the definition of the dimensionless parameter $g_a$ to be defined in Eq. (\[eq:ga2\]), we can relate it to the magnitude of the randomly-fluctuating part of the magnetic field, $\vert \delta B\vert$, by $$\begin{aligned}
\vert \delta B\vert\sim \sqrt{\frac{g_a \hbar E}{{l_c}^3 e^2 v_F}},\end{aligned}$$ where $l_c$ is the correlation length of the vector potential disorder. If we substitute $E=20$ meV, $l_c=10$ nm and $g_a=0.01$, we obtain $\vert \delta B\vert\sim 0.36$ T.

Invariant imbedding method {#sec:met}
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We use the IIM to solve the Dirac equation in the presence of random potentials. Similar methods have been applied in previous studies of the localization of electromagnetic waves in random dielectric media.[@kim1; @lee; @kim6; @kim7] We assume that an electron plane wave is incident from a uniform region ($x>L$) onto the random region ($0\le x\le L$) obliquely at an angle $\theta$ and transmitted to another uniform region ($x<0$). The wave function $\psi_A$ (or equivalently $\psi_B$) in the incident and transmitted regions can be expressed in terms of the reflection coefficient $r$ and the transmission coefficient $t$: $$\begin{aligned}
\psi_A\left(x,L\right)=\begin{cases}
  e^{-ip\left(x-L\right)}+r(L)e^{ip\left(x-L\right)}, & x>L \\
  t(L)e^{-ipx}, & x<0
  \end{cases},\end{aligned}$$ where $r$ and $t$ are regarded as functions of $L$. The $y$ and (negative) $x$ components of the wave vector, 