Chin. Phys. Lett.  2024, Vol. 41 Issue (4): 047101    DOI: 10.1088/0256-307X/41/4/047101
CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES |
Flat Band and $\eta$-Pairing States in a One-Dimensional Moiré Hubbard Model
R. Wang1 and Z. Song2*
1College of Physics and Materials Science, Tianjin Normal University, Tianjin 300387, China
2School of Physics, Nankai University, Tianjin 300071, China
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R. Wang and Z. Song 2024 Chin. Phys. Lett. 41 047101
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Abstract A Moiré system is formed when two periodic structures have a slightly mismatched period, resulting in unusual strongly correlated states in the presence of particle-particle interactions. The periodic structures can arise from the intrinsic crystalline order and periodic external field. We investigate a one-dimensional Hubbard model with periodic on-site potential of period $n_{0}$, which is commensurate to the lattice constant. For large $n_{0}$, the exact solution demonstrates that there is a midgap flat band with zero energy in the absence of Hubbard interaction. Each Moiré unit cell contributes two zero energy levels to the flat band. In the presence of Hubbard interaction, the midgap physics is demonstrated to be well described by a uniform Hubbard chain in which the effective hopping and on-site interaction strength can be controlled by the amplitude and period of the external field. Numerical simulations are performed to demonstrate the correlated behaviors in the finite-sized Moiré Hubbard system, including the existence of an $\eta $-pairing state and bound pair oscillation. This finding provides a method to enhance the correlated effect by a spatially periodic external field.
Received: 27 October 2023      Published: 25 April 2024
PACS:  71.27.+a (Strongly correlated electron systems; heavy fermions)  
  74.78.Fk (Multilayers, superlattices, heterostructures)  
  02.30.Nw (Fourier analysis)  
  02.60.Cb (Numerical simulation; solution of equations)  
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https://cpl.iphy.ac.cn/10.1088/0256-307X/41/4/047101       OR      https://cpl.iphy.ac.cn/Y2024/V41/I4/047101
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