First search for Lorentz and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi><mml:mi>T</mml:mi></mml:math>violation in double beta decay with EXO-200

A search for Lorentz- and $CPT$-violating signals in the double beta decay spectrum of $^{136}\mathrm{Xe}$ has been performed using an exposure of $100\text{ }\text{ }\mathrm{kg}\ifmmode\cdot\else\textperiodcentered\fi{}\mathrm{yr}$ with the EXO-200 detector. No significant evidence of the spectral modification due to isotropic Lorentz-violation was found, and a two-sided limit of $\ensuremath{-}2.65\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\text{ }\text{ }\mathrm{GeV}&lt;{\^a}_{\mathrm{of}}^{(3)}&lt;7.60\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\text{ }\text{ }\mathrm{GeV}$ (90% C.L.) is placed on the relevant coefficient within the Standard-Model Extension (SME). This is the first experimental study of the effect of the SME-defined oscillation-free and momentum-independent neutrino coupling operator on the double beta decay process.