  A search for violation of Lorentz invariance in the production of top quark
pairs ($\mathrm{t\bar{t}}$) is presented. The measured normalized differential
$\mathrm{t\bar{t}}$ production cross section, as function of the sidereal time,
is examined for potential modulations induced by Lorentz-invariance breaking
operators in an effective field theory extension of the standard model (SM).
The cross section is measured from collision events collected by the CMS
detector at a center-of-mass-energy of 13 TeV, corresponding to an integrated
luminosity of 77.8 fb$^{-1}$, and containing one electron and one muon. The
results are found to be compatible with zero, in agreement with the SM, and are
used to bound the Lorentz-violating couplings to be in ranges of 1 - 8 $\times$
10$^{-3}$ at 68% confidence level. This is the first precision test of the
isotropy in special relativity with top quarks at the LHC, restricting further
the bounds on such couplings by up two orders of magnitude with respect to
previous searches conducted at the Tevatron.
