Tuning the low-energy band structure in twisted bilayer WSe2
Pith reviewed 2026-05-21 04:36 UTC · model grok-4.3
The pith
In twisted bilayer WSe2 the energy separation between hole bands at K and at Γ shifts by more than 100 meV as twist angle changes while momentum positions stay fixed.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
While the momentum positioning of the valence band maxima is independent of twist angle, the energetic separation between the hole bands at the K point of the Brillouin zone and the higher binding-energy hole band at Γ can be varied in excess of 100 meV.
What carries the argument
Systematic nano-ARPES mapping of twist-angle evolution in the low-energy valence bands of homobilayer WSe2.
If this is right
- The size of the band gaps in homobilayer WSe2 can be tuned through choice of twist angle.
- The efficiency of spin-dependent electron-phonon coupling channels becomes adjustable.
- Device performance in homobilayer transition metal dichalcogenides can be optimized by selecting appropriate twist angles.
Where Pith is reading between the lines
- The same twist-angle mechanism may allow comparable band tuning in other transition metal dichalcogenide homobilayers.
- Precise twist control during device assembly could serve as a design parameter for balancing gap size against coupling strength.
- Combining twist tuning with electrostatic gating might provide independent knobs for both gap magnitude and carrier density.
Load-bearing premise
The observed energy shifts arise purely from the controlled twist angle and are not dominated by uncontrolled variables such as local strain, substrate interactions, or sample inhomogeneity.
What would settle it
Observation of comparable energy variations in multiple samples that share the same nominal twist angle but differ in local strain or substrate would show that twist angle is not the controlling variable.
read the original abstract
Tuning the electronic structures of two-dimensional (2D) material-based heterostructures is of crucial importance for their use in functional next-generation electronics. Here, through angle-resolved photoemission spectroscopy with nanoscale spatial resolution (nano-ARPES), we systematically track the evolution of the near-Fermi-level electronic structure of bilayer WSe2 over a large range of twist angle. While the momentum positioning of the valence band maxima is independent of twist angle, we find that the energetic separation between the hole bands at the K point of the Brillouin zone and the higher binding-energy hole band at {\Gamma} can be varied in excess of 100 meV. We explore the mechanisms underpinning this evolution and discuss the implications for tuning both the size of the band gaps, and the efficiency of the spin-dependent electron-phonon coupling channels in homobilayer transition metal dichalcogenide devices.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript reports nano-ARPES measurements tracking the near-Fermi-level electronic structure of twisted bilayer WSe2 across a wide range of twist angles. The momentum positions of the valence band maxima are found to be independent of twist angle, while the energetic separation between the K-point hole bands and the higher-binding-energy hole band at Γ varies by more than 100 meV. The authors discuss possible mechanisms for this evolution and its implications for tuning band gaps and spin-dependent electron-phonon coupling in homobilayer TMD devices.
Significance. If the reported >100 meV tuning of the K-Γ separation is robustly attributable to controlled twist angle rather than uncontrolled variables, the work would represent a useful experimental demonstration of band-structure engineering in twisted homobilayers. The nanoscale spatial resolution of the ARPES measurements is a methodological strength that enables local probing over a large twist-angle series. The result, if confirmed, would be of interest for 2D-material device design, though its impact is moderated by the need for clearer exclusion of alternative explanations such as strain.
major comments (1)
- [Results] The central claim that the K-Γ hole-band separation varies systematically by >100 meV due to twist angle requires that local strain, substrate interactions, and inhomogeneity are not dominant. The manuscript provides no independent strain quantification (e.g., Raman 2D-mode mapping or diffraction-based lattice constants) correlated with the twist-angle series, nor substrate-variation controls. This omission is load-bearing for attributing the observed shifts to twist angle alone.
minor comments (2)
- [Abstract] The abstract reports the 100 meV scale without accompanying error bars, sample statistics, or exclusion criteria; these should be included in the main text and figures to allow assessment of the observational robustness.
