Exotic quantum critical point on the surface of three-dimensional topological insulator

In the last few years a lot of exotic and anomalous topological phases were constructed by proliferating the vortexlike topological defects on the surface of the 3d topological insulator (TI) [Fidkowski, Phys. Rev. X 3, 041016 (2013)10.1103/PhysRevX.3.041016; Chen, Phys. Rev. B 89, 165132 (2014)10.1103/PhysRevB.89.165132; Bonderson, J. Stat. Mech. (2013) P0901610.1088/1742-5468/2013/09/P09016; Wang, Phys. Rev. B 88, 115137 (2013)10.1103/PhysRevB.88.115137; Metlitski, Phys. Rev. B 92, 125111 (2015)10.1103/PhysRevB.92.125111]. In this work, rather than considering topological phases at the boundary, we will study quantum critical points driven by vortexlike topological defects. In general, we will discuss a (2+1)d quantum phase transition described by the following field theory: L=ψγμ(∂μ-iaμ)ψ+|(∂μ-ikaμ)φ|2+r|φ|2+g|φ|4, with tuning parameter r, arbitrary integer k, Dirac fermion ψ, and complex scalar bosonic field φ, which both couple to the same (2+1)d dynamical noncompact U(1) gauge field aμ. The physical meaning of these quantities/fields will be explained in the text. Making use of the new duality formalism developed in [Metlitski, Phys. Rev. B 93, 245151 (2016)10.1103/PhysRevB.93.245151; Wang, Phys. Rev. X 5, 041031 (2015)10.1103/PhysRevX.5.041031; Wang, Phys. Rev. B 93, 085110 (2016)10.1103/PhysRevB.93.085110; D. T. Son, Phys. Rev. X 5, 031027 (2015)2160-330810.1103/PhysRevX.5.031027], we demonstrate that this quantum critical point has a quasi-self-dual nature. And at this quantum critical point, various universal quantities such as the electrical conductivity and scaling dimension of gauge-invariant operators, can be calculated systematically through a 1/k2 expansion, based on the observation that the limit k→+ corresponds to an ordinary 3d XY transition.