Tunable $t-t'-U$ Hubbard models in twisted square homobilayers

TL;DR

This paper demonstrates that twisted square lattice homobilayers can be tuned to realize a range of Hubbard models with variable hopping ratios, enabling exploration of diverse quantum phases relevant to high-temperature superconductivity.

Contribution

It introduces a method to tune the $t'/t$ ratio in Hubbard models via twisted bilayers, revealing an emergent symmetry and tunable parameters absent in single layers.

Findings

Emergent symmetry at low twist angles causes $t=0$ in the model.

Inter-layer displacement and magnetic fields can tune $t$ and anisotropy.

Wide range of $t'/t$ ratios accessible for correlated electron studies.

Abstract

Square lattice Hubbard models with tunable hopping ratio $t'/t$ are highly promising for realizing a variety of quantum phases and for shedding light on key puzzles in correlated quantum materials, including higher-temperature superconductivity. We show that twisted square lattice homo-bilayers generically offer such tunability when the flat bands originate from the corner of the Brillouin zone. We reveal an emergent symmetry at low twist-angles, absent in single layers, that necessitates the vanishing of nearest neighbor hopping ($t=0$). This symmetry can be lifted by an inter-layer displacement field or by an in-plane magnetic field, introducing tunable $t$ and anisotropy, allowing access to a wide range of $t'/t$ ratios for correlated electrons on a moir\'e square lattice.