# Numerical analysis of electronic conductivity in graphene with resonant adsorbates: comparison of monolayer and Bernal bilayer

## TL;DR

This study analyzes how resonant adsorbates affect electronic conductivity in monolayer and Bernal bilayer graphene, revealing distinct transport regimes influenced by defect concentration and interlayer hopping.

## Contribution

It provides a comparative analysis of electronic transport in monolayer and bilayer graphene with resonant adsorbates, highlighting the role of additional length scales and defect concentration.

## Key findings

- At low defect concentration, BLG shows different transport properties from MLG regardless of inelastic scattering.
- At higher defect concentration, BLG's transport can resemble that of decoupled MLG depending on inelastic mean free path.
- The study compares tight-binding models with and without extended hopping terms.

## Abstract

We describe the electronic conductivity, as a function of the Fermi energy, in the Bernal bilayer graphene (BLG) in presence of a random distribution of vacancies that simulate resonant adsorbates. We compare it to monolayer (MLG) with the same defect concentrations. These transport properties are related to the values of fundamental length scales such as the elastic mean free path $L_{e}$, the localization length $\xi$ and the inelastic mean free path $L_{i}$. Usually the later, which reflect the effect of inelastic scattering by phonons, strongly depends on temperature $T$. In BLG an additional characteristic distance $l_1$ exists which is the typical traveling distance between two interlayer hopping events. We find that when the concentration of defects is smaller than 1\%--2\%, one has $l_1 \le L_e \ll \xi$ and the BLG has transport properties that differ from those of the MLG independently of $L_{i}(T)$. Whereas for larger concentration of defects $L_{e} < l_1 \ll \xi $, and depending on $L_{i}(T)$, the transport in the BLG can be equivalent (or not) to that of two decoupled MLG. We compare two tight-binding model Hamiltonians with and without hopping beyond the nearest neighbors.