08:50  09:00

Jan Michael Rost (MPIPKS) & Scientific Coordinators
Workshop Opening

09:00  09:40

Bogdan A. Bernevig
(Princeton University)
Majorana spin in magnetic atomic chains
We present a theory of the spinpolarized STM experiments of the Fe magnetic chains on top of a Pb Superconductor. We show that there are some universal characteristics that distinguish the Majorana spin from that of a isolated Shiba state accidentally tuned at zero energy.

09:40  10:20

Felix von Oppen
(Freie Universität Berlin)
Shiba states of real magnetic impurities

10:20  10:40

Alexander Melnikov
(Russian Academy of Sciences)
Nonlocality and dynamic response of Majorana states in fermionic superfluids
The goal of our work is to develop a theoretical description of the essentially nonequilibrium dynamics of Majorana states. We start from the timedependent Bogolubovde Gennes equations and show that the quasiparticle wavefunction evolving in time naturally consists of the contributions corresponding to both positive and negative energies of the stationary BdG Hamiltonian. As a result, the dynamics of two weakly overlapping Majorana states involves the hybridized wavefunctions corresponding to both positive and negative energy levels. This dynamics is substantially determined by the quantum mechanical beating phenomenon similar to the one wellknown from the standard Shroedinger quantum mechanics.
We suggest a microscopic model describing the nonlocal ac response of a pair of Majorana states in fermionic superfluids beyond the tunneling approximation. The timedependent variation of quasiparticle transport parameters is shown to excite finite period beating of the wavefunction between the distant Majorana states with the period governed by the energy splitting of two Majorana states. We propose an experimental test to measure the characteristic time scales of quasiparticle transport through the pair of Majorana states defining, thus, quantitative characteristics of nonlocality known to be a generic feature of Majorana particles.
We consider both the limits of weak and strong Coulomb effects and find that the beating phenomenon survives and is robust to the strong Coulomb blockade influence.
The beating phenomenon is shown to impose important restrictions on the operation frequencies of various Majoranabased devices.

10:40  11:00

Aksel Kobiałka
(Maria CurieSkłodowska University)
Emergence of Majorana quasiparticles in topological superconductors
Recent experiments revealed that zeroenergy bound state coalesces from the Andreev bound states. Such quasiparticle states can be controlled by the magnetic and electrostatic means as shifting of states can create the possibility of its existence and then allow Majorana bound states to leak to the other, nontopological parts of the system.
In our investigation we use microscopic model of the nanowire structure applying the Bogoliubov–de Gennes technique. This is done by studying the gate voltage and magnetic dependence of density of states and band structure at zero energy.
We show a way of understanding of Majorana quasiparticles emergence in said systems as a result of topological phase transitions

11:00  11:30

Coffee break

11:30  12:10

Allan MacDonald
(University of Texas at Austin)
The quantum anomalous hall Majorana platform
I will discuss the phase diagram of thinfilm magneticallydoped topological insulators that are placed on a superconducting substrate and put under the influence of a gatecontrolled displacement field. When viewed in the twodimensional space of displacement field and carrier density control parameters
and brought close to the parameter regime where the quantum anomalous Hall effect is observed, this system has broad regions of both trivial and topological superconducting phases. It follows that quasionedimensional (1D) quantum wires can be written onto the surface of these magnetic topological insulator (MTI) thin films by gate arrays, without requiring exceptionally fine control, and used to control Majorana end state arrays.

12:10  12:30

Szczepan Głodzik
(Maria CurieSkłodowska University)
YuShibaRusinov states of impurities in superconductors  influence of spinorbit coupling
Magnetic impurities in superconducting hosts induce bound states called YuShibaRusinov (YSR) states. It has been recently revealed that the reduced dimensionality of the superconducting substrate can influence the spatial extent of such ingap states. The spinorbit coupling can additionally modify the density of states around an impurity, and even further increase the range of bound states. We will explore the behavior of YSR states induced by single magnetic impurities and dimers embedded in superconducting hosts with different lattices.

