When the substrate is superconducting, the impurity problem experiences a twist. The superconductor’s ground state is already a many-body state of paired particles (cooper pairs). It is impossible to inject a single particle in this ground state. The STM shows signal if the bias is larger than the pairing energy of the ground state particle. In this case, the electron energy is enough to break the Cooper pair and single-particle states are available in the conduction process. An impurity can trap states that will give a signal inside the superconducting gap. Indeed, the local magnetic moment acts as a magnetic field that splits the Cooper pair, creating single particles in the gap. We have recently shown the orbital structure of these in-gap states [1].
Entangled impurities are an extra level of complexity. On a superconductor they lead to the appearance of Majorana fermions. A Majorana fermion is its own antiparticle. Two Majorana fermions annihilate. The strategy is to create a chain of magnetic atoms that host two Majorana fermions at their edges to avoid their annihilation. These particle are compound due to the mixing of Cooper pairs in the presence of spin-orbit and magnetic interactions. Contrary to the other quasiparticles of superconductors, the Majorana fermions do not follow the Fermi-Dirac statistics, they are actually anyons, following fractionary statistics. Majorana fermions in this case is a misnomer and the more precise Majorana bound state should be used. Our present studies of magnetic atoms on a superconductor are very promising. Using the atomic manipulation capabilities of the STM, we can assemble chains of magnetic atoms on the superconductor and study the in-gap states [2]. Our calculations predict that twenty chromium atoms are in the topological phase leading to Majorana bound states.
Calculations for the dI/dV signal over a Cr20 spin chain, as a function of bias (upper left) and tip position over the chain (distance), and a profile along the chain at bias (Energy) zero, from Ref. [3]. Due to the finiteness of the topological gap, the signal does not go to zero between Majoranas. The behavior with the trasnversal and logitudinal spin projection matches what is expected from a topological 1-D superconductor, and the topological invariants predict that the chain is in a topological phase [4].
References:
[1] Mapping the orbital structure of impurity bound states in a superconductores. Deung-Jang Choi, Carmen Rubio-Verdú, Joeri de Bruijckere, Miguel M. Ugeda, Nicolás Lorente and José Ignacio Pascual. Nature Communications 8, 1575 (2017)
[2] Influence of magnetic ordering between Cr adatoms on the Yu-Shiba-Rusinov states of the β-Bi2Pd superconductor. Deung-Jang Choi, Carlos García Fernández, Edwin Herrera, Carmen Rubio-Verdú, Miguel M. Ugeda, Isabel Guillamón, Hermann Suderow, José Ignacio Pascual, and Nicolás Lorente. Phys. Rev. Lett. 120, 167001 (2018)
[3] Atomic manipulation of in-gap states in the β−Bi2Pd superconductor, Cristina Mier, Jiyoon Hwang, Jinkyung Kim, Yujeong Bae, Fuyuki Nabeshima, Yoshinori Imai, Atsutaka Maeda, Nicolás Lorente, Andreas Heinrich, and Deung-Jang Choi*, Phys. Rev. B 104, 045406 (2021)
[4] Calculations of in-gap states of ferromagnetic spin chains on s-wave wide-band superconductors, Cristina Mier, Deung-Jang Choi, Nicolás Lorente, Phys. Rev. B 104, 245415 (2021)
