Electronic states in the gap of a superconductor inherit intriguing many-body properties from the superconductor. Here, we create these in-gap states by manipulating Cr atomic chains on the β-Bi 2 Pd superconductor. We find that the topological properties of the in-gap states can greatly vary depending on the crafted spin chain. These systems make an ideal platform for nontrivial topological phases because of the large atom-superconductor interactions and the existence of a large Rashba coupling at the Bi-terminated surface. We study two spin chains, one with atoms two lattice parameters apart and one with √ 2 lattice parameters. Of these, only the second one is in a topologically nontrivial phase, in agreement with the spin interactions for this geometry.

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Combining the complex ordering ability of molecules with their local magnetic properties is a little-explored technique to tailor spin structures on surfaces. However, revealing the molecular geometry can be demanding. Nickelocene (Nc) molecules present a large spin-flip excitation leading to clear changes of conductance at the excitationthreshold bias. Using a superconducting tip, we have the energy resolution to detect small shifts of the Nc spin-flip excitation thresholds, permitting us to reveal the different individual environment of Nc molecules in an ordered layer. This knowledge allows us to reveal the adsorption configuration of a complex molecular structure formed by Nc molecules in different orientations and positions. As a consequence, we infer that Nc layers present a strong non-collinear magnetic moment arrangement.

Magnetic impurities create in-gap states on superconductors. Recent experiments explore the topological properties of one-dimensional arrays of magnetic impurities on superconductors, because in certain regimes p-wave pairing can be locally induced leading to new topological phases. A byproduct of the new accessible phases is the appearance of zero-energy edge states that have non-Abelian exchange properties and can be used for topological quantum computation. Despite the large amount of theory devoted to these systems, most treatments use approximations that render their applicability limited when comparing with usual experiments of 1D impurity arrays on wide-band superconductors. These approximations either involve tight-binding-like approximations where the impurity energy scales match the minute energy scale of the superconducting gap and are many times unrealistic, or they assume strongly-bound in-gap states. Here, we use a theory for s-wave superconductors based on a wide-band normal metal, with any possible energy scale for the magnetic impurities and develop an efficient way of computing the well-known topological invariants of infinite chains. We perform concrete calculations on ferromagnetic spin chains using BCS Green's function for the superconductor and including Rashba coupling to compare with recent experimental results. The infinite-chain properties can be analytically obtained, giving us a way to compare with finite-chain calculations. We show that it is possible to converge to the infinite limit by doing finite-size numerical calculation, paving the way for numerical calculations not based on analytical Green's functions. As an application, we show that energy oscillations around zero with increasing number of atoms in the spin chain does not reflect the topological origin of the low-energy state.

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SumariaI . Semblanza biogrdfica 3. lntroducción a 10s fragmcntas y carlas 2. Escritor 4. Teano. Carrar, fragrncntos y scntencias La tradidón mtigua2 nos da noticia de la existencia histórica de Teano, a la que se considera como la primera mujer fildsofa, si bien su celebridad parece atribuirse a su vinculo matrimonial y discipular con Pitagoras. En relación a su genealogia, sin embargo, 10s testimonios de 10s doxógrafos anriguos son contradictori~~. Dió enes Laercio3 nos dice que la mujer de Pitágora era Teano,. P . , hija de Brontino , de llnaje crotoniata, pero tarnbien nos indica que para utros doxógrafos era mujer de Brontino y discípula de Pitágoras5. De su unión con Pitágoras tuvo como hijo a Telauges, que sucedió a su padre en la dirección I . El siguienre articulo es parte del trabajo que viene realizando, desde el curso acadirnico 1991-1992, el seminario Fjlorofia i G¿nerc, de la Universitat de Barcelona, con el propósi-to de recuperar la producción hlosófica de las mujcres. Las partcs primera y regunda, que nos describen la vida y obra de nuestra aurora, han sido realizadas por Fék Pardo, licenciado en Filosofia; la tercera, que prttcnde dar algumr notar sobre la mujer y el pitagorisma, par Cristina Mier, licenciada en Pilosofía, y la cuarta, que conrirne las rraducciones, por Mcrci Gutiérrer, licenciada en Filologia Griega y