Fermion-induced quantum critical points in two-dimensional Dirac semimetals

摘要

In this paper we investigate the nature of quantum phase transitions between two-dimensional Dirac semimetals and Z_3-ordered phases (e.g., Kekule valence-bond solid), where cubic terms of the order parameter are allowed in the quantum Landau-Ginzberg theory and the transitions are putatively first order. From large-N renormalization-group (RG) analysis, we find that fermion-induced quantum critical points (FIQCPs) [Z.-X. Li et al., Nat. Commun. 8,314 (2017)] occur when N (the number of flavors of four-component Dirac fermions) is larger than a critical value N_c. Remarkably, from the knowledge of space-time supersymmetry, we obtain an exact lower bound for N_c, i.e., N_c > 1/2. (Here the "1/2" flavor of four-component Dirac fermions is equivalent to one flavor of four-component Majorana fermions). Moreover, we show that the emergence of two length scales is a typical phenomenon of FIQCPs and obtain two different critical exponents, i.e., v ≠ v', by large-N RG calculations. We further give a brief discussion of possible experimental realizations of FIQCPs.