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Lorentz symmetry appears as a quite robust feature of the stronglyinteracting Dirac materials even though the lattice interactions break such asymmetry. We here demonstrate that the Lorentz symmetry is restored at thequantum-critical point (QCP) separating the tilted Dirac semimetal, breakingthis symmetry already at the noninteracting level, from a gapped $s-$wavesuperconducting instability. To this end, we employ a one-loop$\epsilon=(3-D)-$expansion close to the $D=3$ upper critical dimension of thecorresponding Gross-Neveu-Yukawa field theory. In particular, we show that thetilt parameter is irrelevant and ultimately vanishes at the QCP separating thetwo phases. In fact, as we argue here, such a Lorentz symmetry restoration maybe generic for the strongly interacting tilted Dirac semimetals, irrespectiveof whether they feature mirror-symmetric or mirror-asymmetric tilting, and isalso insensitive to whether the instability represents an insulator or a gappedsuperconductor. The proposed scenario can be tested in the quantum Monte Carlosimulations of the interacting tilted Dirac fermion lattice models.

Tilted Dirac superconductor at quantum criticality: Restoration of Lorentz symmetry