Magnetic manipulation of topological states in p-wave superconductors

Abstract

Substantial experimental investigation has provided evidence for spin-triplet pairing in diverse classes of materials and in a variety of artificial heterostructures. A fundamental challenge in actual experiments is how to manipulate the topological behavior of p-wave superconductors (PSCs) that could open perspectives for applications. Such a control knob is naturally provided by the spintriplet character of the PSC order parameter, described by the spin d-vector. Therefore, in this work we investigate the magnetic field response of one-dimensional (1d) PSCs and demonstrate that the structure of the Cooper pair spin-configuration is crucial to set topological phases with an enhanced number of Majorana fermions per edge, N , ranging from N = 0 to 4. The topological phase diagram, consisting of phases with Majorana modes at the edge, becomes significantly modified when one tunes the strength of the applied field and allows for long range hopping amplitudes in the 1d PSC. We find transitions between phases with different number of Majorana fermions per edge that can be both induced by a variation of the hopping strength and a spin rotation of d. Hence, the interplay of the applied magnetic field and the internal spin degree of freedom of the PSC opens a new promising route for engineering topological phases with large number of Majorana modes.

Nodal Andreev spectra in multi-Majorana three-terminal Josephson junctions

“…with Eqs. (11), (16), and (17) applying. The wave function of the two bound states at the right edge of the TSC at x = 0 can be represented in the same manner as…”

“…The former aspect is the source of anomalous proximity effects [9,10], while the latter is particularly attractive for implementing cutting-edge functionalities, including the coherent control and manipulation of the Cooper pairs. Due to the intrinsic coupling between spin and orbital degrees of freedom, spin-triplet SCs exhibit nonstandard response to Zeeman/ferromagnetic fields [11][12][13][14][15][16][17], spin-sensitive Josephson transport [18][19][20][21][22][23][24][25][26], and pave the way to energy efficient superconducting spintronics [27]. Even more, p-wave SCs constitute the prototypical topological superconductors (TSCs) harboring protected zero-energy modes, the so-called Majorana bound states (MBSs), whose manipulation open perspectives for topological quantum computing [4,[28][29][30].…”

“…In this work, we investigate the emergence and design of topologically nontrivial ABS bands in multi-terminal Josephson contacts consisting of 1D TSCs which accommodate multiple MBSs per edge. Such multi-MBS topological scenarios become accessible in both intrinsic [12,13,[15][16][17]88] or effective [52][53][54][55][56][57][58][59][60][72][73][74][75]98] p-wave spin-triplet SCs, with the chiral symmetry being associated with a Kramers degeneracy or a sublattice symmetry. Considering the 2D synthetic space of the two independent phase differences appearing between the superconducting leads of a three-terminal junction, we demonstrate that the ABS dispersions feature point nodes or nodal lines which depend on the number of MBSs occurring at the junction interface.…”

Magnetoelectrically tunable Andreev bound state spectra and spin polarization in p -wave Josephson junctions

“…We insist that the emerging time-reversal symmetry does not lead to a Kramers degeneracy, because it satisfies Θ 2 = I, with I the identity operator. The particular symmetry class allows for 0, 1, 2 MBSs per edge for this Hamiltonian when open boundary conditions are considered, and under the condition that edge-driven re-organization effects are not taken into account [13,14]. The MBS state vectors are in this case eigenstates of the chiral-symmetry operator Π, i.e.…”

Odd-frequency pairing in a nonunitary p-wave superconductor with multiple Majorana fermions

“…The number of Majorana fermions, corresponding to the winding number, that can exist at each edge of the Kitaev chain is one. Considering higherorder hopping and magnetic fields in a p-wave superconductor with spin degrees of freedom allows us to access topological phases with multiple Majorana fermions [26,27].…”