microscopic origin of the scattering mechanisms and $f^{0}$ is the equilibrium distribution function.

The collision integral is given by $$\begin{aligned}
\left(\frac{df}{dt}\right)_{{\rm coll.}}=\int\frac{d^2k'}{(2\pi)^2}w({\vec{k}},{\vec{k}'})\left[f({\vec{k}},{\vec{\mathcal{E}}}, T)-f({\vec{k}'}, {\vec{\mathcal{E}}}, T)\right]\nonumber\\
\label{eq4}\end{aligned}$$

Using the relaxation time approximation, the nonequilibrium distribution function cannot be exactly calculated and provides an inadequate explanation for the full aspects of the anisotropic features of the transport properties.

In the next section, we have implemented an approach for finding the exact solution to the linear-response Boltzmann equation for two dimensional anisotropic systems [@Vyborny; @bzare2016; @Faridi; @moslem-bp2]. Within the lowest order of the Born approximation, the scattering rates $w({\vec{k}},{\vec{k}'})$, using the Fermi golden rule are given by $$\begin{aligned}
w({\vec{k}}, {\vec{k}'})=\frac{2\pi}{\hbar}n_{{\rm imp}}\big\vert\langle {\vec{k}'}|\hat{V}|{\vec{k}'}\rangle\big\vert^2 \delta(\varepsilon_{\vec{k}}-\varepsilon_{\vec{k}'})\end{aligned}$$

where $n_{{\rm imp}}$ is the background random-charged impurity density and $\hat{V}_{{\vec{k}}-{\vec{k}'}}$ is the Fourier transformation of the interaction potential between an electron and a single impurity.

The short-ranged impurities are approximated with a zero-range hard-core potential $\hat{V}_{{\vec{k}}-{\vec{k}'}}=V_{0}$, while the long-ranged electron-electron Coulomb potential, owing to the charged impurities, is screened by other electrons of the system, according to the Thomas-Fermi approximation.

By invoking the expression for $f(\theta, \phi)$ into Eq. (\[currents\]) for the charge and heat currents, the response matrix, which relates the resulting generalized currents to the driving forces, 