Identifying Majorana Modes using Atomic Scale Shot-Noise – MMNOISE

Distinguishing Majorana bound states (MBS) from conventional sub-gap states such as Yu-Shiba-Rusinov (YSR) states has proved challenging. A diagnostic that has been suggested to provide a clear-cut distinction between MBS and YSR modes are current noise measurements. Even before the first experimental signatures of possible MBS were reported, the idea that noise measurements may be able to discern MBS from YSR states was explored theoretically. Although the initially proposed two-probe geometry is experimentally challenging, later studies found that single-probe measurements also show a distinctly different signal in the noise for MBS and YSR. The distinction in signature arises from the notion that the YSR can be interpreted as a pair of Majorana modes that are equally coupled to the STM tip, whereas the MBS is a single mode. This means for example that for the YSR both spin orientations and particle character are present, whereas the MBS has a single spin and particle character, leading to different tunnelling processes and therefore different noise. In particular, when Andreev reflection dominates the tunnelling process, the noise for a YSR mode is predicted to be enhanced (F>1), whereas that of the MBS is equal to it or even suppressed (F≤1). Additionally, whereas there is a strong spatial dependence of the noise for both YSR modes and Andreev bound states, the noise for the MBS is spatially nearly independent. Given the high spatial resolution of our shot-noise scanning tunnelling microscope, this signature will allow us to even more clearly distinguish MBS modes from YSR and ABS modes.

One claim of Majorana modes focussed on sub-gap states along a one dimensional defect in superconducting Fe(Se,Te). It was found that the lattice left and right of the defect has a phase shift of π, as would be the case for a structural domain wall. Assuming that the superconducting state then also has a phase shift of π, the in-gap states were claimed to be dispersing Majorana modes. Using our low temperature STM, we revealed the true origin of the one dimensional defect and its in-gap states. After improving the reliability of the technique to determine the phase shift of the lattice, our measurements of nearly one hundred different measurements of 1D defect shows that the phase shift is in fact on average π/2. Additionally, we observed similar sub-gap states on surface defects without any phase shift, and, in a few instances, an absence of sub-gap states on defects that do have a phase shift. We also demonstrate the ability to manipulate the 1D defects using the electric field between the tip and the sample, directly visualizing the presence of all surface atoms on the defect. Altogether, these results show that the defects are not a structural domain wall, but originate from strings of atomic scale sub-surface debris, and that the states are topologically trivial. This work was published in Nature Communications 15, 3774 (2024).

Next, we focussed on excess Fe impurities that were shown to have a robust zero bias state. Instead of a single state at zero, however, our mK experiments showed multiple in-gap states. Occasionally these would be at zero energy as well, but upon changing the tip-sample distance we were able to shift them away from zero - which would be impossible for a Majorana zero mode. The ability to shift sub-gap states, however, allowed us to study the interplay between different sub-gap states. Intriguingly, most of the theory developed to describe sub-gap states has been based on one simplified assumption introduced more than 50 years ago: that the magnetic impurity can be treated as a classical object, a small magnet with fixed orientation. By shifting the energy of the sub-gap states, we show that they are not independent classical objects, but are in fact strikingly correlated, requiring a fully quantum description beyond the conventional classical framework. These findings have been published in Nature Communications 15, 8526 (2024).

Lastly, we have started the final step of our journey by measuring vortex cores in Fe(Se,Te). These results are at the moment still preliminary.

Although our results on the 1D defect and the excess Fe atoms thus far have unfortunately shown them to be topologically trivial, the vortex cores may not fare the same fate. We are currently measuring the noise in the vortex cores of Fe(Se,Te) in order to find out. If they indeed are topologically non-trivial, we will explore whether their exotic character can be exploited for further study.

Using atomic scale current noise measurements, we will unambiguously establish the presence or absence of Majorana bound states (MBS) that have been suggested to exist on individual Fe impurities, vortex cores and 1D crystalline defects in the iron based superconductor Fe(Se,Te). Unlike other non-invasive detection techniques, theoretical calculations show that the current noise of MBS is distinctly different from other in-gap modes. Preliminary measurements on the latter with our MHz-enabled scanning tunnelling microscope show that we can access the relevant tunnelling regime, have sufficient signal-to-noise to reliably carry out the measurement and confirm the theoretical predictions for these modes. If MBS are indeed present in one or more of the proposed scenarios, we will directly proceed to attempt readout and manipulation of the MBS, for which numerous proposals have been put forth that are feasible with the proposed system and our setup.