# Designer fermion models in functionalized graphene bilayers

## TL;DR

This paper presents a method to engineer tunable fermionic Hamiltonians in graphene bilayers by functionalizing with defects and applying electric fields, enabling control over lattice models and phase transitions.

## Contribution

It introduces a novel approach to realize and control fermionic lattice models in graphene bilayers using defect engineering and electric fields.

## Key findings

- Tunable fermionic models can be realized in graphene bilayers.
- Electric fields enable control over coupling regimes.
- Transition between weak and strong coupling can be electrically induced.

## Abstract

We propose a method to realize a broad class of tunable fermionic Hamiltonians in graphene bilayer. For that matter, we consider graphene bilayer functionalized with sp$^3$ defects that induce zero energy resonances hosting an individual electron each. The application of an off-plane electric field opens up a gap, so that the zero energy resonance becomes an in-gap bound state whose confinement scales inversely with the gap. Controlling both the distance among the defects and the applied electric field, we can define fermionic models, even lattices, whose hoppings and Coulomb interactions can be tuned. We consider in detail the case of triangular and honeycomb artificial lattices and we show how, for a given arrangement of the sp$^3$ centers, these lattices can undergo an electrically controlled transition between the weak and strong coupling regimes.