Tomography of Zero-Energy End Modes in Topological Superconducting Wires

Phase diagram of a model for topological superconducting wires

“…This is due to the symmetry properties of the Hamiltonian. 20 In the more general case, when λ and B are not perpendicular, it is not possible to follow the approach outlined above. In this case, we use the Zak Berry phase to construct the topological invariant.…”

“…More recently, there has been experimental research as well as theoretical studies in similar models, including those for time-reversal invariant topological superconductors, 12,13 of the effects of MZMs in Josephson junctions, in particular because the dependence on the applied magnetic flux introduces an additional control knob. [13][14][15][16][17][18][19][20] In particular, it has been recently proposed that the current-phase relation measured in Josephson junctions may be used to find the parameters that define the MZMs. 20 A possible difficulty in these experiments is the slow thermalization to the ground state in the presence of a gap.…”

“…[13][14][15][16][17][18][19][20] In particular, it has been recently proposed that the current-phase relation measured in Josephson junctions may be used to find the parameters that define the MZMs. 20 A possible difficulty in these experiments is the slow thermalization to the ground state in the presence of a gap. 21 A way to circumvent this problem is to rotate the magnetic field slowly from a direction not perpendicular to the SOC in which the system is in a gapless superconducting phase, in which thermalization is easier.…”

“…21 A way to circumvent this problem is to rotate the magnetic field slowly from a direction not perpendicular to the SOC in which the system is in a gapless superconducting phase, in which thermalization is easier. 20 Therefore, it is convenient to know the phase diagram of the system and the extension of this gapless phase. How-ever, in spite of the fact that the model of Refs.…”

Braiding higher-order Majorana corner states through their spin degree of freedom

“…Meanwhile, the MZM wave function is fully spin-polarized [15][16][17][18][19], resulting in universal spin-triplet superconducting correlation [20][21][22][23][24]. Accordingly, these spin properties can cause spin-dependent transport phenomena such as spinselective Andreev reflection and topological φ 0 -junction [16,17,[25][26][27][28][29][30], which can serve as the evidence of MZMs beyond the ZBCP. Remarkably, the latter comes from the spin-dependent Josephson coupling, which is not only useful in measuring the fermion-parity of two MZMs fusion but also essential to implement the MZMs braiding [5,27,[31][32][33][34].…”