Quantum superconducting criticality in graphene and topological insulators

Abstract

We correct our previous conclusion regarding the fate of a charged quantum critical point across the superconducting transition for two dimensional massless Dirac fermion. Within the leading order expansion, we now find that the requisite number of four-component Dirac fermion flavors (N f ) for the continuous phase transition through a charged critical point is N f > 18.2699. For N f ≥ 1/2, the critical number of bosonic flavors for this transition is significantly reduced as compared to the value determined in the absence of the Dirac fermions in the theory.

Emergent Fermi surfaces, fractionalization and duality in supersymmetric QED

“…One reason is that supersymmetry does not seem to be directly realized in any condensed matter systems of interest. This situation may now be changing -see [3][4][5][6] for proposals which could realize supersymmetric field theories in condensed matter laboratories. Another reason, from a more theoretical perspective, is that finite density generically breaks SUSY explicitly, and so a priori it is not clear whether the techniques of supersymmetry can help one understand phenomena of interest in field theory at finite density.…”

Four-loop critical exponents for the Gross-Neveu-Yukawa models

“…In the this scenario it was argued that at the QCP the Z 3 gets enhanced to an emergent Uð1Þ symmetry leading to a set of critical exponents that is shared with the N ¼ 2 chiral XY model [55][56][57]. Another intriguing scenario where the chiral XY model is relevant are the surface states of three-dimensional topological insulators where emergent supersymmetry has been conjectured at the quantum critical point [43,46,58]. This implies a field content with fermion flavor number N ¼ 1=2.…”

“…Applications of this model in the condensed-matter context can be found in the quantum critical behavior of superconducting states in graphene where the number of fermion flavors is N ¼ 2, see, e.g., Ref. [46], where also an explicit choice for the Clifford algebra is discussed. Further, the case N ¼ 2 is relevant to a Kekulé valence bond solid transition in graphene [52][53][54] which is described by a complex order parameter, however, with a discrete Z 3 symmetry.…”

“…In the chiral XY model there are two specific values for the number of fermion flavors N which are relevant to condensed-matter applications, i.e., the quantum transition of surface states in topological insulators [43,46,58] as covered by the choice N ¼ 1=2 and the superconducting transition in graphene [46] where N ¼ 2. Further, the case N ¼ 2 is relevant to a Kekulé transition in graphene [52][53][54][55] which is described by a complex Z 3 order parameter [56,57], however, exhibits emergent Uð1Þ symmetry at the QCP.…”

“…Therefore, we do not give an explicit representation, here and in the following, and only note that different physical applications come with various explicit representations of the Clifford algebra, see for example Refs. [46] and [43]. The conjugate of the Dirac field is given byψ ¼ ψ † γ 0 .…”