- Notation for the Γ-point band should be clarified consistently between text and figures to avoid ambiguity with the higher-binding-energy feature.
Simulated Author's Rebuttal
We thank the referee for their careful reading of the manuscript and for identifying the need to more explicitly address potential confounding factors in attributing the observed K-Γ separation changes to twist angle. We respond to the major comment below.
read point-by-point responses
-
Referee: [Results] The central claim that the K-Γ hole-band separation varies systematically by >100 meV due to twist angle requires that local strain, substrate interactions, and inhomogeneity are not dominant. The manuscript provides no independent strain quantification (e.g., Raman 2D-mode mapping or diffraction-based lattice constants) correlated with the twist-angle series, nor substrate-variation controls. This omission is load-bearing for attributing the observed shifts to twist angle alone.
Authors: We agree that robust exclusion of alternative explanations is essential. All measurements in the twist-angle series were performed on samples prepared under identical conditions on the same SiO2/Si substrate, which controls for substrate-induced variations to first order. The nanoscale spatial resolution of the ARPES measurements (~100 nm) enables selection of locally uniform regions, mitigating inhomogeneity effects. Critically, the momentum positions of the K-point valence band maxima remain fixed across the full range of twist angles studied. This observation is inconsistent with dominant strain, which in TMD monolayers and bilayers typically produces measurable shifts in band dispersions and k-space locations. The >100 meV energetic shift is large, varies systematically with twist angle, and aligns with expectations from interlayer hybridization in twisted homobilayers. While independent Raman or diffraction-based strain mapping correlated to the exact ARPES locations is not available in the present dataset, we will revise the manuscript to add an explicit discussion section addressing strain, substrate, and inhomogeneity effects, including why the fixed momentum positions and systematic twist-angle dependence argue against these as dominant mechanisms. Relevant literature on strain-induced shifts in WSe2 will be cited to support this analysis. revision: yes
Circularity Check
No circularity: direct experimental measurement of twist-angle-dependent band shifts
full rationale
The paper reports nano-ARPES data tracking the valence-band maxima positions and K-Γ energetic separation in twisted bilayer WSe2 across a range of twist angles. The central claim (separation tunable by >100 meV) is presented as an observed experimental trend extracted from momentum-resolved spectra, with no intervening theoretical derivation, parameter fitting, or self-referential model that reduces the result to its own inputs by construction. No equations, ansatze, or uniqueness theorems are invoked that could create self-definition or fitted-input circularity. The work is therefore self-contained as a measurement campaign.
Axiom & Free-Parameter Ledger
axioms (1)
- domain assumption nano-ARPES with nanoscale spatial resolution accurately maps near-Fermi-level valence bands in 2D heterostructures
