Fano interference and a slight fluctuation of the Majorana hallmark

Abstract

According to the Phys. Rev. B 84, 201308(R) (2011), an isolated Majorana state bound to one edge of a long enough Kitaev chain in the topological phase and connected to a quantum dot, results in a robust transmittance of $1/2$ at zero-bias. In this work, we show that the removal of such a hallmark can be achieved by using a metallic surface hosting two adatoms in a scenario where there is a lack of symmetry in the Fano effect, which is feasible by coupling the Kitaev chain to one of these adatoms. Thus in order to detect this feature experimentally, one should apply the following two-stage procedure: (i) first, attached to the adatoms, one has to lock AFM tips in opposite gate voltages (symmetric detuning of the levels) and measure by an STM tip, the zero-bias conductance; (ii) thereafter, the measurement of the conductance is repeated with the gates swapped. For the absolute value of the detuning away from the Fermi energy and in the case of strong coupling tip-host, this approach reveals in the transmittance, a persistent dip placed at zero-bias and immune to the aforementioned permutation, but characterized by an amplitude that fluctuates slightly around $1/2$. However, in the case of a tip acting as a probe, the adatom decoupled from the Kitaev chain becomes completely inert and no fluctuation is observed. Therefore, the STM tip must be considered in the same footing as the "host+adatoms" system. As a result, we have found that despite the small difference between these two Majorana dips, the zero-bias transmittance as a function of the symmetric detuning yields two distinct behaviors, in which one of them is unpredictable by the standard Fano's theory. Therefore, to access such a non trivial pattern of Fano interference, the hypothesis of the STM tip acting as a probe should be discarded.