Band engineering in 2D superlattices with rotation-symmetry-mismatched interfaces

Two-dimensional (2D) moiré superlattices, formed by stacking individual layers such as 2H transition metal dichalcogenides (TMDs) with accurately twisted angles, have garnered significant attention due to their potential to host phenomena due to strong electron correlations, including unconventional superconductivity, moiré excitons, Wigner crystalline states, and orbital ferromagnetism. The moiré potentials and flat bands play a key role in driving these correlated phenomena. However, several emergent aspects of the physics of TMDs-based moiré superlattices remain unexplored. First, flat bands have so far only been observed at "magic" twisted angles and below the valence band maximum (VBM) in TMDs superlattices. Whether it is possible to generate flat bands at arbitrary angles and push these bands to the highest occupied states—where novel quantum phenomena are expected to emerge—remains an open challenge. Second, 2H TMDs hold three-fold rotational (C₃) symmetry. The breaking of C₃ symmetry by stacking it on two-fold rotational symmetry (C₂) layers such as black phosphorous can bring novel photovoltaic phenomena in 2H TMDs such as spontaneous photocurrent due to band hybridization between C₃ and C₂ layers. However, the physics behind the C₃ symmetry breaking and the detailed mechanism of band hybridization remains understudied to date. These questions can be effectively addressed via a direct visualization of the electronic band structure. New developments in micro angle-resolved photoemission spectroscopy (micro-ARPES) can now provide the necessary space resolution to study these heterostructures with the further advantage of providing both a high energy and momentum resolution.

In this work, Z. Zhang et al. studied the first example of electronic band structure properties in a C₃ layer/C₂ layer stacked superlattice, MoS₂-black phosphorus. The atomic structure and the corresponding Brillouin zone of the superlattice with a twist angle of θ are shown in Fig. 1a. Regardless of the twist angles between MoS₂ and black phosphorus, a breaking of the C₃ symmetry for the highest occupied MoS₂ states is directly observed in the constant energy cut of 3D ARPES maps. This is demonstrated by comparing the pristine MoS₂ (MoS₂ on BN) with the MoS₂-black phosphorus regions, as shown in Fig. 1b. Additionally, micro-ARPES reveals the formation of anisotropic flat bands and minigaps at the Γ valley, as seen in Fig. 1c, where these properties are highly dependent on the orientation of the underlying black phosphorus layer. Moreover, a giant energy renormalization of approximately 140 meV is visualized in Fig. 1d, leading to a shift of the VBM from the K point to the Γ point. All these effects are explained by Density Functional Theory (DFT) calculations, indicating that they arise from strong hybridization between the Mo d_z²  orbitals of the monolayer MoS₂ and the P p_x orbitals of the black phosphorous, as depicted in Fig. 1e. This understanding of the electronic structure modulation in monolayer MoS₂, induced by the substrate black phosphorus through rotational symmetry breaking and interlayer hybridization, opens up novel possibilities for generating flat bands at arbitrary twist angles in 2D heterostructures and manipulating anisotropic properties in TMDs.

Figure 1: a) The atomic structure and the corresponding Brillouin zone of the superlattice with a twist angle of θ. (b) Constant energy cut maps of pristine monolayer MoS₂ (top panel) and MoS₂-bP superlattices with θ=8.5° (bottom panel). (c) Valence bands of pristine monolayer MoS₂ and MoS₂-bP along the armchair (AC), AC+45° and zigzag (ZZ) directions in superlattices with θ=8.5°. (d) Band renormalization between pristine MoS₂ and MoS₂ on black phosphorus. (e) The unfolded bands projected onto Mo d_z²  (cyan) and d_x²+y² (magenta) and P p_x orbitals (yellow) from DFT calculation. Adapted from Z. Zhang et al., Nat. Commun. 16, 763 (2025), with permission from Nature Communications.

Micro-ARPES experiments were carried out at the Spectromicroscopy beamline of Elettra using photons with energies of hν=27 eV and hν=74 eV. DFT calculations have been performed using the OpenMX code. The exchange-correlation potential was expressed in the generalized gradient approximation using the Perdew-Burke-Ernzerhof (PBE) schema. Norm conserving full relativistic pseudopotentials including a partial core correction and spin-orbit coupling was used. Dispersion interactions have been included using the Grimme-D2 method.

This research was conducted by the following research team:

Zailan Zhang¹, Alberto Zobelli^2,3, Chaofeng Gao⁴, Yingchun Cheng⁴, Jiuxiang Zhang², Jonathan Caillaux², Lipeng Qiu⁵, Songlin Li⁵, Mattia Cattelan⁶, Viktor Kandyba⁶, Alexei Barinov⁶, Mustapha Zaghrioui⁷, Azzedine Bendounan³, Jean-Pascal Rueff³, Weiyan Qi⁸, Luca Perfetti⁸, Evangelos Papalazarou², Marino Marsi², Zhesheng Chen^9
1 School of Physics, Nanjing University of Science and Technology, Nanjing, China
² Laboratoire de Physique des Solides, CNRS, Université Paris-Saclay, Orsay, France
3 Synchrotron Soleil, Saint-Aubin, France.
⁴ Key Laboratory of Flexible Electronics & Institute of Advanced Materials, Nanjing Tech University, Nanjing, China
⁵ School of Electronic Science and Engineering, Nanjing University, Nanjing, China
⁶ Elettra-Sincrotrone Trieste, Trieste, Italy
⁷ Laboratoire GREMAN, CNRS, IUT de BLOIS, Blois, France
⁸ Laboratoire des Solides Irradiés, CNRS, Institut Polytechnique de Paris, Palaiseau, France
⁹ School of Material Science and Engineering, Nanjing University of Science and Technology, Nanjing, China

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