Signatures of Majorana bound states in scanning gate microscopy of hybrid nanowires

TL;DR

The paper shows that scanning gate microscopy can locally perturb a proximitized nanowire to create tunable Majorana segments, producing energy splittings that oscillate with magnetic field and depend on tip position. By analyzing both local and nonlocal conductance as the tip scans, the authors demonstrate how true Majorana bound states can be distinguished from quasi‑Majorana and disorder‑induced states, and how weaker tip potentials enable MBS mixing and anticrossings. The approach remains effective in disordered wires, where SGM can identify topological versus trivial zero‑bias peaks and reveal underlying Majorana physics even when global parameters alone are inconclusive. Overall, SGMs offer a spatially resolved, robust probe for Majorana physics in hybrid nanowires and related proximitized systems, with potential extensions to partially covered 2D platforms and Josephson‑junction geometries.

Abstract

We theoretically study scanning gate microscopy of a superconductor-proximitized semiconducting wire focusing on the potential for detection of Majorana bound states. We exploit the possibility to create a local potential perturbation by the scanning gate tip which allows controllable modification of the spatial distribution of the Majorana modes, which is translated into changes in their energy structure. When the tip scans across the system, it effectively divides the wire into two parts with controllable lengths, in which two pairs of Majorana states are created when the system is in the topological regime. For strong values of the tip potential, the pairs are decoupled, and the presence of Majorana states can be detected via local tunneling spectroscopy that resolves the energy splittings resulting from the Majorana states wave functions overlap. Importantly, as the system is probed spatially via the tip, this technique can distinguish Majorana bound states from quasi-Majorana states localized on smooth potential barriers. We demonstrate that for weaker tip potentials, the two neighboring Majorana states hybridize, opening pronounced anticrossings in the energy spectra which are reflected in local conductance maps and which result in non-zero non-local conductance features. Finally, we demonstrate that the scanning gate microscopy technique can be used to discriminate between the trivial and topological nature of the zero-bias conductance peak in disordered wires.

Figures (11)

• Figure 1: Scheme of the considered system. A proximitized stripe (green) that hosts MBSs (yellow) connected to two normal leads (gray) through tunneling barriers (dark green) is scanned by the atomic force microscopy tip (dark blue) which decouples the system into two parts with varied lengths.
• Figure 2: (a) Energy spectrum versus the magnetic field of a proximitized wire and the respective local conductance map (b) obtained without the SGM tip.
• Figure 3: (a) and (c) the energy spectra of a proximitized wire versus the magnetic field in the presence of the SGM tip. (b) and (d) the local conductance maps in the tunneling regime. The top row is obtained for the SGM tip located at $x_{\mathrm{tip}} = 1000$ nm while the bottom on for $x_{\mathrm{tip}} = 500$ nm.
• Figure 4: Conductance spectroscopy maps versus the position of the tip along the wire for (a) $B$ = 1 T and (b) $B$ = 2 T.
• Figure 5: (a) and (b) the energy spectra versus the position of the tip along the wire. The colors denote the weight of the probability density located on the left side of the tip. (c) and (d) with violet show the cross-section of the probability density for $y = 50$ nm for the states whose corresponding energy levels are denoted with symbols in panels (a) and (b). The green curves in (c) and (d) depict the potential profile in the wire due to SGM tip. Panels (a) and (c) correspond to $B = 1$ T while (b) and (d) to $B = 2$ T.