## Periodic Reporting for period 1 - ARTE (Atomic Research for Topological Engineering)

Reporting period: 2015-05-01 to 2017-04-30

Topological quantum computation (TQC) is a revolutionary technique which allows to have error-free, robust, fast processing and a smaller computing system. TQC is the next generation of the computation. In this project, we would like to implement TQC by means of atomic manipulation in a scanning tunneling microscope (STM). STM is the tool to image and measure the electronic states of objects on a surface using quantum tunneling through a vacuum barrier between the probe(tip) and the sample. This project aims at building the foundations to make TQC possible.

Majorana fermions are composite particles, like many other quasiparticles found in condensed matter. Using these Majorana fermion particles, it is theoretically predicted TQC in reality. When a Majorana fermion binds to a defect, Majorana bound states emerge, and the transformations between those states are the keys that will permit us to perform TQC.

The discovery of new exotic states of matter by 1-D chains of magnetic atoms on superconductors brings a lot of interest to the TQC field. That is because we can use to manipulate and make different trajectory of Majorana Fermions that live in those new exotic states such as the Majorana bound states in the system. The objectives are then to study and evaluate different types of spin-chains on several superconducting substrates to explore and eventually fabricate the Majorana bound states that are at the base of TQC.

Majorana fermions are composite particles, like many other quasiparticles found in condensed matter. Using these Majorana fermion particles, it is theoretically predicted TQC in reality. When a Majorana fermion binds to a defect, Majorana bound states emerge, and the transformations between those states are the keys that will permit us to perform TQC.

The discovery of new exotic states of matter by 1-D chains of magnetic atoms on superconductors brings a lot of interest to the TQC field. That is because we can use to manipulate and make different trajectory of Majorana Fermions that live in those new exotic states such as the Majorana bound states in the system. The objectives are then to study and evaluate different types of spin-chains on several superconducting substrates to explore and eventually fabricate the Majorana bound states that are at the base of TQC.

To achieve this objective, a progressive plan is devised, starting from studying simple superconducting substrates to adsorbed magnetic atoms on superconducting surfaces using STM.

First of all, before manipulating the atoms on superconductor, we studied magnetic Mn chains built on one thin insulating layer (Cu2N) ontop of metal surface Cu(100). Atomic magnetic chains are very interesting objects that reveal the complexities of quantum magnetic interactions. Thanks to the advances in low-temperature STM, these objects have been created and studied with unprecedented precision. In this work, we disclose our discovery of electronic edge states in Mn magnetic chains and that their behaviour has bearing on the actual magnetic ordering of the atomic chains. We characterise the edge states to find that they are associated with an orbital on each of the two edge Mn atoms and that their character depends on the number of Mn atoms in the chain. We show that this odd/even behaviour is a consequence of the magnetic ordering of the chain.

As a next step, using well-know type I-superconducting substrate lead (Pb), we investigated single magnetic atoms such as Fe and Cr. We observed exotic properties like Shiba states which are coming from the magnetic moment in a quasi-particles (Cooper pairs). This magnetic impurity on a superconductor forms a magnetic scattering potential due to the breaking of Cooper pair. The Shiba state has been seen on Cr atoms inside the superconducting gap. And by doing dI/dV mapping at the certain energies, we manage to see the orbital contribution which originates the Shiba states.

Furthermore, we used type II-superconductor Bi2Pd as a substrate and studied single magnetic impurities eventually to build the atomic chains. First we tried with Fe atoms and basically Fe atoms quench the superconductivity of Bi2Pd. So we deposit other kinds of atoms such as Mn, Cr and Co atoms. We are creating atomic chains by manipulating atoms with intrinsic magnetic moments on Bi2Pd surfaces. We are able to map out what kind of orbitals contribute to form Shiba states by measuring the dI/dV maps at the certain energies. The Shiba states are quasi-particle localized states at a magnetic impurity due to the exchange interaction between the magnetic moment of the atomic chain and the electronic spin from the substrate. The atomic magnetic moment acts as a classical magnet that simply scatters the electrons. The existence of a gap at the Fermi energy due to the superconductor pairing leads to the localization of the scattered electrons and a single quasi-particle peak appears in the gap in the dI/dV spectra.

