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Probing Majorana Flat Bands in Nodal $d_{x^2-y^2}$-wave Superconductors with Rashba Spin-Orbit Coupling

We show that Majorana fermions associated with Majorana flat bands emerge as zero energy modes on the [110] edge of single layer or multilayer nodal superconductors with $d_{x^2-y^2}$-wave pairing and Rashba spin-orbit coupling. Moreover, as long as the global inversion symmetry of the single layer or multilayer superconductor is broken, and in the presence of an in-plane magnetic field parallel to the [110] edge, the Majorana fermions together with usual fermionic Andreev bound states induce a triple-peak structure in tunnelling spectroscopy experiments. Importantly, we show that the zero bias conductance peak is induced by Majorana fermions. Therefore, tunnelling spectroscopy can be used to probe Majorana fermions in nodal $d_{x^2-y^2}$-wave superconductors.