Tilting of the magnetic field in Majorana nanowires: Critical angle and zero-energy differential conductance

Abstract

Semiconductor nanowires with strong spin-orbit coupling and proximity-induced s-wave superconductivity in an external magnetic field have been the most promising settings for approaches towards experimental evidence of topological Majorana zero-modes. We investigate the effect of tilting the magnetic field relative to the spin-orbit coupling direction in a simple continuum model and provide an analytical derivation of the critical angle, at which the topological states disappear. We also obtain the differential conductance characteristic of a junction with a normal wire for different tilting angles and propose a qualitative change of the dependence of the zero-energy differential conductance on the tunnel barrier strength at the critical angle as a new criterion for establishing the topological nature of the observed signal.

Orbital effect of magnetic field on the Majorana phase diagram

“…This means that whenever E n changes sign at a certain momentum, the band structure becomes gapless. This tilting of the band structure [26] [shown in the middle panels in Fig. 2, where E n (k) = −E m (k)] is a strong effect that does not vanish with superconducting gap or spin orbit, and can easily become larger than the induced gap, rendering the creation of Majoranas impossible.…”

Anomalous Josephson effect in semiconducting nanowires as a signature of the topologically nontrivial phase

“…The first inequality is the generalization of the well known topological condition |h x | > h c at h z = 0, 12,13 while the second condition ensures that the spectrum remains gapped. 34,35 Except Secs. III A and III B, where we provide analytic expressions for the anomalous current in short junctions at |h z | ≪ ∆, we use a tight-binding approximation to the Hamiltonian (1).…”

Majorana states and magnetic orbital motion in planar hybrid nanowires

“…Besides, in 1D wires the effect of tilting the magnetic field implies the additional requirement of the so-called projection rule ∆ B sin θ sin φ < ∆ s . 33,36 This is due to the indirect gap closing of the infinite wire energy bands at ±k c due to the tilted field, where k c is a non vanishing wave number. As discussed in Sec.…”