Fingerprints of Majorana fermions in current-correlation measurements from a superconducting tunnel microscope

We compute various current-correlation functions of electrons flowing from a topological nanowire to the tip of a superconducting scanning tunnel microscope and identify fingerprints of a Majorana bound state. In particular, the spin resolved cross correlations are shown to display a clear distinction between the presence of a such an exotic state (negative correlations) and an Andreev bound state (positive correlations). Similarity and differences with measurements with a normal tunnel microscope are also discussed, like the robustness to finite temperature, for instance.

Figure 1

The system consists of a grounded TN driven in the topological phase (i.e., $V_z^2>{\mathrm{\Delta }}_s^2+{\mu }^2$) carrying MBSs at its ends and in proximity with a biased SC STM tip. This tip is approached above the MBS allowing us to detect the noise as well as the spin current correlations of the current flowing between them. Note that the spin current correlations can be extracted using a spin filter along the output signal. In our study, we are deep in the topological phase meaning that the magnetic field is sufficiently large to polarize all the spins of the TN in its direction.

Figure 2

Normalized spin current correlations ${\mathrm{F}}_{\uparrow \downarrow }\equiv P_{\uparrow \downarrow }/e\langle I_1\rangle$ as a function of $\lambda$ for a MBS/ABS in the case of a SC STM tip (red/grey solid lines) and of a N STM tip (red/grey dashed lines).