Emergent Spacetime Supersymmetry at Superconducting Quantum Criticality of a single Dirac Cone

No definitive evidence of spacetime supersymmetry (SUSY) that transmutes fermions into bosons and vice versa has been revealed in nature so far. Moreover, whether spacetime SUSY in 2+1 and higher dimensions can emerge in generic lattice microscopic models remains open. Here, we introduce a lattice realization of a single Dirac fermion in 2+1 dimensions with attractive interactions that preserves both time-reversal and chiral symmetries. By performing sign-problem-free determinant quantum Monte Carlo simulations, we show that the interacting single Dirac fermion in 2+1 dimensions features a superconducting quantum critical point (QCP). More remarkably, we demonstrate that the N=2 spacetime SUSY in 2+1D emerges at the superconducting QCP by showing that the fermions and bosons have identical anomalous dimensions 1/3, a hallmark of the emergent SUSY [1]. We further show some experimental signatures which may be measured to test such emergent SUSY in candidate systems such as the surface Dirac cone of 3D topological insulators.
[1] Zi-Xiang Li, Abolhassan Vaezi, Christian B. Mendl, Hong Yao, arXiv:1711.04772 (to appear in Science Advances)