computer Physics Communications 183, 1269–1289 (2012)

2012
[41]

(#!) !!"(#!) !#

You, J.-Y . et al. Moiré excitons in generalized Wigner crystals. Proc. Natl. Acad. Sci. U.S.A. 123, e2531259123 (2026). Acknowledgements A.Y.J., H.Y., and Q.L. acknowledge support from the donors of the ACS Petroleum Research Fund under Doctoral New Investigator (DNI) Grant #68101-DNI5. A.Y.J. also acknowledges support from the University of California, ...

2026

[1] [1]

Jin, C. et al. Observation of moiré excitons in WSe2/WS2 heterostructure superlattices. Nature 567, 76–80 (2019)

2019

[2] [2]

Seyler, K. L. et al. Signatures of moiré-trapped valley excitons in MoSe2/WSe2 heterobilayers. Nature 567, 66–70 (2019)

2019

[3] [3]

Park, H. et al. Dipole ladders with large Hubbard interaction in a moiré exciton lattice. Nat. Phys. 19, 1286–1292 (2023)

2023

[4] [4]

Regan, E. C. et al. Emerging exciton physics in transition metal dichalcogenide heterobilayers. Nat Rev Mater 7, 778–795 (2022)

2022

[5] [5]

Guo, J. et al. Moiré-controllable exciton localization and dynamics through spatially-modulated inter- and intralayer excitons in a MoSe2/WS2 heterobilayer. Nat Commun 16, 11257 (2025)

2025

[6] [6]

Naik, M. H. et al. Intralayer charge-transfer moiré excitons in van der Waals superlattices. Nature 609, 52–57 (2022)

2022

[7] [7]

Wang, X. et al. Intercell moiré exciton complexes in electron lattices. Nat. Mater. 22, 599–604 (2023)

2023

[8] [8]

Kistner-Morris, J. et al. Electric-field tunable Type-I to Type-II band alignment transition in MoSe2/WS2 heterobilayers. Nat Commun 15, 4075 (2024)

2024

[9] [9]

Jauregui, L. A. et al. Electrical control of interlayer exciton dynamics in atomically thin heterostructures. Science 366, 870–875 (2019)

2019

[10] [10]

Tang, Y . et al. Tuning layer-hybridized moiré excitons by the quantum-confined Stark effect. Nat. Nanotechnol. 16, 52–57 (2021)

2021

[11] [11]

Ruiz-Tijerina, D. A. & Fal’ko, V . I. Interlayer hybridization and moiré superlattice minibands for electrons and excitons in heterobilayers of transition-metal dichalcogenides. Phys. Rev. B 99, 125424 (2019)

2019

[12] [12]

Polovnikov, B. et al. Field-induced hybridization of moiré excitons in MoSe$_2$/WS$_2$ heterobilayers. Phys. Rev. Lett. 132, 076902 (2024)

2024

[13] [13]

Barré, E. et al. Optical absorption of interlayer excitons in transition-metal dichalcogenide heterostructures. Science 376, 406–410 (2022)

2022

[14] [14]

Evrard, B. et al. ac Stark Spectroscopy of Interactions between Moiré Excitons and Polarons. Phys. Rev. X 15, 021002 (2025)

2025

[15] [15]

Qi, R. et al. Thermodynamic behavior of correlated electron-hole fluids in van der Waals heterostructures. Nat Commun 14, 8264 (2023)

2023

[16] [16]

C., Potasz, P

Morales-Durán, N., Hu, N. C., Potasz, P. & MacDonald, A. H. Nonlocal Interactions in Moiré Hubbard Systems. Phys. Rev. Lett. 128, 217202 (2022)

2022

[17] [17]

Ciorciaro, L. et al. Kinetic magnetism in triangular moiré materials. Nature 623, 509–513 (2023)

2023

[18] [18]

Qi, R. et al. Perfect Coulomb drag and exciton transport in an excitonic insulator. Science 388, 278–283 (2025)

2025

[19] [19]

Regan, E. C. et al. Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices. Nature 579, 359–363 (2020)

2020

[20] [20]

Tang, Y . et al. Simulation of Hubbard model physics in WSe2/WS2 moiré superlattices. Nature 579, 353–358 (2020)

2020

[21] [21]

Xu, Y . et al. Correlated insulating states at fractional fillings of moiré superlattices. Nature 587, 214–218 (2020)

