Quantum superconducting criticality in graphene and topological insulators

Abstract

The field theory of the semimetal-superconductor quantum phase transition for graphene and surface states of topological insulators is presented. The Lagrangian possesses the global U(1) symmetry, with the self-interacting complex bosonic order-parameter and the massless Dirac fermions coupled through a Yukawa term. The same theory also governs the quantum critical behavior of graphene near the transition towards the bond-density-wave (Kekule) insulator. The local U(1) gauged version of the theory which describes the quantum semimetal-superconductor transition in the ultimate critical regime is also considered. Due to the Yukawa coupling the transitions are found to be always continuous, both with and without the fluctuating gauge field. The critical behavior is addressed within the dimensional regularization near four space-time dimensions, and the calculation of various universal quantities, including critical exponents and the universal mass-ratio, is reported.

4 pages, no figures +(Supplementary: 6 pages and 5 figures), Published version, New discussion on pairing criticality of surface states of topological crystalline insulator, New references

References in corpus (11)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Topological Crystalline Insulators
• The space group classification of topological band insulators
• Interactions and phase transitions on graphene's honeycomb lattice
• Electron fractionalization in two-dimensional graphenelike structures
• Theory of interacting electrons on the honeycomb lattice
• Density waves and Cooper pairing on the honeycomb lattice
• Emergence of supersymmetry at a critical point of a lattice model
• BCS-BEC crossover on the two-dimensional honeycomb lattice
• Unconventional superconductivity on honeycomb lattice: the theory of Kekule order parameter
• Induced superconductivity in the three-dimensional topological insulator HgTe