Dynamical leakage of Majorana mode into side-attached quantum dot

Quench dynamics of Fano-like resonances in the presence of the on-dot superconducting pairing

“…A comparison of a time scale to typical values of dot-lead coupling in experiments on quantum dot -superconductor hybrids shows that time of reaching equilibrium ranges from few to few hundreds of nanoseconds depending on strength of coupling to the Fermi sea and interdot connection. Comparing our results to those obtained when QD 2 was substitute by one end of topological chain hosting Majorana particles [37] we found that establishing of both ordinary and anomalous resonances takes considerably more time than it is required for Majorana mode to leak into the region of QD. n 2↑ (s) = d † 2↑ (s) d2↑ (s) .…”

“…All this oscillations do not thermalize unless the system is hybridized to continuum of states. Such continuum acts as damping force for classical oscillations [37,42]. Therefore, if one is looking for a time of achieving steady-state solutions, the time scale is predominantly defined by energy of the coupling to metallic lead.…”

“…In order to find time dependent statistical averages we derive the closed set of ordinary differential equations of motion in terms of the Heisenberg notation d dt Ô(t) = i [ Ĥ, Ô] and apply the 4th order Runge-Kutta (RK4) method for numerical calculations of time evolution for each average. Details of this procedure were introduced in the previous work on dynamics of Majorana-QD hybrid [37].…”

“…In three terminal heterostructure comprising two metallic and one superconducting electrode, charge transport is provided by three types of processes: (i) ballistic single electron transfer (ET) from L to R electrode, (ii) direct Andreev reflection (DAR), where single electron from L electrode is converted to a Cooper pair propagating in the SC electrode with simultaneous reflection of hole back to L electrode, and (iii) cross Andreev reflection (CAR), in which the hole is reflected to second metallic electrode (R). For the static case these three processes can be evaluated using the following Landauer-like formulas [37,44]:…”

“…Theoretical analysis of transient effects in quantum dot hybrids in various configurations have already been studied by a few authors [30][31][32][33][34][35][36] including ourselves [37]. Dynamics of Fano-type interference however, have been presented only in [38].…”