Identifying the pairing symmetry in sodium cobalt oxide by Andreev edge states: Theoretical analysis

We study the Andreev edge states with different pairing symmetries and boundary topologies on semi-infinite triangular lattice of ${\text{Na}}_{x}{\text{CoO}}_{2}\ensuremath{\cdot}y{\text{H}}_{2}\text{O}$. A general mapping from the two-dimensional lattice to the one-dimensional tight-binding model is developed. It is shown that the phase diagram of the Andreev edge states depends on the pairing symmetry and also on the boundary topology. Surprisingly, the structure of the phase diagram crucially relies on the nodal points on the Fermi surface and can be explained by an elegant gauge argument. We compute the momentum-resolved local density of states near the edge and predict the hot spots which are measurable in Fourier-transformed scanning tunneling spectroscopy.

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