Odd-even rule for zero-bias tunneling conductance in coupled Majorana wire arrays

Abstract

A semiconducting nanowire with strong Rashba coupling and in proximity of a superconductor hosts Majorana edge modes. An array of such nanowires with inter-wire coupling gives an approximate description of a two-dimensional topological superconductor, where depending on the strength of the magnetic field and the chemical potential, a rich phase diagram hosting trivial and different types of non-trivial phases can be achieved. Here, we theoretically consider such a two-dimensional assembly of spin-orbit coupled superconducting nanowires and calculate the collective tunneling conductance between normal electrodes and the wires in the topological regime. When the number of wires in the assembly is $N$, as a consequence of the way the Majorana bonding and anti-bonding states form, we find that $N$ conductance peaks symmetric about the bias $V = 0$ appear, for even $N$. When $N$ is odd, a ZBCP also appears. Such an assembly can be realized by standard nano-fabrication techniques where individual nanowires can be turned $ON$ or $OFF$ by using mechanical switch (or local top gating) to make $N$ either even or odd -- thereby switching the ZBCP $OFF$ or $ON$, respectively. Hence, our results can be used to realize and detect topological superconductivity efficiently, unambiguously and in a controlled manner.