Tuning topological superconductivity in helical Shiba chains by supercurrent

Abstract

Recent experimental investigations of arrays of magnetic atoms deposited on top of a superconductor have opened a new chapter in the search for topological superconductivity. We generalize the microscopic model derived by Pientka et al. [Phys. Rev. B 88, 155420 (2013)] to accommodate the effects of finite supercurrent in the host material. Previously it was discovered that helical chains with nonplanar textures are plagued by a gapless phase. We show that by employing supercurrent it is possible to tune the chain from the gapless phase to the topological gapped phase. It is also possible to tune the chain between the trivial and the topological gapped phase, the size of which may be dramatically increased due to supercurrent. For planar textures supercurrent mainly contributes to proliferation of the gapless phase. Our predictions, which could be probed in scanning tunneling microscope experiments, are encouraging for the observation and manipulation of Majorana states. Introduction. Finding novel realizations for topological superconductivity and accompanying Majorana states has become a major source of inspiration in quantum condensed matter physics [1][2][3]. The possibility of engineering Majorana bound states (MBS), particlelike entities that could serve as building blocks of topological quantum computation [4][5][6][7], has been the primary driving force in the recent developments. Magnetic Shiba chains [8][9][10][11][12][13][14], consisting of arrays of magnetic atoms deposited on top of a superconducting host material, were recognized as promising candidates for topological superconductivity. In addition, the recent ground-breaking experiment in ferromagnetic chains presented persuasive signatures of topological superconductivity [15]. Magnetic realizations of topological superconductivity have attracted attention, since they commonly circumvent the need for materials with strong spin-orbit coupling or exotic superconducting pairing [16][17][18][19][20][21][22]. Shiba chains are particular representatives of magnetic topological systems with special advantages. Nearby magnetic atoms form effectively one-dimensional (1D) band that may undergo a topological phase transition to a 1D topological superconductor with Majorana end states, similar to nanowire realization [23][24][25][26]. Shiba chains are exceptionally disorder free and allow accessing the local density of state (LDOS) in scanning tunneling microscope (STM) experiments, enabling spatial mapping of the Majorana wave functions.Previous work on Shiba chains mostly employed a shortrange hopping model which obeys the correct symmetries and captures some qualitative features of the topological properties [8][9][10][11]. A substantial step was taken by Pientka et al., who provided a microscopic derivation of a long-range hopping model [12,13] for helical magnetic order [27], arising possibly from the Ruderman-Kittel-Kasuya-Yosida (RKKY) and the spin-orbit interaction. The iron-based Shiba chains in the recent experiment were found to be ferromagnetic. ...

Self-stabilizing temperature-driven crossover between topological and nontopological ordered phases in one-dimensional conductors

“…The induced superconductivity then becomes of the topological p-wave type, and Majorana bound states appear at the two ends of the 1D wire. A system with such a spiral magnetic order is indeed equivalent [12][13][14][15][16][17][18]21,[28][29][30][33][34][35][36][37] to the original proposals for topological superconductivity in nanowires [7,8]. Remarkably, by this mechanism, the topological superconducting phase emerges naturally as the ground state without any fine tuning.…”

“…As a remarkable feature, topological superconductivity can be created artificially by contacting specific materials with a conventional s-wave superconductor. For instance, it arises at the interface between the surface states of a three-dimensional topological insulator and an s-wave superconductor [6], in one-dimensional (1D) semiconducting wires with a strong spin-orbit interaction (SOI) and a Zeeman magnetic field with proximitized superconductivity [7][8][9][10][11], or in arrays of magnetic nanoparticles or magnetic adatoms on top of a superconducting surface [12][13][14][15][16][17][18][19][20][21][22], such as iron adatoms on lead [23][24][25].The systems we consider in this Rapid Communication exhibit a topological phase emerging from self-organization of magnetic moments embedded in 1D conductors with proximity induced superconductivity. This situation may apply to semiconducting wires with extrinsic magnetic impurities or intrinsic moments such as nuclear spins, or a conducting wire made of magnetic adatoms on a superconducting surface.…”

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

“…Both routes to topological superconductivity result in a p-wave pairing term in the low-energy theory, providing the link to Kitaev's toy model * Corresponding author: teemuo@boojum.hut.fi [24], the prototype of one-dimensional (1D) topological superconductivity. However, microscopic theories aiming at a quantitative understanding need to implement the long-range coupling of Shiba states arising from a slow decay of wave functions e −r/ξ r ( e −r/ξ r 1/2 in two dimensions) at distances smaller than the superconducting coherence length ξ [21][22][23]25,26]. The long-range nature of the effective tight-binding models leads to significant differences from Kitaev's model and in physically relevant systems the long coherence length limit ξ → ∞ provides an excellent starting point for studies [21,22].…”

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.…”