The electric dipole moment (EDM) of an atom could arise also from $P$-odd and $T$-odd electron-nucleon couplings. In this work we investigate a general class of dimension-$6$ electron-nucleon ($e$-$N$) nonminimal interactions mediated by Lorentz-violating (LV) tensors of rank ranging from $1$ to $4$. The possible couplings are listed as well as their behavior under $C$, $P$ and $T$, allowing us to select the couplings compatible with EDM physics. The unsuppressed contributions of these couplings to the atoms Hamiltonian can be read as EDM-equivalent. The LV coefficients magnitudes are limited using EDM experimental data to the level of $3.2times 10^{-13} text{(GeV)}^{-2}$ or $1.6times10^{-15} text{(GeV)}^{-2}$.
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