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

TL;DR

This paper explores how a one-dimensional moiré Hubbard model exhibits flat bands and $ ext{eta}$-pairing states, revealing new ways to control and enhance correlated electronic behaviors using periodic external fields.

Contribution

It demonstrates the existence of flat bands and $ ext{eta}$-pairing states in a 1D moiré Hubbard model, showing control via external field parameters and providing insights into correlated states.

Findings

Existence of a midgap flat band with zero energy in the non-interacting case.

Hubbard interaction leads to $ ext{eta}$-pairing states and bound pair oscillations.

Control of effective hopping and interaction strength through external field parameters.

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.