axes, which were generally referred to as the armchair ($x$) and zigzag ($y$) axes, are considered.

Due to the fact that the long-range charge-impurity Coulomb interaction is mostly the dominant scatterers in samples, here we consider the Coulomb interaction. To this end, we use an interaction potential, as is commonly used for a 2D electron gas, given by the static Thomas-Fermi (TF) screening type [@ando] $$\begin{aligned}
V_{{\vec{k}}- {\vec{k}}'}=2\pi e^{2}/[\epsilon(\vert{\vec{k}}-{\vec{k}}'\vert+q_{_{{\rm TF}}})],\end{aligned}$$ where $q_{_{{\rm TF}}}=2\pi e^{2}D(E)/\epsilon$ is the Thomas-Fermi screening vector with the density of states of the system, $D(E)$. We assume that the scattering charge centers are at the SiO$_{2}$-borophane interface, thus we use the dielectric constant of this common substrate which is about $\epsilon=2.45$. Meanwhile, we note that we set $T\sim20~{\rm K}$ in all calculated quantities.

In Fig. (\[fig3\]), the conductivity of borophane (in units of $e^2/h$) as a function of the chemical potential $\mu$, is plotted in the presence of LR potential, along the $x$ ($\sigma_{xx}$), and $y$ ($\sigma_{yy}$), directions. The conductivity of graphene is also shown. As can be seen, a significant orientation dependent electrical conductivity is observed, where the conductivity in the armchair direction $\sigma_{xx}$ is more than the zigzag conductivity $\sigma_{yy}$. On the other hand, contrary 