First of all, before manipulating the atoms on superconductor, we studied magnetic Mn chains built on one thin insulating layer (Cu2N) ontop of metal surface Cu(100). Atomic magnetic chains are very interesting objects that reveal the complexities of quantum magnetic interactions. Thanks to the advances in low-temperature STM, these objects have been created and studied with unprecedented precision. In this work, we disclose our discovery of electronic edge states in Mn magnetic chains and that their behaviour has bearing on the actual magnetic ordering of the atomic chains. We characterise the edge states to find that they are associated with an orbital on each of the two edge Mn atoms and that their character depends on the number of Mn atoms in the chain. We show that this odd/even behaviour is a consequence of the magnetic ordering of the chain.

As a next step, using well-know type I-superconducting substrate lead (Pb), we investigated single magnetic atoms such as Fe and Cr. We observed exotic properties like Shiba states which are coming from the magnetic moment in a quasi-particles (Cooper pairs). This magnetic impurity on a superconductor forms a magnetic scattering potential due to the breaking of Cooper pair. The Shiba state has been seen on Cr atoms inside the superconducting gap. And by doing dI/dV mapping at the certain energies, we manage to see the orbital contribution which originates the Shiba states.

Furthermore, we used type II-superconductor Bi2Pd as a substrate and studied single magnetic impurities eventually to build the atomic chains. First we tried with Fe atoms and basically Fe atoms quench the superconductivity of Bi2Pd. So we deposit other kinds of atoms such as Mn, Cr and Co atoms. We are creating atomic chains by manipulating atoms with intrinsic magnetic moments on Bi2Pd surfaces. We are able to map out what kind of orbitals contribute to form Shiba states by measuring the dI/dV maps at the certain energies. The Shiba states are quasi-particle localized states at a magnetic impurity due to the exchange interaction between the magnetic moment of the atomic chain and the electronic spin from the substrate. The atomic magnetic moment acts as a classical magnet that simply scatters the electrons. The existence of a gap at the Fermi energy due to the superconductor pairing leads to the localization of the scattered electrons and a single quasi-particle peak appears in the gap in the dI/dV spectra.

This project is to explore the physical basis of TQC. To achieve this, the project focuses on developing experiments that may permit future topological quantum operations using a low-temperature STM.

We are assembling chains of magnetic atoms on the superconducting surfaces and we expect to create a magnetic chain, with a sizeable exchange interaction among atoms and with a large spin-orbit coupling. The gap of the superconductor leads to the localization of excitations such as the Shiba states. But Majorana states are also possible. Majorana states are magnetic excitations of the chains. Due to the exchange scattering of Cooper pairs off the magnetic chain and the spin-orbit interaction, Majorana states are states of composite quasi-particles. The finite-size of the chain leads to localization of some states at the edges. The low-energy states of these localized states turn out to follow anyon statistics that are primordial for topological quantum computing.

We extend out studies to self-assembling molecular magnetic chains on well-characterized superconducting surfaces to overcome the limit of number of atoms that can be manipulated by STM tip. Therefore, this is a multidisciplinary project with the final scientific objective of creating the physical foundations for TQC.

TQC claims that anyons (particles that do not follow Bose or Fermi statistics) can be used for computations. Producing these Majorana bound states is crucial for fabricating anyons that can be used to experiment and to eventually produce topological quantum computations. My present work aims at producing these anyons on atomic chains on Bi2Pd making use of its large spin-orbit coupling and superconducting properties.

We are assembling chains of magnetic atoms on the superconducting surfaces and we expect to create a magnetic chain, with a sizeable exchange interaction among atoms and with a large spin-orbit coupling. The gap of the superconductor leads to the localization of excitations such as the Shiba states. But Majorana states are also possible. Majorana states are magnetic excitations of the chains. Due to the exchange scattering of Cooper pairs off the magnetic chain and the spin-orbit interaction, Majorana states are states of composite quasi-particles. The finite-size of the chain leads to localization of some states at the edges. The low-energy states of these localized states turn out to follow anyon statistics that are primordial for topological quantum computing.

We extend out studies to self-assembling molecular magnetic chains on well-characterized superconducting surfaces to overcome the limit of number of atoms that can be manipulated by STM tip. Therefore, this is a multidisciplinary project with the final scientific objective of creating the physical foundations for TQC.

TQC claims that anyons (particles that do not follow Bose or Fermi statistics) can be used for computations. Producing these Majorana bound states is crucial for fabricating anyons that can be used to experiment and to eventually produce topological quantum computations. My present work aims at producing these anyons on atomic chains on Bi2Pd making use of its large spin-orbit coupling and superconducting properties.