Excess photon-assisted noise of Majorana and Andreev bound states

Photon-assisted tunneling arises under an ac bias, with the drive frequency setting the photon energy. The excess photon-assisted noise is defined as the difference between the shot noise under a combined dc and ac bias and that under a dc bias alone. We investigate this quantity in tunneling into Majorana or Andreev bound states, which are of great interest in the search for topological superconductors. Under a harmonic bias $V(t)=V_{\mathrm{d}\mathrm{c}}[1-\cos (\mathrm{\Omega }t)]$, the excess photon-assisted noise exhibits distinct behaviors: for Majorana or quasi-Majorana bound states, it undergoes multiple sign reversals as $V_{\mathrm{d}\mathrm{c}}$ increases and vanishes at nonzero integer values of $e{V}_{\mathrm{d}\mathrm{c}}\mathrm{/}\mathrm{\Omega }$ (with $e$ the elementary charge), whereas for zero-energy Andreev bound states–particularly those producing nearly quantized zero-bias conductance peaks–it remains strictly negative over the entire $V_{\mathrm{d}\mathrm{c}}$ range.