Organizing Principles for Moiré Quantum Matter
Abstract
Moiré flat bands in van der Waals bilayers are usually discussed through a small set of mechanisms associated with the $Γ$ and $K$ valleys of hexagonal crystals, and more recently with $M$-valleys systems. Here we show that this view is incomplete. The momentum-space location and effective local orbital character of the monolayer's band edge, in conjunction with the moiré symmetry and the symmetry representations of the resulting bands, provide a general set of organizing variables for the emergent low-energy moiré Hamiltonian. Applying fully relaxed first-principles calculations, band unfolding and symmetry-representation analysis to more than 600 commensurate twisted bilayers spanning all 2D lattice classes, we identify several routes to moiré quantum matter beyond the conventional single-orbital paradigm. The resulting flat bands realize trigonal, honeycomb, square, checkerboard and kagome-like Hubbard models with single-orbital, multi-orbital and multi-site Hilbert spaces; spin-orbit-coupled multi-orbital flat bands exhibit symmetry-indicated topology beyond the conventional $K$-valley setting; and nonsymmorphic moiré symmetries enforce semimetallic flat-band connectivity. Analogous quasi-one-dimensional flat-band structures are found in $M$-valley hexagonal systems and $X$-valley square or rectangular systems resulting from emergent momentum-space nonsymmorphic symmetries. Separately, coupled multi-valley manifolds with kagome-like connectivity are identified in several systems whose parent band edges lie at non-high-symmetry points. These results establish a valley-orbital-symmetry framework for connecting parent-material electronic structure to emergent moiré Hamiltonians relevant to correlated, topological and symmetry-enforced moiré phases.
Authors 19
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Affiliation as printed
College of Physics and Electronic Engineering , Key Laboratory of Micro-Nano Optoelectronic Materials and Devices ,
Tsientang Institute for Advanced Study , Zhejiang 310024 , China
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Max Planck Institute for the Structure and Dynamics of Matter
Affiliation as printed
Max Planck Institute for the Structure and Dynamics of Matter , Luruper Chaussee 149 , 22761 Hamburg , Germany
Tsientang Institute for Advanced Study , Zhejiang 310024 , China
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City University of Hong Kong · Songshan Lake Materials Laboratory
Affiliation as printed
Department of Materials Science and Engineering , City University of Hong Kong , Kowloon Tong , Hong Kong , SAR 999077 , P. R. China
Songshan Lake Materials Laboratory , 523808 Dongguan , Guangdong , China
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Max Planck Institute for the Structure and Dynamics of Matter · Flatiron Institute
Affiliation as printed
Center for Computational Quantum Physics (CCQ) , The Flatiron Institute , New York , New York 10010 , USA
Max Planck Institute for the Structure and Dynamics of Matter , Luruper Chaussee 149 , 22761 Hamburg , Germany
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Donostia International Physics Center
Affiliation as printed
Donostia International Physics Center (DIPC) , Paseo Manuel de Lardizábal. 20018 , San Sebastián , Spain
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Donostia International Physics Center
Affiliation as printed
Donostia International Physics Center (DIPC) , Paseo Manuel de Lardizábal. 20018 , San Sebastián , Spain
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Affiliation as printed
School of Physics , Liaoning University , Shenyang 110036 , PR China
Tsientang Institute for Advanced Study , Zhejiang 310024 , China
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National Laboratory of Solid State Microstructures · Nanjing University
Affiliation as printed
National Laboratory of Solid-State Microstructures , School of Physics , Nanjing University , Nanjing 210093 , China
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Liaoning University · State Key Laboratory on Integrated Optoelectronics
Affiliation as printed
School of Physics , Liaoning University , Shenyang 110036 , PR China
State Key Laboratory of Integrated Optoelectronics ,
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Liaoning University · State Key Laboratory on Integrated Optoelectronics
Affiliation as printed
School of Physics , Liaoning University , Shenyang 110036 , PR China
State Key Laboratory of Integrated Optoelectronics ,
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Affiliation as printed
State Key Laboratory of High Pressure and Superhard Materials ,
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National Laboratory of Solid State Microstructures · Nanjing University
Affiliation as printed
National Laboratory of Solid-State Microstructures , School of Physics , Nanjing University , Nanjing 210093 , China
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State Key Laboratory on Integrated Optoelectronics
Affiliation as printed
State Key Laboratory of Integrated Optoelectronics ,
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Max Planck Institute for the Structure and Dynamics of Matter · RWTH Aachen University
Affiliation as printed
Institut für Theorie der Statistischen Physik , RWTH Aachen University and JARA-Fundamentals of Future Information Technology , 52056 Aachen , Germany
Max Planck Institute for the Structure and Dynamics of Matter , Luruper Chaussee 149 , 22761 Hamburg , Germany
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Affiliation as printed
International Center for Quantum Materials ,
Tsientang Institute for Advanced Study , Zhejiang 310024 , China
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