Proposed as a fundamental symmetry describing our universe, spacetime supersymmetry (SUSY) has not been discovered yet in nature. Nonetheless, SUSY may emerge in low-energy and long-wavelength physics of condensed matter systems. In this talk, I will focus on three interesting cases of emergent SUSY. Firstly, from renormalization group analysis, we demonstrate the first example of emergent spacetime SUSY in 3D that occurs at the quantum superconducting transition in 3D Weyl semimetals [1]. Secondly, we show that 2D supersymmetric quantum electrodynamics with dynamical gauge bosons and fermionic gauginos emerges naturally at the pair-density-wave quantum phase transition on the surface of a correlated topological insulator hosting three Dirac cones, such as the candidate topological Kondo insulator SmB6 [2]. Thirdly, by performing sign-problem-free Majorana-quantum-Monte-Carlo [3,4] simulations of an interacting 2D topological superconductor, we show convincing evidences that the N=1 SUSY emerges at its edge quantum critical point (EQCP). Remarkably, near the EQCP, we find that the edge Majorana fermion acquires a mass which is identical with that of its bosonic superpartner. To the best of our knowledge, this is the first observation that fermions and bosons have equal dynamically-generated masses, a hallmark of emergent SUSY [5].
