Abstract

We present a systematic theoretical study on the structural and electronic properties of twisted trilayer transition metal dichalcogenide WSe2, where two independent moiré patterns form between adjacent layers. Using a continuum approach, we investigate the optimized lattice structure and the resulting energy band structure, revealing fundamentally different electronic behaviors between helical and alternating twist configurations. In helical trilayers, lattice relaxation induces αβ and βα domains, where the two moiré patterns shift to minimize overlap, while in alternating trilayers, αα′ domains emerge with aligned moiré patterns. A key feature of trilayer TMDs is the summation of moiré potentials from the top and bottom layers onto the middle layer, effectively doubling the potential depth. In helical trilayers, this mechanism generates a Kagome lattice potential in the αβ domains, giving rise to flat bands characteristic of Kagome physics. In alternating trilayers, the enhanced potential confinement forms deep triangular quantum wells, distinct from those found in bilayer systems. Beyond these bulk states arising from the commensurate domains, the global moiré-of-moiré electronic spectrum exhibits isolated boundary modes localized at domain intersections. Furthermore, we demonstrate that a moderate perpendicular electric field can switch the layer polarization near the valence band edge, providing an additional degree of tunability. In particular, it enables tuning of the hybridization between orbitals on different layers, allowing for the engineering of diverse and controllable electronic band structures. Our findings highlight the unique role of moiré potential summation in trilayer systems, offering a broader platform for designing moiré-based electronic and excitonic phenomena beyond those achievable in bilayer TMDs.

Abstract

We present a systematic theoretical study on the structural and electronic properties of twisted trilayer transition metal dichalcogenide WSe2, where two independent moiré patterns form between adjacent layers. Using a continuum approach, we investigate the optimized lattice structure and the resulting energy band structure, revealing fundamentally different electronic behaviors between helical and alternating twist configurations. In helical trilayers, lattice relaxation induces αβ and βα domains, where the two moiré patterns shift to minimize overlap, while in alternating trilayers, αα′ domains emerge with aligned moiré patterns. A key feature of trilayer TMDs is the summation of moiré potentials from the top and bottom layers onto the middle layer, effectively doubling the potential depth. In helical trilayers, this mechanism generates a Kagome lattice potential in the αβ domains, giving rise to flat bands characteristic of Kagome physics. In alternating trilayers, the enhanced potential confinement forms deep triangular quantum wells, distinct from those found in bilayer systems. Beyond these bulk states arising from the commensurate domains, the global moiré-of-moiré electronic spectrum exhibits isolated boundary modes localized at domain intersections. Furthermore, we demonstrate that a moderate perpendicular electric field can switch the layer polarization near the valence band edge, providing an additional degree of tunability. In particular, it enables tuning of the hybridization between orbitals on different layers, allowing for the engineering of diverse and controllable electronic band structures. Our findings highlight the unique role of moiré potential summation in trilayer systems, offering a broader platform for designing moiré-based electronic and excitonic phenomena beyond those achievable in bilayer TMDs.

Abstract

We present a systematic theoretical study on the structural and electronic properties of twisted trilayer transition metal dichalcogenide WSe2, where two independent moiré patterns form between adjacent layers. Using a continuum approach, we investigate the optimized lattice structure and the resulting energy band structure, revealing fundamentally different electronic behaviors between helical and alternating twist configurations. In helical trilayers, lattice relaxation induces αβ and βα domains, where the two moiré patterns shift to minimize overlap, while in alternating trilayers, αα′ domains emerge with aligned moiré patterns. A key feature of trilayer TMDs is the summation of moiré potentials from the top and bottom layers onto the middle layer, effectively doubling the potential depth. In helical trilayers, this mechanism generates a Kagome lattice potential in the αβ domains, giving rise to flat bands characteristic of Kagome physics. In alternating trilayers, the enhanced potential confinement forms deep triangular quantum wells, distinct from those found in bilayer systems. Beyond these bulk states arising from the commensurate domains, the global moiré-of-moiré electronic spectrum exhibits isolated boundary modes localized at domain intersections. Furthermore, we demonstrate that a moderate perpendicular electric field can switch the layer polarization near the valence band edge, providing an additional degree of tunability. In particular, it enables tuning of the hybridization between orbitals on different layers, allowing for the engineering of diverse and controllable electronic band structures. Our findings highlight the unique role of moiré potential summation in trilayer systems, offering a broader platform for designing moiré-based electronic and excitonic phenomena beyond those achievable in bilayer TMDs.

Abstract

We present a systematic theoretical study on the structural and electronic properties of twisted trilayer transition metal dichalcogenide WSe2, where two independent moiré patterns form between adjacent layers. Using a continuum approach, we investigate the optimized lattice structure and the resulting energy band structure, revealing fundamentally different electronic behaviors between helical and alternating twist configurations. In helical trilayers, lattice relaxation induces αβ and βα domains, where the two moiré patterns shift to minimize overlap, while in alternating trilayers, αα′ domains emerge with aligned moiré patterns. A key feature of trilayer TMDs is the summation of moiré potentials from the top and bottom layers onto the middle layer, effectively doubling the potential depth. In helical trilayers, this mechanism generates a Kagome lattice potential in the αβ domains, giving rise to flat bands characteristic of Kagome physics. In alternating trilayers, the enhanced potential confinement forms deep triangular quantum wells, distinct from those found in bilayer systems. Beyond these bulk states arising from the commensurate domains, the global moiré-of-moiré electronic spectrum exhibits isolated boundary modes localized at domain intersections. Furthermore, we demonstrate that a moderate perpendicular electric field can switch the layer polarization near the valence band edge, providing an additional degree of tunability. In particular, it enables tuning of the hybridization between orbitals on different layers, allowing for the engineering of diverse and controllable electronic band structures. Our findings highlight the unique role of moiré potential summation in trilayer systems, offering a broader platform for designing moiré-based electronic and excitonic phenomena beyond those achievable in bilayer TMDs.