Changing effective mass of electron using electric potential?

The Dirac equation for an electron in the presence of an electromagnetic 4-potential $A_mu$, where $hbar=c=1$, is given by

$$gamma^mubig(ipartial_mu-eA_mubig)psi-m_epsi=0.tag{1}$$

I assume the Weyl basis so that

$$psi=begin{pmatrix}psi_Lpsi_Rend{pmatrix}hbox{ and }gamma_0=begin{pmatrix}0&II&0end{pmatrix}.tag{2}$$

I assume that the electron is stationary so that
$${bfhat{p}}psi=-inablapsi=(0,0,0).tag{3}$$

Finally I assume that an electric potential $phi_{E}$ exists so that we have
$$A_mu=(-phi_{E},0,0,0).tag{4}$$

Substituting into the Dirac equation $(1)$ we find
$$ibegin{pmatrix}0&II&0end{pmatrix}frac{partial}{partial t}begin{pmatrix}psi_Lpsi_Rend{pmatrix}+e phi_Ebegin{pmatrix}0&II&0end{pmatrix}begin{pmatrix}psi_Lpsi_Rend{pmatrix}-m_ebegin{pmatrix}psi_Lpsi_Rend{pmatrix}=0.tag{5}$$
Writing out the two equations for $phi_L$ and $phi_R$, contained in Eqn $(5)$, explicitly we obtain

$$begin{eqnarray*}
ifrac{partialpsi_R}{partial t} &=& m_e psi_L – e phi_E psi_Rtag{6}
ifrac{partialpsi_L}{partial t} &=& -e phi_E psi_L + m_e psi_R.tag{7}
end{eqnarray*}$$

Adding and subtracting Eqns. $(6)$ and $(7)$ we obtain

$$begin{eqnarray*}
ifrac{partial}{partial t}big(psi_L+psi_Rbig) &=& big(m_e – e phi_Ebig)big(psi_L+psi_Rbig)tag{8}
ifrac{partial}{partial t}big(psi_L-psi_Rbig) &=& big(-m_e – e phi_Ebig)big(psi_L-psi_Rbig).tag{9}
end{eqnarray*}$$

It seems to me that Eqn. $(8)$ describes an electron with an effective rest mass/energy $M_e=m_e-ephi_E$ and Eqn. $(9)$ describes a positron with an effective rest mass/energy $M_p=m_e+ephi_E$.

If we can change the effective mass of electrons/positrons by changing the electric potential $phi_E$ then can we change the dynamics of electrons in atoms by applying a large $phi_Esim m_e/e$?