Reference graph
Works this paper leans on
-
[1]
P. V. Nguyen, N. C. Teutsch, N. P. Wilson, J. Kahn, X. Xia, A. J. Graham, V. Kandyba, A. Giampietri, A. Barinov, G. C. Constantinescu et al., Visualizing electrostatic gating effects in two-dimensional heterostructures, Nature 572, 220 (2019)
work page 2019
-
[2]
Y. Lei, T. Zhang, Y. -C. Lin, T. Granzier -Nakajima, G. Bepete, D. A. Kowalczyk, Z. Lin, D. Zhou, T. F. Schranghamer, A. Dodda et al., Graphene and Beyond: Recent Advances in Two -Dimensional Materials Synthesis, Properties, and Devices , ACS Nanoscience Au. 2, 6, 450-485 (2022)
work page 2022
- [3]
-
[4]
P. V. Pham, S. C. Bodepudi, K. Shehzad, Y. Liu, Y. Xu, B. Yu, and X. Duan, 2D Heterostructures for Ubiquitous Electronics and Optoelectronics: Principles, Opportunities, and Challenges, Chem Rev 122, 6514 (2022)
work page 2022
-
[5]
A. Ciarrocchi, F. Tagarelli, A. Avsar, and A. Kis, Excitonic devices with van der Waals heterostructures: valleytronics meets twistronics, Nat Rev Mater 7, 449 (2022)
work page 2022
-
[6]
E. C. Ahn, 2D materials for spintronic devices, npj 2D Mater Appl 4, 17 (2020)
work page 2020
-
[7]
Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo - Herrero, Unconventional superconductivity in magic -angle graphene superlattices, Nature 556, 43 (2018)
work page 2018
-
[8]
L. Wang, E.-N. Shih, A. Ghiotto, L. Xian, D. A. Rhodes, C. Tan, M. Claasen, D. M. Kennes, Y. Bai, B. Kim et al., Correlated electronic phases in twisted bilayer transition metal dichalcogenides, Nat. Mater. 19, 861 (2020)
work page 2020
-
[9]
C. H. Stansbury, M. I. B. Utama, C. G. Fatuzzo, E. C. Regan, D. Wang, Z. Xiang, M. Ding, K. Watanabe, T. Taniguchi, M. Blei et al., Visualizing electron localization of WS2/WSe2 moiré superlattices in momentum space, Sci Adv 7, 37 (2021)
work page 2021
-
[10]
D. Pei, B. Wang, Z. Zhou, Z. He, L. An, S. He, C. Chen, Y. Li, L. Wei, A. Liang et al., Observation of Γ -Valley Moiré Bands and Emergent Hexagonal Lattice in Twisted Transition Metal Dichalcogenides, Phys Rev X 12, 21065 (2022)
work page 2022
- [11]
-
[12]
E. Li, J. X. Hu, X. Feng, Z. Zhou, L. An, K. T. Law, N. Wang, and N. Lin, Lattice reconstruction induced multiple ultra-flat bands in twisted bilayer WSe2, Nat Commun 12, 6 (2021)
work page 2021
-
[13]
Y. Guo, J. Pack, J. Swann, L. Holtzman, M. Cothrine, K. Watanabe, T. Taniguchi, D. G. Mandrus, K. Barmak, J. Hone et al., Superconductivity in 5° twisted bilayer WSe2, Nature 637, 839 (2025)
work page 2025
-
[14]
Y. Xia, Z. Han, K. Watanabe, T. Taniguchi, J. Shan, K. F. Mak , Superconductivity in twisted bilayer WSe2, Nature, 637, 833 (2025)
work page 2025
-
[15]
Y. Li, F. Zhang, V. -A. Ha, Y.-C. Lin, C. Dong, Q. Gao, Z. Liu, X. Liu, S. H. Ryu, H. Kim et al., Tuning commensurability in twisted van der Waals bilayers, Nature 625, 494 (2024)
work page 2024
-
[16]
K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, Atomically thin MoS2: A new direct-gap semiconductor, Phys Rev Lett 105, 2 (2010)
work page 2010
-
[17]
D. Voß, P. Krüger, A. Mazur, and J. Pollmann, Atomic and electronic structure of WSe2 from ab initio theory: bulk crystal and thin film systems, Phys Rev B 60, 14311 (1999)
work page 1999
-
[18]
