Several recent works have predicted that unconventional and topological superconductivity can arise in graphene, either intrinsically or by proximity effect. Then, the analysis of the spectroscopic and transport properties in graphene would be a valuable source of information in the study of the emergent superconducting order parameter. Using Green's functions techniques, we study the transport properties of a finite size ballistic graphene layer placed between a normal state electrode and a graphene lead with proximity-induced unconventional superconductivity. Our microscopic description of such a junction allows us to consider the effect of edge states in the graphene layer and the imperfect coupling to the electrodes. The tunnel conductance through the junction and the spectral density of states feature a rich interplay between graphene's edge states, interface bound states formed at the graphene-superconductor junction, Fabry-Pérot resonances originated from the finite size of the graphene layer, and the characteristic Andreev surface states of unconventional superconductors. Within our analytical formalism, we identify the separate contribution from each of these subgap states to the conductance and density of states. Our results provide an advisable tool to determine experimentally the pairing symmetry of unconventional superconductivity that can arise in graphene.

Many proposals to generate a time-reversal invariant topological superconducting phase are based on imposing a π phase difference between the superconducting leads proximitizing a nanostructure. We show that this phase can be induced on a thin film of a topological insulator like Bi2Se3 in proximity to a single s-wave superconductor. In our analysis we take into account the parity degree of freedom of the electronic states which is not included in effective Dirac-like surface theories. We find that the topological phase can be reached when the induced interparity pairing dominates over the intraparity one. Application of an electric field perpendicular to the film extends the range of parameters where the topological phase occurs. arXiv:1812.00931v1 [cond-mat.supr-con]

This work presents a Green’s function approach, originally implemented in graphene with well-defined edges, to the surface of a strong 3D topological insulator with a sequence of proximitized superconducting (S) and ferromagnetic (F) surfaces. This consists of the derivation of the Green’s functions for each region by the asymptotic solutions method and their coupling by a tight-binding Hamiltonian with the Dyson equation to obtain the full Green’s functions of the system. These functions allow the direct calculation of the momentum-resolved spectral density of states, the identification of subgap interface states and the derivation of the differential conductance for a wide variety of configurations of the junctions. We illustrate the application of this method for some simple systems with two and three regions, finding the characteristic chiral state of the quantum anomalous Hall effect at the NF interfaces, and chiral Majorana modes at the NS interfaces. Finally, we discuss some geometrical effects present in three-region junctions such as weak Fabry–Pérot resonances and Andreev bound states.

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