2020

[22] [22]

Huang, X. et al. Correlated insulating states at fractional fillings of the WS2/WSe2 moiré lattice. Nat. Phys. 17, 715–719 (2021)

2021

[23] [23]

Tang, Y . et al. Dielectric catastrophe at the Wigner-Mott transition in a moiré superlattice. Nat Commun 13, 4271 (2022)

2022

[24] [24]

Polovnikov, B. et al. Implementation of the bilayer Hubbard model in a moiré heterostructure. Preprint at https://doi.org/10.48550/arXiv.2404.05494 (2024)

work page doi:10.48550/arxiv.2404.05494 2024

[25] [25]

Han, Z. et al. Topological Kondo insulator in MoTe2/WSe2 moiré bilayers. Nat. Phys. https://doi.org/10.1038/s41567-026-03170-1 (2026) doi:10.1038/s41567-026-03170-1

work page doi:10.1038/s41567-026-03170-1 2026

[26] [26]

Scherzer, J. et al. Correlated magnetism of moiré exciton-polaritons on a triangular electron-spin lattice. Preprint at https://doi.org/10.48550/arXiv.2405.12698 (2024)

work page doi:10.48550/arxiv.2405.12698 2024

[27] [27]

Lu, Z. et al. Nature of Emergent Moiré Excitations in MoSe2 /WS2 Moiré Superlattices. Nano Lett. 26, 4096–4102 (2026)

2026

[28] [28]

Gu, J. et al. Remote imprinting of moiré lattices. Nat. Mater. 23, 219–223 (2024)

2024

[29] [29]

Guo, X. et al. Mott Insulator Polariton in a MoSe2/WS2 Moiré Lattice. Nano Lett. 25, 15680–15685 (2025)

2025

[30] [30]

Cai, J. et al. Signatures of fractional quantum anomalous Hall states in twisted MoTe2. Nature 622, 63–68 (2023)

2023

[31] [31]

Liu, E. et al. Exciton-polaron Rydberg states in monolayer MoSe2 and WSe2. Nat Commun 12, 6131 (2021)

2021

[32] [32]

Jin, C. et al. Stripe phases in WSe2/WS2 moiré superlattices. Nat. Mater. 20, 940–944 (2021)

2021

[33] [33]

Phys. Rev. Research 2, 033087 (2020)

2020

[34] [34]

Li, Q. et al. Tunable quantum criticalities in an isospin extended Hubbard model simulator. Nature 609, 479–484 (2022)

2022

[35] [35]

Zhou, Y ., Sheng, D. N. & Kim, E.-A. Quantum Melting of Generalized Wigner Crystals in Transition Metal Dichalcogenide Moiré Systems. Phys. Rev. Lett. 133, 156501 (2024)

2024

[36] [36]

Thompson, A. P. et al. LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. Computer Physics Communications 271, 108171 (2022)

2022

[37] [37]

Parametrization of Stillinger–Weber potential based on valence force field model: application to single-layer MoS2 and black phosphorus

Jiang, J.-W. Parametrization of Stillinger–Weber potential based on valence force field model: application to single-layer MoS2 and black phosphorus. Nanotechnology 26, 315706 (2015)

2015

[38] [38]

H., Maity, I., Maiti, P

Naik, M. H., Maity, I., Maiti, P. K. & Jain, M. Kolmogorov–Crespi Potential For Multilayer Transition-Metal Dichalcogenides: Capturing Structural Transformations in Moiré Superlattices. J. Phys. Chem. C 123, 9770–9778 (2019)

2019

[39] [39]

P., Burke, K

Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 77, 3865–3868 (1996)

1996

[40] [40]

Deslippe, J. et al. BerkeleyGW: A massively parallel computer package for the calculation of the quasiparticle and optical properties of materials and nanostructures. Computer Physics Communications 183, 1269–1289 (2012)

2012

[41] [41]

(#!) !!"(#!) !#

You, J.-Y . et al. Moiré excitons in generalized Wigner crystals. Proc. Natl. Acad. Sci. U.S.A. 123, e2531259123 (2026). Acknowledgements A.Y.J., H.Y., and Q.L. acknowledge support from the donors of the ACS Petroleum Research Fund under Doctoral New Investigator (DNI) Grant #68101-DNI5. A.Y.J. also acknowledges support from the University of California, ...

2026