Tilted Dirac superconductor at quantum criticality: Restoration of Lorentz symmetry

Abstract

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

22 pages, 4 figures

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Cited by in corpus (4)

• Yukawa-Lorentz symmetry of interacting non-Hermitian birefringent Dirac fermions
• Yukawa-Lorentz Symmetry of Tilted Non-Hermitian Dirac Semimetals at Quantum Criticality
• Minimal Hamiltonian deformations as bulk probes of effective non-Hermiticity in Dirac materials
• Quantum Criticality of Type-I and Critically Tilted Dirac Semimetals