Quantum critical points in tunneling junction of topological superconductor and topological insulator

•Tunneling junctions between topological superconductor and topological insulator are investigated.•There is a non-trivial stable fixed point in integer topological insulator case at low energies.•The edge of topological insulator breaks up into two sections at the junction.•One side couples strongly to the Majorana fermion and exhibits perfect Andreev reflection.•The other side decouples and exhibits perfect normal reflection.

The tunneling junction between one-dimensional topological superconductor and integer (fractional) topological insulator (TI), realized via point contact, is investigated theoretically with bosonization technology and renormalization group methods. For the integer TI case, in a finite range of edge interaction parameter, there is a non-trivial stable fixed point which corresponds to the physical picture that the edge of TI breaks up into two sections at the junction, with one side coupling strongly to the Majorana fermion and exhibiting perfect Andreev reflection, while the other side decouples, exhibiting perfect normal reflection at low energies. This fixed point can be used as a signature of the Majorana fermion and tested by nowadays experiment techniques. For the fractional TI case, the universal low-energy transport properties are described by perfect normal reflection, perfect Andreev reflection, or perfect insulating fixed points dependent on the filling fraction and edge interaction parameter of fractional TI.