  New two dimensional systems like surface of topological insulator and
graphene offer a possibility to experimentally investigate situations
considered "exotic" just a decade ago. One of those is the quantum phase
transition of the "chiral" type in electronic systems with relativistic
spectrum. Phonon mediated ("conventional") pairing in the Dirac semimetal
appearing on the surface of topological insulator leads to transition into a
chiral superconducting state, while exciton condensation in these gapless
systems has been envisioned long time ago in the physics of the narrow band
semiconductors. Starting from the microscopic Dirac Hamiltonian with local
attraction or repulsion, the BCS type gaussian approximation is developed in
the framework of functional integrals. It is shown that due to an
"ultra-relativistic" dispersion relation there is a quantum critical point
governing the zero temperature transition to a superconducting or the exciton
condensed state. The quantum transitions that have critical exponents very
different from the conventional ones. They belong to the chiral universality
class. We discuss the application of these results to recent experiments in
which surface superconductivity was found in topological insulators and
estimate feasibility of the phonon pairing.
