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arXiv · 2105.03615

Flat band and $\eta $-pairing states in one-dimensional Moir\'{e} Hubbard model

R. Wang·Z. Song
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Abstract

A moir\'{e} 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 models with periodic on-site potential of period $n_{0}$, which is commensurate to the lattice constant. For large $% n_{0}$, exact solution demonstrates that there is a midgap flat band with zero energy in the absence of Hubbard interaction. Each moir\'{e} 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 moir\'{e} Hubbard system, including the existence of $\eta $-pairing state, and bound pair oscillation. This finding provides a method to enhance the correlated effect by a spatially periodic external field.

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R. Wang, Z. Song. 2021-05-08. Flat band and $\eta $-pairing states in one-dimensional Moir\'{e} Hubbard model. https://doi.org/10.1088/0256-307x%2F41%2F4%2F047101

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