The Bravais lattice constants of the conventional orthorhombic unit cell (contains four atoms, as seen in Fig. \[lattice\] ) of the buckled crystal structures of borophene and borophane, are $a = 1.62$ Å , $b = 2.85$Å  and $a = 1.92$ Å , $b= 2.81$ Å , respectively [@Piazza14; @Xu16; @Tang2007]. Notice that the buckling height of $h= 0.96$ Å  in borophene reduces to $h= 0.81$ Å, upon hydrogen adsorption in borophane [@Padilhapccp16].

In combination with first-principles calculations and starting from the simplified linear combination of atomic orbitals approach , M. Nakhaee [*et al.*]{} have constructed a tight-binding model in the two-centre approximation for borophene and borophane [@Peeters-Hamilton]. The Slater and Koster approach is applied to calculate the TB coefficients of these two systems.

Our starting point is the low-energy continuum Hamiltonian for borophane  [@Peeters-Hamilton], that describes an anisotropic and tilted Dirac crossing along the $ \Gamma $-X direction in the rectangular Brillouin zone. In the vicinity of two nonequivalent Dirac points ${\bf K}_D=(\pm 0.64,0)$Å$^{-1}$  [@zabolotskiy2016strain; @Peeters-Hamilton; @Sadhukhan2017; @Ezawa2017; @Islam2017]

$$H = \hbar v_{x} k_{x}\sigma_{x} + \hbar v_{y}k_{y} \sigma_{y} + \hbar v_{t}k_{x} \sigma_{0}.
\label{boeqn}$$

Here, $\sigma_{x},\sigma_{y} $ are the Pauli matrices for the pseudospin representing the lattice degree of freedom 