| Summary: | <p> Originally proposed in high energy physics as particles, which are their own anti-particles, Majorana fermions have never been observed in experiments. However, possible signatures of their condensed matter analog, zero energy, charge neutral, quasiparticle excitations, known as Majorana zero modes (MZMs), are beginning to emerge in experimental data. The primary method of engineering topological superconductors capable of supporting MZMs is through proximity-coupled semiconductor nanowires with strong Rashba spin-orbit coupling and an applied magnetic field. Recent tunneling transport experiments involving these materials, known as semiconductor-superconductor heterostructures, were capable for the first time of measuring quantized zero bias conductance plateaus, which are robust over a range of control parameters, long believed to be the smoking gun signature of the existence of MZMs. The possibility of observing Majorana zero modes has garnered great excitement within the field due to the fact that MZMs are predicted to obey non-Abelian quantum statistics and therefore are the leading candidates for the creation of qubits, the building blocks of a topological quantum computer. In this work, we first give a brief introduction to Majorana zero modes and topological quantum computing (TQC). We emphasize the importance that having a true topologically protected state, which is not dependent on local degrees of freedom, has with regard to non-Abelian braiding calculations. We then introduce the concept of partially separated Andreev bound states (ps-ABSs) as zero energy states whose constituent Majorana bound states (MBSs) are spatially separated on the order of the Majorana decay length. Next, through numerical calculation, we show that the robust 2<i> e<sup>2</sup>/h</i> zero bias conductance plateaus recently measured and claimed by many in the community to be evidence of having observed MZMs for the first time, can be identically created due to the existence of ps-ABSs. We use these results to claim that all localized tunneling experiments, which have been until now the main way researchers have tried to measure MZMs, have ceased to be useful. Finally, we outline a two-terminal tunneling experiment, which we believe to be relatively straight forward to implement and fully capable of distinguishing between ps-ABSs and true topologically protected MZMs.</p><p>
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