Transport spectroscopy ofNSnanowire junctions with Majorana fermions

Abstract

We investigate transport through normal-superconductor nanowire junctions in the presence of spin-orbit coupling and magnetic field. As the Zeeman field crosses the critical bulk value B c of the topological transition, a Majorana bound state (MBS) is formed, giving rise to a sharp zero-bias anomaly (ZBA) in the tunneling differential conductance. We identify novel features beyond this picture in wires with inhomogeneous depletion, such as the appearance of two MBSs inside a long depleted region for B < B c . The resulting ZBA is in most cases weakly split and may coexist with Andreev bound states near zero energy. The ZBA may appear without evidence of a topological gap closing. This latter aspect is more evident in the multiband case and stems from a smooth pinch-off barrier. Most of these features are in qualitative agreement with recent experiments [V. Mourik et al., Science 336, 1003(2012]. We also discuss the rich phenomenology of the problem in other regimes which remain experimentally unexplored. and semiconductors with strong spin-orbit (SO) coupling. 4-8In proximity to s-wave superconductors, these systems behave as topological superconductors (TSs) when the excitation gap is closed and reopened again: as the gap crosses zero, Majorana bound states (MBSs) appear wherever the system interfaces with a nontopological insulator (see Refs. 9 and 10 for reviews).The TS transition occurs when an external Zeeman field B exceeds a critical value B c ≡ μ 2 + 2 defined in terms of the Fermi energy μ and the induced s-wave pairing . 7,8 This prediction has spurred a great deal of experimental activity towards detecting MBSs in hybrid superconductorsemiconductor systems. Indeed, signatures of Majorana detection have been recently reported in Ref. 11. These experiments (and subsequently Refs. 12 and 13) clearly show the emergence of a zero-bias anomaly (ZBA) in differential conductance dI/dV measurements as B increases. It has been predicted that such a ZBA reflects tunneling into the MBS.14-16 Crucially, the emerging ZBA, which signals the TS transition, should be accompanied by a closing and reopening of the excitation gap.17,18 something which is, however, not observed. Other experimental findings, such as ZBA splitting and coexistence of Andreev bound states (ABSs) and MBSs, 11 also need further analysis.Motivated by this, we present here a detailed study of transport through normal-superconductor (NS) junctions containing topological wires. As in the experiment, the wires are tunnel-coupled to the normal reservoir by a pinch-off gate V p (to allow for transport spectroscopy using dI/dV ), and are depleted by an additional gate V d in order to bring B c down to accessible fields (since the induced potential U d lowers the Fermi energy μ → μ − U d ). The depletion profile, however, is necessarily inhomogeneous, since it cannot extend deep into the superconducting side due to efficient screening, see Fig. 1 and Ref. 11. We find that for this class of devices, a number of distinct transport regimes arise as the va...

Zero-energy pinning from interactions in Majorana nanowires

“…Within a non-interacting picture, 14,15 the only solution to this conflict is to assume values of the spin-orbit coupling much larger than the ones estimated for InAs or InSb NWs. 16 Apart from the exponential suppression, ε M is expected to cross zero energy (parity crossings where Q M changes) in an oscillatory fashion [17][18][19] as a function of magnetic field, chemical potential, or length. Both the exponential suppression and the oscillatory behavior of ε M have recently been demonstrated experimentally.…”

Majorana fermion induced nonlocal current correlations in spin-orbit coupled superconducting wires

“…16,17 However, the origin of these ZBCPs remains a subject of debate. [18][19][20][21][22][23][24][25] In this work, instead of studying MF induced local Andreev reflections, [18][19][20][21][22][23][24][25] we explore the nonlocal properties of MFs. We show that shot noise, which can be used to probe the fractional charges, [26][27][28][29] and their anyonic statistics 30,31 in fractional quantum Hall states, can also be used to probe MFs in superconducting wires due to MF enhanced crossed Andreev reflections (CARs).…”

To Close or Not to Close: The Fate of the Superconducting Gap Across the Topological Quantum Phase Transition in Majorana-Carrying Semiconductor Nanowires

“…We emphasize that this behavior is dictated by the localization properties of the low-energy wave functions in various regions of the phase diagram. These properties are not expected to change qualitatively in the presence of a smooth confining potential [23], finite temperature [24], or weak disorder [25] (see the Supplemental Material for details ?? ).…”