Transport Signatures of Floquet Majorana Fermions in Driven Topological Superconductors

Floquet Majorana fermions are steady states of equal superposition of electrons and holes in a periodically driven superconductor. We study the experimental signatures of Floquet Majorana fermions in transport measurements and show, both analytically and numerically, that their presence is signaled by a quantized conductance sum rule over discrete values of lead bias differing by multiple absorption or emission energies at drive frequency. We also study the effects of static disorder and find that the quantized sum rule is robust against weak disorder. Thus, we offer a unique way to identify the topological signatures of Floquet Majorana fermions.

Figure 1

The evolution of the Floquet spectrum of a quantum wire with $L$ sites vs $\Omega$ for a square-wave chemical potential. The arrows show the frequencies used for the transport calculations in Fig. 3.

Figure 2

Differential conductance $\sigma =dI/dV$ vs bias $V$ in a single-terminal setup for a static system with $L=80$, $\Delta /w=0.6$, $\mu /w=0.25$, and $\nu /w=\pi /25$. The (blue) dots are calculated from the analytical expression of peak heights.

Figure 3

Differential conductances $\sigma$ (top row) and $\tilde{\sigma }$ (bottom row) of the driven system as a function of bias $V/\Omega$ in a two-terminal setup. The parameters $\Delta$, ${\mu }_1$, ${\mu }_2$, and $t_1/t_2$ are as in Fig. 1, $\nu /w=2\pi /25$, and the other parameters are (a),(d) $L=40$, $\Omega /2w=0.37$, (b),(e) $L=70$, $\Omega /2w=0.49$, (c),(f) $L=40$, $\Omega /2w=0.75$. The frequencies are marked by arrows in Fig. 1.

Figure 4

Differential conductance in a two-terminal setup averaged over 50 disorder configurations. The parameters are as in Fig. 3a, 3d and disorder strength ${\mu }_d=0.28w=0.38\Omega$.