Inspired by the recent experimental observation of topological superconductivity in ferromagnetic chains, we consider a dilute 2D lattice of magnetic atoms deposited on top of a superconducting surface with a Rashba spin-orbit coupling. We show that the studied system supports a generalization of px + ipy superconductivity and that its topological phase diagram contains Chern numbers higher than ξ/a ( 1), where ξ is the superconducting coherence length and a is the distance between the magnetic atoms. The signatures of nontrivial topology can be observed by STM spectroscopy in finite-size islands.

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.

In this work we will explore the properties of superconducting surfaces decorated by twodimensional ferromagnetic adatom lattices. As discovered recently [Röntynen and Ojanen, Phys. Rev. Lett. 114, 236803 (2015)], in the presence of a Rashba spin-orbit coupling these systems may support topological superconductivity with complex phase diagrams and high Chern numbers. We show how the long-range hopping nature of the effective low-energy theory generically gives rise to a phase diagram covered by a Chern mosaic -a rich pattern of topological phases with large Chern numbers. We study different lattice geometries and the dependence of energy gaps and abundance of different phases as a function of system parameters. Our findings establish the studied system as one of the richests platforms for topological matter known to date.

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. ...

In this work we consider the influence of potential impurities deposited on top of two-dimensional chiral superconductors. As discovered recently, magnetic impurity lattices on an s-wave superconductor may give rise to a rich topological phase diagram. We show that a similar mechanism takes place in chiral superconductors decorated by nonmagnetic impurities, thus avoiding the delicate issue of magnetic ordering of adatoms. We illustrate the method by presenting the theory of potential impurity lattices embedded on chiral p-wave superconductors. While a prerequisite for the topological state engineering is a chiral superconductor, the proposed procedure results in vistas of nontrivial descendant phases with different Chern numbers. DOI: 10.1103/PhysRevB.94.060505 Introduction. Engineering novel quantum phases of matter with exotic properties is a rapidly growing trend in contemporary physics. The main goal is to employ simpler and wellunderstood ingredients and methods to create more complex structures with desirable properties. Recent promising efforts to realize [1][2][3] topological superconductivity in nanowire systems [4,5] demonstrate the power of the approach. While it seems unlikely that Nature directly provides us with Majorana quasiparticles that could be employed in quantum information applications [6], it is increasingly probable that those can be achieved in the laboratory. In the spirit of engineering novel controllable states of matter, we show how to realize a complex hierarchy of topological phases with potential impurity superstructures adsorbed on chiral superconductors. Magnetic atoms on s-wave superconductors give rise to Yu-Shiba-Rusinov subgap states [7][8][9][10] which have been probed experimentally by scanning tunneling microscopy (STM) [11][12][13][14]. Superstructures fabricated from magnetic atoms are currently under active experimental [15][16][17] and theoretical research [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. Intriguing properties of these systems include the possibility for various one-dimensional (1D) topological superconducting phases with Majorana bound states and rich two-dimensional (2D) topological phases [34][35][36][37]. A topologically nontrivial phase is known to arise in 1D ferromagnetic arrays when the underlying superconductor has a strong Rasha spin-orbit coupling or in arrays with helical magnetic textures. In 1D structures there are theoretical arguments why magnetic self-tuning could result in a nontrivial ground state [20][21][22]28,32,38], though in real systems there are a number of complications. In particular, in 2D structures the nature and tunability of magnetic textures is a delicate and largely unsolved question.Very recently it was proposed that potential impurities could be utilized to realize interesting topological states in 1D structures [39] and 2D toy models [40]. The procedure requires a non-s-wave superconductor host material with chiral or helical pairing components but circumvents the need for specific magnetic tex...