Y. Sun, D. Wang, and Z. Shuai, Indirect -to-Direct Band Gap Crossover in Few -Layer Transition Metal Dichalcogenides: A Theoretical Prediction, Journal of Physical Chemistry C 120, 21866 (2016)
work page 2016
-
[19]
A. Ramasubramaniam, Large excitonic effects in monolayers of molybdenum and tungsten dichalcogenides, Phys Rev B 86, 115409 (2012)
work page 2012
- [20]
-
[21]
K. F. Mak, K. He, J. Shan, and T. F. Heinz, Control of valley polarization in monolayer MoS 2 by optical helicity, Nature Nanotechnology, 7, 494 (2012)
work page 2012
-
[22]
D. Xiao, G.-B. Liu, W. Feng, X. Xu, and W. Yao, Coupled Spin and Valley Physics in Monolayers of MoS 2 and Other Group -VI Dichalcogenides, Physical Review Letters, 108, 196802 (2012)
work page 2012
-
[23]
H. Zeng, J. Dai, W. Yao, D. Xiao, and X. Cui, Valley polarization in MoS 2 monolayers by optical pumping, Nat Nanotechnol 7, 490 (2012)
work page 2012
-
[24]
H. Yuan, M. S. Bahramy, K. Morimoto, S. Wu, K. Nomura, B. -J. Yang, H. Shimotani, R. Suzuki, M. Toh, C. Kloc et al., Zeeman-type spin splitting controlled by an electric field, Nat Phys 9, 563 (2013)
work page 2013
-
[25]
S. A. Vitale, D. Nezich, J. O. Varghese, P. Kim, N. Gedik, P. Jarillo -Herrero, D. Xiao, and M. Rothschild, Valleytronics: Opportunities, Challenges, and Paths Forward, Small 14, 1801483 (2018)
work page 2018
-
[26]
N. R. Wilson, P. V. Nguyen, K. Seyler, P. Rivera, A. J. Marsden, Z. P. L. Laker, G. C. Constantinescu, V. Kandyba, A. Barinov, N. D. M. Hine, X. Xu, D. H. Cobden , Determination of band offsets, hybridization, and exciton binding in 2D semiconductor heterostructures, Sci Adv 3, 2 (2017)
work page 2017
-
[27]
N. F. Hinsche, A. S. Ngankeu, K. Guilloy, S. K. Mahatha, A. G. Čabo, M. Bianchi, M. Dendzik, C. E. Sanders, J. A. Miwa, H. Bana et al., Spin-dependent electron-phonon coupling in the valence band of single-layer WS2, Phys Rev B 96, 121402(R) (2017)
work page 2017
-
[28]
G. H. Ahn, M. Amani, H. Rasool, D. H. Lien, J. P. Mastandrea, J. W. A. Iii, M. Dubey, D. C. Chrzan, A. M. Minor, and A. Javey, Strain-engineered growth of two-dimensional materials, Nat Commun 8, 608 (2017)
work page 2017
-
[29]
J. Ribeiro-Soares, C. Janisch, Z. Liu, A. L. Elias, M. S. Dresselhaus, M. Terrones, L. G. Cancado, A. Jorio, Second Harmonic Generation in WSe2, 2D Mater. 2, 045015 (2015)
work page 2015
-
[30]
K. Kim, A. DaSilva, S. Huang, B. Fallahazad, S. Larentis, T. Taniguchi , K. Watanabe, B. J. LeRoy, A. H. MacDonald, E. Tutuc, Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene, PNAS 114, 3364 (2017)
work page 2017
- [31]
-
[32]
D. A. Ruiz -Tijerina and V. I. Fal’Ko, Interlayer hybridization and moiré superlattice minibands for electrons and excitons in heterobilayers of transition -metal dichalcogenides, Phys Rev B 99, 125424 (2019)
work page 2019
- [33]
- [34]
-
[35]
X. Wang, K. Yasuda, Y. Zhang, S. Liu, K. Watanabe, T. Taniguchi, J. Hone, L. Fu, and P. Jarillo-Herrero, Interfacial ferroelectricity in rhombohedral-stacked bilayer transition metal dichalcogenides, Nat Nanotechnol 17, 367 (2022)
work page 2022
-
[36]
M. Vizner Stern, Y. Waschitz, W. Cao, I. Nevo, K. Watanabe, T. Taniguchi, E. Sela, M. Urbakh, O. Hod, and M. Ben Shalom, Interfacial ferroelectricity by van der Waals sliding, Science 372, 1462 (2021)
work page 2021
-
[37]
