Extended Data Fig. 2: Non-symmetric device spectra.
From: Evidence of topological superconductivity in planar Josephson junctions
Calculated topological phase diagrams and energy spectra for a left–right asymmetric junction (here the asymmetry is introduced by having ∆L \(\ne \)∆R). As explained in the Methods, the left–right symmetry may be broken by disorder27,28, different geometric sizes of the superconducting leads, or different coupling of the 2DEG to the superconductors on the two sides of the junctions. a, Topological phase diagram as a function of \({E}_{{\rm{Z}}}\) and µ for \(\phi \) = 0, π, calculated from the tight-binding Hamiltonian for JJ1 with infinite length (see Methods). b, Topological phase diagram as a function of \({E}_{{\rm{Z}}}\) and \(\phi \) for different values of µ, as indicated by the horizontal ticks in a. The diagrams were calculated for a junction with W1 = 80 nm, WS1 = 160 nm, left-induced gap ∆L = 150 µeV, right-induced gap ∆R = 100 µeV and α = 100 meV Å. c–g, Calculated energy spectra as a function of \(\phi \) for different values of the Zeeman energy. The spectra were obtained for the same parameters used in a and b, except for L1 = 1.6 µm. Note that the gap for the fine-tuned chemical potential µ = 79.25 meV, which closes at \(\phi \) = π and \({E}_{{\rm{Z}}}\) = 0 for a left–right symmetric junction (see Extended Data Fig. 1a, c), now becomes non-zero, and is approximately \(| {{\Delta }}_{{\rm{L}}}-{{\Delta }}_{{\rm{R}}}\)|. As a result, the topological transition for \(\phi \) = π occurs at finite Zeeman field. For the chosen parameters, the system undergoes a topological transition at \({E}_{{\rm{Z}}}\) = 0.02 meV for \(\phi \) = π and at \({E}_{{\rm{Z}}}\) = 0.1 meV for \(\phi \) = 0. The lowest subgap states are shown in red and indicate two Majorana zero modes at the edges of the junction in the topological regime. The behaviour of the calculated Majorana modes is qualitatively consistent with that of the observed zero-bias peaks in tunnelling conductance. h, i, Probability density \({\left|\Psi \right|}^{2}\) of the Majorana wavefunction calculated as a function of the spatial directions x and y in JJ1 for \({E}_{{\rm{Z}}}\) = 0.13 meV and \(\phi \) = 0, π.
