Emergent space-time supersymmetry in 3D Weyl and 2D Dirac semimetals

TL;DR

This paper demonstrates the emergence of space-time supersymmetry in three-dimensional Weyl semimetals at the critical point of a phase transition involving pair density waves, supported by theoretical models and renormalization group analysis.

Contribution

It provides the first explicit lattice model showing emergent (3+1)D space-time supersymmetry at a continuous phase transition in Weyl semimetals.

Findings

PDW is the leading instability in the model.

Emergent N=2 space-time SUSY at the PDW transition.

Potential experimental signatures discussed.

Abstract

Supersymmetry (SUSY) interchanges bosons and fermions but no direct evidences of it have been revealed in nature yet. In this letter, we observe that fluctuating pair density waves (PDW) consist of two complex order parameters which can be superpartners of the unavoidably-doubled Weyl fermions in three-dimensional lattice models. We construct explicit fermionic lattice models featuring 3D Weyl fermions and show that PDW is the leading instability via a continuous phase transition as short-range interactions exceed a critical value. Using renormalization group, we theoretically show that N=2 space-time SUSY emerges at the continuous PDW transitions in 3D Weyl semimetals, which we believe is the first realization of emergent (3+1)D space-time SUSY in microscopic lattice models. We further discuss possible routes to realize such lattice models and experimental signatures of emergent SUSY at the PDW criticality.