12:30  14:20

Lunch

14:20  15:00

Christophe Brun
(CNRS and UPMC)
Twodimensional topological superconductivity in Pb/Co/Si(111)
Gerbold C. Ménard1, Sébastien Guissart2, Christophe Brun1, Mircea Trif2, François Debontridder1, Raphaël T. Leriche1, Dominique Demaille1, Dimitri1,3, Pascal Simon2 and Tristan Cren1
1Institut des Nanosciences de Paris, Université Pierre et Marie Curie (UPMC),CNRSUMR 7588, 4 place Jussieu, 75252 Paris, France
2Affiliation Laboratoire de Physique des Solides, CNRS, Univ. ParisSud, Université ParisSaclay, 91405 Orsay Cedex, France
3Laboratoire de physique et d’étude des matériaux, LPEMUMR8213/CNRSESPCI ParisTechUPMC, 10 rue Vauquelin, 75005 Paris, France
Email: Christophe.Brun@upmc.fr
Key words: 2D superconductivity; atomic monolayers; topological superconductivity.
Majorana states are predicted to appear as edge states of topological superconductors, in a similar way as Dirac surface states appears at the edge of topological insulators. Spectroscopic signatures of Majorana bound states were claimed to be observed in onedimensional (1D) InAs nanowires proximitycoupled to a bulk superconductor [1]. Then NadjPerge et al. [2] have realized a chain of Fe adatoms on a Pb(110) crystal that is supposed to induce locally a 1D topological pwave superconductivity. Zeroenergy bound states were observed at the extremity of some the Fe chain and interpreted as Majorana excitations [2]. Nevertheless this interpretation is challenged by close to zeroenergy Shiba states [3].
We have recently decided to follow a different strategy using a twodimensional superconducting system consisting in a monolayer of Pb atoms grown on Si(111) [4]. We have shown that the strong spinorbit coupling of Rashba type present in the superconductivity of the Pb/Si(111) monolayer can be revealed through the filling of ingap quasiparticle states by scattering from nonmagnetic disorder at 300 mK [5]. Following Rashba and Gor’kov this shows that a mixed singlettriplet superconductivity exists in our Pb monolayer [6]. Nanomagnetic disks made of CoSi alloy grown below the Pb/Si(111) monolayer were used to induce locally 2D topological superconductivity by combining a strong local Zeeman field with a mixed singlettriplet 2D superconductor. We have observed that dispersive edge states appear in the superconducting gap at the boundary of the magnetic domains [7]. We have interpreted these spectroscopic features as signatures of a locally induced 2D topological superconductivity. Indeed, we expect to get propagative dispersive Majorana edge states around 2D topological domains since the edges have a 1D character.
References
1. V. Mourik et al., “Signatures of Majorana Fermions in Hybrid SuperconductorSemiconductor Nanowire Devices” Science 346, 602 (2012).
2. S. NadjPerge et al., “Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor” Science 336, 1003 (2014).
3. M. Ruby et al., “End States and Subgap Structure in ProximityCoupled Chains of Magnetic Adatoms” PRL 115, 197204 (2015).
4. T. Zhang et al. “Superconductivity in oneatomiclayer metal films grown on Si(111) ” Nature Phys. 444, 10 (2014).
5. C. Brun et al., “Remarkable effects of disorder on superconductivity of single atomic layers of lead on silicon” Nature Phys. 444, 10 (2014).
6. E.I. Rashba and L.V. Gor’kov, ”Superconducting 2D System with Lifted Spin Degeneracy: Mixed SingletTriplet State” PRL 444, 10 (2010).
7. G. C. Ménard et al., “Twodimensional topological superconductivity in Pb/Co/Si(111)”, Nature commun. 8, 2040 (2017) doi:10.1038/s4146701702192x

15:00  15:40

Teemu Ojanen
(Aalto University)
Engineering 2d topological states by adatoms
Recent experiments have reported convincing evidence of 1d topological superconductivity in systems comprising of linear arrangements of magnetic atoms. In my talk I will explain why these developments could only be a starting point of engineering a myriad of topological states in 2d systems. The more exotic examples of these include topological superconductors with high Chern numbers and amorphous topological states in random systems. I also discuss prospects of fabricating Chern insulators with similar approach.

15:40  16:00

Andrej Mesaros
(Laboratoire de Physique des Solides)
Ingap excitations due to defects in topological superconductor with spinorbit coupling
Recent microscopy experiments on superconducting monolayer of lead(Pb) grown over clusters of cobalt atoms have raised urgent questions about robust ingap electronic states in presence of strong spinorbit coupling and magnetism.
Using analytics and exact diagonalization we find that a vortex defect in Rashba coupling fully explains puzzling features of this experiment: 1) Vortex on the magnetic island localizes a state at scale far smaller than superconducting coherence length; 2) The state is protected by large energy gap; 3) Island edge states are however localized on the coherence scale. The theory predicts that the defect state is a single Majorana state, welllocalized, and remarkably wellisolated in energy. In contrast, a typical superconducting vortex would exhibit a tower of ingap excited states.
We also study the Majorana states in superconducting vortices in mixed singlettriplet superconductors. We find that multiple Majorana states can be topologically protected in a single vortex, and explain how the Zeeman field can stabilize them. The multiple Majorana states still give nontrivial braiding properties to a vortex. Finally, we discuss the experimental feasibility of these Majorana states in a superconductor under magnetic field.

16:00  16:30

Coffee break

16:30  17:30

OPTIMA18 Colloquium
Chair: Inti Sodemann (MPIPKS)
Ali Yazdani (Princeton University)
Engineering and Visualizing Majoranas in Chains and Hinges
A variety of onedimensional electronic systems can be engineered to host topological superconductivity and Majorana zero modes. In this talk, I’ll describe experiments on two different onedimensional platforms. One is based on chains of magnetic atoms the work on which grew out of early efforts on the study of localized Bogoliubov quasiparticles near individual magnetic atoms on a superconductors. We have now performed a series of experiments to establish the presence of Majorana’s in this system, including a recent study of their spin polarization. A second system is based on introducing superconductivity on the hinge states of a high order topological insulator. Using combination of magnetism and superconductivity, we are exploring how Majorana zero mode can emerge in this system.

18:30  19:30

Dinner

19:30  21:30

Poster session
