Minimal conductivity and signatures of quantum criticality in ballistic graphene bilayer

TL;DR

This paper investigates the ballistic conductivity of graphene bilayer with next-nearest neighbor hoppings, revealing a universal scaling behavior and signatures of quantum criticality similar to disordered systems, despite being ballistic and interaction-free.

Contribution

It demonstrates one-parameter scaling and identifies a fixed point in the conductivity of ballistic graphene bilayer with next-nearest neighbor hoppings, linking it to quantum criticality phenomena.

Findings

Conductivity approaches a universal value of approximately 0.95 for large system sizes.

The system exhibits a scaling flow with an attractive fixed point, indicating quantum critical behavior.

The results resemble those predicted for disordered Dirac fermions, despite the system being ballistic and non-interacting.

Abstract

We study the ballistic conductivity of graphene bilayer in the presence of next-nearest neighbor hoppings between the layers. An undoped and unbiased system was found in Ref. [1] to show a nonuniversal (length-dependent) conductivity $\sigma(L)$, approaching the value of $\sigma_\star=3/\pi\simeq{}0.95$ for large $L$. Here we demonstrate one-parameter scaling and determine the scaling function $\beta(\sigma)=d\ln{}\!\sigma/d\ln{}\!L$. The scaling flow has an attractive fixed point [$\,\beta(\sigma_\star)=0$, $\beta'(\sigma_\star)<0\,$] reproducing the scenario predicted for random impurity scattering of Dirac fermions with Coulomb repulsion, albeit the system considered is perfectly ballistic and interactions are not taken into account. The role of electrostatic bias between the layers is also briefly discussed.