work, with a comprehensive investigation of topological properties  [@X.Fan2018], by fitting the $k.p$ model with the DFT results, the corresponding Fermi velocities for Dirac fermions are evaluated to be $v_F^x=8.0$, $v_F^y=5.2$, $v_t=3.4$, for monolayer borophene and $v_F^x=13.9$, $v_F^y=7.7$, $v_t=3.5$, for monolayer borophane, respectively, all in units of ($10^{5}\,m/s $).

Zabolotskiy *et al.*  [@zabolotskiy2016strain] have developed a tight-binding model Hamiltonian for a 2D Dirac semimetal 8-$ Pmmn $ borophene, evaluated in Ref. [@zhou2014semimetallic]. In this work, the Hamiltonian parameters were found from a fit to the DFT data and the resulting electronic structure reproduces the main features of the DFT band structure, including the Dirac points at the Fermi level. Within their model Hamiltonian, the velocities $v_x,v_y,v_{t}$ in vicinity to the K point are given by the following expressions

$$\begin{aligned}
&v_\mathrm{t} = -\frac{\partial^2P/\partial k_y\partial E}{\partial^2P/\partial E^2},\nonumber\\
v_x^2 &=-\frac{\partial^2P/\partial k_x^2}{\partial^2P/\partial E^2},\quad
v_y^2 = v_\mathrm{t}^2-\frac{\partial^2P/\partial k_y^2}{\partial^2P/\partial E^2};\\
&\frac{\partial E}{\partial k_x}=\pm v_x,\quad \frac{\partial E}{ \partial k_y}=\pm v_y+v_\mathrm{t}. \label{slopes}
\label{}\end{aligned}$$

where $P=P(E,\mathbf{k})$ is the characteristic polynomial for energy $E$ and momentum $\mathbf{k}$, and $E=E(\mathbf{k})$ is the eigenvalue. The three velocities are given by $\{v_x,v_y,v_\mathrm{t}\}$=$\{0.86,0.69,0.32\}$ $\times10^6  m/s$  [@zabolotskiy2016strain].

Cheng *et al.*  [@T.Cheng17], developed an effective Hamiltonian around the Dirac point, to a linear term of the 