wave vector, and obtained an analytical formula for prediction of the intrinsic carrier mobility in 2D materials with tilted Dirac cones and combine it with first-principles calculations to determine the properties of semimetallic borophene and borophane. Their predicted velocities in 8-$ Pmmn $ borophene are $v_F^x=7.85$, and $v_F^y= 5.34$, and for monolayer borophane, they are $v_F^x=13.48$, $v_F^y= 7.7$, along the x and y directions, respectively, and the tilting velocities are $v_t=-3.45$, and $v_t=-3.86$ in 8-$ Pmmn $ borophene and borophane, respectively. Note that the all velocities are in units of ($10^{5}\,m/s $).

The contour lines are drawn at $0.05$ eV intervals in both electron (solid-navy) and hole-doped cases (dashed-green).We demonstrate the band dispersion of borophane (Eq.\[diseq\]) in Fig. \[dispersion\], where we have compared our used model Hamiltonian (Eq.\[boeqn\]) with that calculations, based on the density functional theory and non-equilibrium Green’s function approaches [@Anpccp2018], the so-called NEGF-DFT method.

The corresponding eigenfunction for the Dirac electrons is given by the following equation

$$\label{wave}
\psi^{\tau}({\vec{k}})=\frac{1}{\sqrt{2A}}\left[\begin{array}[c]{c}
                                   \tau e^{-i\beta_{\vec{k}}}\\
                                   1
                                  \end{array}\right]e^{i\vec{k}\cdot\vec{r}},$$

where $A$ is the system area and $\beta_{k}=\tan^{-1}\left[ v_y k_y/v_x k_x \right]$.

Furthermore, By invoking the band energy dispersion given by Eq. (\[diseq\]), the $x$ and $y$ components of the velocity can be calculated 