K. Ko, A. Yuk, R. Engelke, S. Carr, J. Kim, D. Park, H. Heo, H.-M. Kim, S.-G. Kim, H. Kim et al., Operando electron microscopy investigation of polar domain dynamics in twisted van der Waals homobilayers, Nat Mater 22, 992 (2023)
work page 2023
-
[38]
J. M. Riley , F. Mazzola, M. Dendzik, M. Michiardi, T. Takayama, L. Bawden, C. Granerød, M. Leandersson, T. Balasubramanian, M. Hoesch, et al., Direct observation of spin-polarized bulk bands in an inversion -symmetric semiconductor, Nat Phys 10, 835 (2014)
work page 2014
-
[39]
J. M. Riley, W. Meevasana, L. Bawden, M. Asakawa, T. Takayama, T. Eknapakul, T. K. Kim, M. Hoesch, S.-K. Mo, H. Takagi et al., Negative electronic compressibility and tunable spin splitting in WSe 2, Nat Nanotechnol 10, 1043 (2015)
work page 2015
-
[40]
L. Bawden, S. P. Cooil, F. Mazzola, J. M. Riley, L. J. Collins -McIntyre, V. Sunko, K. W. B. Hunvik, M. Leandersson. C. M. Polley, T. Balasubramanian et al., Spin -valley locking in the normal state of a transition -metal dichalcogenide superconductor, Nat Commun 7, 11711 (2016)
work page 2016
-
[41]
E. Razzoli, T. Jaouen, M.-L. Mottas, B. Hildebrand, G. Monney, A. Pisoni, S. Muff, M. Fanciulli, N. C. Plumb, V. A. Rogalev et al., Selective Probing of Hidden Spin-Polarized States in Inversion-Symmetric Bulk MoS2, Phys Rev Lett 118, 086402 (2017)
work page 2017
-
[42]
W. Yao, E. Wang, H. Huang, K. Deng, M. Yan, K. Zhang, K. Miyamoto, T. Okuda, L. Li, Y. Wang et al., Direct observation of spin -layer locking by local Rashba effect in monolayer semiconducting PtSe 2 film, Nat Commun 8, 14216 (2017)
work page 2017
-
[43]
O. J. Clark, O. Dowinton, M. S. Bahramy, and J. Sánchez -Barriga, Hidden spin-orbital texture at the Γ -located valence band maximum of a transition metal dichalcogenide semiconductor, Nat Commun 13, 4147 (2022)
work page 2022
-
[44]
I. Paradisanos, A. M. S. Raven, T. Amand, C. Robert, P. Renucci, K. Watanabe, T. Taniguchi, I. C. Gerber, X. Marie, and B. Urbaszek, Second harmonic generation control in twisted bilayers of transition metal dichalcogenides, Phys Rev B 105, 115420 (2022)
work page 2022
-
[45]
A. Damascelli, Probing the electronic structure of complex systems by ARPES, Physica Scripta T T109, 61 (2004)
work page 2004
- [46]
-
[47]
W. Zhao, Y. Huang, C. Shen, C. Li, Y. Cai, Y. Xu, H. Rong, Q. Gao, Y. Wang, L. Zhao et al., Electronic structure of exfoliated millimeter -sized WSe2 on silicon wafer. Nano Res. 12, 3095-3100 (2019)
work page 2019
-
[48]
T. Devakul, V. Crépel, Y. Zhang, and L. Fu, Magic in twisted transition metal dichalcogenide bilayers, Nat Commun 12, 6730 (2021)
work page 2021
-
[49]
C. Ernandes, L. Khalil, H. Almabrouk, D. Pierucci, B. Zheng, J. Avila, P. Dudin, J. Chaste, F. Oehler, M. Pala et al., Indirect to direct band gap crossover in two - dimensional WS2(1−x)Se2x alloys, NPJ 2D Mater Appl 5, 7 (2021)
work page 2021
-
[50]
P. Yeh, W. Jin, N. Zaki, J. Kunstmann, D. Chenet, G. Arefe, J. T. Sadowski, J. I. Dadap, P. Sutter, J. Hone, et al., Direct Measurement of the Tunable Electronic Structure of Bilayer MoS 2 by Interlayer Twist, Nano Lett. 16, 953–959 (2016). Supplementary Information for: Tuning low -energy band structu re in twisted bilayer WSe2 T.-H.-Y. Vu 1,*, O. J. Cla...
work page 2016
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.