Formation of Majorana fermions in finite-size graphene strips

Abstract

We investigate the formation of Majorana fermions in finite-size graphene strips with open boundary conditions in both directions, in the presence of an in-plane magnetic field and in the proximity of a superconducting substrate. We show that for long enough strips the Majorana states can form in the presence of a Rashba-like spin-orbit coupling, as well as in the presence of an inhomogeneous magnetic field. We find that, unlike infinite graphene ribbons in which Majorana states arise solely close to the bottom of the band and the Van Hove singularities, for finite-size systems this can happen also at much smaller doping values, close to the Dirac points, and depends strongly on the type of the short edges of the systems (e.g. armchair vs. zigzag), as well as on the width of the ribbons.

Bulk boundary correspondence and the existence of Majorana bound states on the edges of 2D topological superconductors

“…iσ denotes the annihilation (creation) operator of an electron of spin σ at site i, and δ ij are the nearest neighbor vectors. This model has been carefully studied both in the presence of a superconducting proximity effect [36][37][38][39][40] , as well as without it 31,32 . We will define the lattice spacing a = 1 and = 1 throughout.…”

“…Two-dimensional topological superconductors, including for example p-wave or s-wave pairing, have also received a lot of attention, 3,[17][18][19][20][21][22][23][24][25][26][27][28][29][30] and including the model we consider here of a system with spin-orbit coupling, in the presence of superconducting proximity and a Zeeman field, as well as other related models. [31][32][33][34][35][36][37][38][39][40] . In two dimensions (2D) the bulk-boundary correspondence relates the Chern number, ν, to the number of protected bands connecting the bulk states above and below the gap [41][42][43][44][45] arising in a ribbon structure.…”

Suppression of the overlap between Majorana fermions by orbital magnetic effects in semiconducting-superconducting nanowires

“…Majorana fermions (MFs) in condensed matter systems have been at the center of attention over many years. They have been predicted to emerge in such systems as semiconducting nanowires [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], p-wave superconductors [18][19][20][21], graphene-like systems [22][23][24][25][26][27][28][29][30], and chains of magnetic atoms [31][32][33][34][35][36], with some of these proposals implemented experimentally [37][38][39][40][41][42][43][44][45][46]. In this work, we focus on Rashba nanowire setups [2,3], which have been widely implemented experimentally [37][38][39]…”

Topology from triviality

“…in Refs. [31], [32]. In this paper we model it as a random variation of the values of the chemical potentials µ N W and µ SC with an intensity of 2% around their average values, both in the substrate and in the nanowire.…”

“…We test the topological character of the NW and the formation of Majorana fermions in the NW using the Majorana polarization (MP). [28][29][30][31][32] The topological character of the bulk SC is also calculated numerically and the corresponding bulk phase transition is indicated by a vertical line at ∆ s ∼ 0.86t. First we note that the resulting phase diagram agrees qualitatively with the one obtained using the continuum model in the previous section (see Fig.…”