Absence of emergent supersymmetry at superconducting quantum critical points in Dirac and Weyl semimetals

Understand

Supersymmetry plays a crucial role in superstring theory and high-energy physics, but has never been observed in experiments.

• Recently, an effective space-time supersymmetry was argued to emerge in the low-energy region by tuning Dirac or Weyl semimetal to approach a superconducting quantum critical point, at which the Dirac or Weyl fermion and the bosonic order parameter are both massless.
• Here, we study under what circumstances can space-time supersymmetry be realized at a quantum critical point.
• We demonstrate that the Yukawa-type coupling between the massless fermion and massless boson can dynamically generate an infinite number of non-supersymmetric terms in the effective field theory of the boson.