Interplay of topological phases in magnetic adatom-chains on top of a Rashba superconducting surface

Abstract

We investigate the topological properties and the accessible Majorana fermion (MF) phases arising in a hybrid device consisting of a chain of magnetic adatoms placed on the surface of a conventional superconductor with Rashba spin-orbit coupling (SOC). By identifying the favored classical magnetic ground state of the adatom chain, we extract the corresponding phase diagram which exhibits an interplay of ferromagnetic (FM), antiferromagnetic (AFM) and spiral orders. We determine the parameter regime for which the FM or AFM phases dominate over the spiral and additionally become stable against thermal and quantum fluctuations. For the topological analysis we focus on the FM and AFM cases and employ a low-energy effective model relying on Shiba bound states. We find that for both magnetic patterns the hybrid system behaves as a topological superconductor which can harbor one or even two MFs per edge, due to chiral symmetry. As we show, the two magnetic orderings lead to qualitatively and quantitatively distinct topological features that are reflected in the spatial profile of the MF wavefunctions. Finally, we propose directions on how to experimentally access the diverse MF phases by varying the adatom spacing, the SOC strength, or the magnetic moment of the adatoms in consideration.Materials with Rashba spin-orbit coupling (SOC) have recently attracted renewed attention due to their pivotal role for realizing artificial topological superconductors (TSCs) which harbor Majorana fermions (MFs) [1][2][3][4][5]. Early proposals involved materials with SOC, such as topological insulators [6], noncentrosymmetric SCs [7], and Rashba semiconductors [8][9][10][11], which stimulated significant experimental progress. Remarkably, a number of promising but yet not fully conclusive MF-signatures have been already reported in semiconductor-based heterostructures [12][13][14][15]. The unsettled witnessing of MFs [16][17][18] constitutes a strong motivation for engineering and testing alternative hybrid devices. For instance, platforms based on magnetic adatoms which can be manipulated and probed via spin-polarized and spatially-resolved scanning tunneling microscopy (STM) techniques, appear capable of unambiguously revealing the presence of MFs.This new perspective opened the door for new MF devices based on magnetic adatoms on the surface of conventional superconductors. One finds implementations with magnetic adatoms where the ordering is random [19], spiral [20-29], antiferromagnetic (AFM) with SOC induced by the combination of Zeeman fields and supercurrents [30], and ferromagnetic (FM) on top of a superconducting surface with Rashba SOC [31,32]. According to very recent experimental findings [33], MFs seem to indeed emerge in magnetic adatom hybrid devices, where the ordering of the chain appears to be FM. This type of ordering can lead to MFs only if Rashba SOC is present, arising from the broken inversion associated with the Pb superconducting substrate. In fact, this is a plausible scenario for Pb which owes already a non-...

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

“…Near the center of the gap the LDOS is suppressed in the bulk but enhanced on the edges due to the topological edge states. The figure corresponds to the case ξ/a = 10, ε0/∆ = −0.22, kF a/π = 4.9, λ = 0.05 the interplay of RKKY coupling, Rashba coupling and crystal field splitting [18]. The key ingredients leading to the rich topological properties discovered in our work are the coexistence of superconductivity, the ferromagnetic ordering of adatoms and the Rashba coupling on the surface, all of which are confirmed in Ref.…”

“…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.…”

Shiba chains of scalar impurities on unconventional superconductors

“…If these adatoms order magnetically the chain can become a 1D topological superconductor, even if the underlying superconductor is of s-wave spin-singlet type. [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] The key point in this construction is that magnetic impurities in s-wave superconductors feature socalled Shiba midgap bound states, 18,21,[27][28][29][30] which can hybridize along the chain and experience band inversion. The appearance of Shiba states can be intuitively understood from "Anderson's theorem", 31 stating that s-wave superconductivity is (locally) suppressed by magnetic impurities.…”

Topological properties of helical Shiba chains with general impurity strength and hybridization

“…In higher dimensions the situation is not so clear, although numerical evidence supports qualitatively similar behavior [29]. However, surface effects and the crystal-field splitting of the host material may give rise to ferromagnetic and antiferromagnetic ordering [30]. Disorder effects may modify this picture [31] but it is not clear at this point which sources of disorder are relevant for Shiba systems.…”