Majorana states in helical Shiba chains and ladders

Abstract

Motivated by recent proposals to realize Majorana bound states in chains and arrays of magnetic atoms deposited on top of a superconductor, we study the topological properties of various chain structures, ladders and two-dimensional arrangements exhibiting magnetic helices. We show that magnetic domain walls where the chirality of a magnetic helix is inverted support two protected Majorana states giving rise to a tunneling conductance peak twice the height of a single Majorana state. The topological properties of coupled chains exhibit nontrivial behaviour as a function of the number of chains beyond the even-odd dichotomy expected from the simple Z2 nature of coupled Majorana states. In addition, it is possible that a ladder of two or more coupled chains exhibit Majorana edge states even when decoupled chains are trivial. We formulate a general criterion for the number of Majorana edge states in multichain ladders and discuss some experimental consequences of our findings.

Topological Superconductivity and High Chern Numbers in 2D Ferromagnetic Shiba Lattices

“…The detailed properties of the 1D long-range Shiba models [14][15][16][17][18][19][20][21] are known to have important differences compared to the short-range toy models [22][23][24][25]. We show that the competition between a large number of long-range hopping terms gives rise to a complicated Chern number hierarchy.…”

Topological superconductivity and anti-Shiba states in disordered chains of magnetic adatoms

“…The general helical chain is in symmetry class D; however, the planar helical chain (θ = π/2) is in class BDI [20]. For simplicity, we will here focus on the Z 2 topological phase of the planar chain, as the Z 2 boundaries are independent of θ .…”

“…Different aspects of these systems are under intense experimental [3][4][5] and theoretical [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] investigation at the moment. While the application potential of magnetic chains seem more rigid compared to the semiconducting nanowire-based realizations [24][25][26][27][28] of topological superconductivity, they also offer important advantages over them.…”

Josephson current in a normal-metal nanowire coupled to a superconductor/ferromagnet/superconductor junction

“…Then, by the bulk-edge correspondence, a superconducting nanowire hosts a Majorana fermion (MF) as the end state [28][29][30], which is one of the important factors to realize quantum computation [31][32][33][34]. It has also been reported that a chain of ferromagnetic atoms on a superconductor forms a topologically nontrivial state, where the ABS within the superconducting gap is localized around the edge as a MF [35][36][37][38][39][40][41][42][43][44]. The common feature in these one-dimensional topological superconducting systems is that both pair potential and magnetization coexist in all sites of the nanowire.…”