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$O(N)$ ab initio calculation scheme for large-scale moiré structures

Journal Article · · Physical Review. B
 [1];  [2];  [3];  [4];  [5]
  1. Chinese Academy of Sciences (CAS), Beijing (China); OSTI
  2. Princeton University, NJ (United States); University Paris-Diderot (France)
  3. Princeton University, NJ (United States)
  4. Hong Kong University of Science and Technology (HKUST) (Hong Kong)
  5. Chinese Academy of Sciences (CAS), Beijing (China); Songshan Lake Materials Laboratory, Dongguan (China)

Here we present a two-step method specifically tailored for band structure calculation of the small-angle moiré-pattern materials which contain tens of thousands of atoms in a unit cell. In the first step, the self-consistent field calculation for the ground state is performed with the O(N) Krylov subspace method implemented in openmx. Second, the crystal momentum-dependent Bloch Hamiltonian and overlap matrix are constructed from the results obtained in the first step and only a small number of eigenvalues near the Fermi energy are solved with shift-invert and Lanczos techniques. By systematically tuning two key parameters, the cutoff radius for electron hopping interaction and the dimension of the Krylov subspace, we obtained the band structures for both rigid and corrugated twisted bilayer graphene structures down to the first magic angle (θ = 1.08°) with high enough accuracy at affordable costs. The band structures are in good agreement with those from tight-binding models, continuum models, plane-wave pseudopotential based ab initio calculations, and experimental observations. This method is also shown to be efficient in twisted double-bilayer graphene and bilayer WSe2. We think this two-step method can play a crucial role in other twisted two-dimensional materials, especially those with much more complex band structure and where the effective model is hard to construct.

Research Organization:
Princeton University, NJ (United States)
Sponsoring Organization:
USDOE Office of Science (SC); National Natural Science Foundation; Ministry of Science and Technology of China; Chinese Academy of Sciences; K. C. Wong Education Foundation; Beijing Natural Science Foundation; Beijing Municipal Science and Technology Commission; Simons Foundation; Gordon and Betty Moore Foundation; John Simon Guggenheim Memorial Foundation; National Science Foundation; Office of Naval Research (ONR)
Grant/Contract Number:
SC0016239
OSTI ID:
1979737
Journal Information:
Physical Review. B, Journal Name: Physical Review. B Journal Issue: 12 Vol. 105; ISSN 2469-9950
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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