
Pascal Simon
(chair)
Bound states in topological superconductors

09:00  09:30

Annica BlackSchaffer
(Uppsala University)
Majorana bound state localization, energy oscillations, and disorder robustness in magnetic impurity chains on conventional superconductors
Magnetic impurities on the surface of spinorbit coupled but otherwise conventional superconductors offer the possibility to create topological phases with Majorana bound states (MBSs) without having to apply an external magnetic field. In this talk I will present some of our resent results in modeling both magnetic wires and islands on the surface of spinorbit coupled superconductors, including an accurate treatment of the superconducting state through a selfconsistent approach. In particular, I will show how wire end point MBSs very strongly hybridize with the ingap YuShibaRusinov (YSR) states, causing large oscillations in the MBSs energies. Still, by treating the MBSs as topological boundary modes dependent only on the effective mass gap, we arrive at a fully parameterfree fitting of the Majorana localization length, which stays very short. I will also show how the wire end point MBSs are very robust against disorder, despite individual YSR states being extremely sensitive to disorder.

09:30  10:00

Tristan Cren
(CNRS)
YuShibaRusinov bound states and topological superconductivity in 2D systems
Individual local magnetic moments act destructively on Cooper pairs, leading to discrete spinpolarized states inside the superconducting energy gap as predicted by Yu, Shiba and Rusinov (YSR) [1,2,3]. Rusinov suggested that around magnetic atoms the decaying YSR wavefunction should have a spatially oscillating structure. We experimentally evidenced YSR bound states with spatially oscillating particlehole asymmetry extending tens of nanometers from individual iron atoms embedded in a 2HNbSe2 crystal and in Pb/Si(111) monolayer [4]. We theoretically elucidate how reduced dimensionality enhances the spatial extent of these bound states and describe their energy and spatial structure.
The large spatial extent of the YSR states in 2D superconductors can be use with profit for stabilizing topological phases in arrays of magnetic impurities. Zero bias anomalies localized at the edge of a Fe chain of Pb(110) were recently interpreted as fingerprints of the emergence of topological superconductivity [5]. In contrast to the 1D case, twodimensional superconductors have a onedimensional boundary which naturally leads to chiral Majorana edge states characterized by a Diraclike dispersion. We have recently observed some hint of dispersive Majorana edge states in a single atomic layer Pb superconductor. This material has strong triplet correlations but is not topological by itself [6]. We will show that by applying a Zeeman field with the help of a buried CoSi nanomagnet one can provoke a transition to a topological state [7]. In addition to their dispersive edge states, 2D topological superconductors are also supposed to support localized Majorana bound states in topological defects. We will show that some recent measurements seem to support this theoretical prediction [8].
References
[1] L. Yu, Bound state in superconductors with paramagnetic impurities, Acta Phys. Sin. 21, 75 (1965).
[2] H. Shiba, Classical Spins in Superconductors, Prog. Theor. Phys. 40, 435 (1968).
[3] A.I. Rusinov, On the theory of gapless superconductivity in alloys containing paramagnetic impurities, JETP Lett. 9, 85 (1969).
[4] G. Ménard et al., Coherent longrange magnetic bound states in a superconductor, Nature Physics 11, 1013 (2015)
[5] S. NadjPerge et al., Science 346, 602 (2014)
[6] C. Brun et al., “Remarkable effects of disorder on superconductivity of single atomic layers of lead on silicon” Nature Phys. 444, 10 (2014).
[7] Gerbold C. Ménard, et al., Twodimensional topological superconductivity in Pb/Co/Si (111), Nature communications 8, 2040 (2017)
[8] G. C. Ménard, et al., Isolated pairs of Majorana zero modes in a disordered superconducting lead monolayer, arXiv:1810.09541 (2018)

10:00  10:30

Jens Wiebe
(University of Hamburg)
YuShibaRusinov bands of artificial spin chains on highZ superconductors
Chains of magnetic atoms on highZ swave superconductors can exhibit topological superconductivity and may host Majorana bound states at their ends [18]. Most previous experimental work towards the realization of such systems focused on the selfassembly of chains [9,10] where a full control of the atomic composition in the chain is difficult to achieve. In this study, we use superconducting Ta and Re substrates which enable scanning tunneling microscope tip induced assembly of chains with a control on the chemical composition and position of each individual atom in the chain [11,12]. We investigate the evolution of the YuShibaRusinov states [13] of the building blocks of the chains, the single atoms [14], into bands in the two extreme regimes, i.e. the dilute chain and wire limits. For particular combinations of substrate and adatom species, we find indications for topological superconductivity in the wire limit [12].
We acknowledge funding by the ERC via the Advanced Grant ADMIRE (No. 786020).
[1] T.P. Choy et al. PRB 84, 195442 (2011); [2] I. Martin et al., PRB 85, 144505 (2012); [3] Klinovaja et al., PRL 111, 186805 (2013); [4] F. Pientka et al., PRB 88, 155420 (2013); [5] B. Braunecker et al., PRL 111, 147202 (2013); [6] M. M. Vazifeh et al., PRL 111, 206802 (2013); [7] J. Li et al. PRB 90, 235433 (2014); [8] M. Schecter et al., PRB 93, 140503 (2016); [9] S. NadjPerge et al., Science 346, 6209 (2014); [10] M. Ruby et al., Nano Letters 17, 4473, (2017); [11] A. Kamlapure et al., Nature Comm. 9, 3253 (2018); [12] H. Kim et al., Science Advances 4, eaar5251 (2018); [13] A. V. Balatsky et al., Rev. Mod. Phys. 78, 373 (2006); [14] L. Cornils et al., PRL 119, 197002 (2017).

10:30  11:00

Yuli V. Nazarov
(Delft University of Technology)
Weyl singularities in superconducting nanostructures
We review Weyl singularities of the Andreev bound state spectrum in multiterminal supeconducting nanostructures and discuss the recent developments in the field:
Weyl disks, coupled Weyl points, spinweyl double qubits.

11:00  11:05

group picture

11:05  11:30

coffee break


Reinhold Egger
(chair)
Majorana bound states

11:30  12:00

Roman Lutchyn
(University of California)
Topological superconductivity in full shell proximitized nanowires
We consider a new model system supporting Majorana zero modes based on semiconductor nanowires with a full superconducting shell. We demonstrate that, in the presence of spinorbit coupling in the semiconductor induced by a radial electric field, the winding of the superconducting order parameter leads to a topological phase supporting Majorana zero modes. The topological phase persists over a large range of chemical potentials and can be induced by a predictable and weak magnetic field piercing the cylinder. The system can be readily realized in semiconductor nanowires covered by a full superconducting shell, opening a pathway for realizing topological quantum computing proposals.

12:00  12:30

Pascal Simon
(University Paris Sud)
Majorana zero modes around the deformable edge of a magnetic skyrmion
Magnetic skyrmions are nanoscale particlelike spin configurations that are efficiently created and manipulated. They hold great promises for nextgeneration spintronics applications. In parallel to these developments, the interplay of magnetism, superconductivity and spinorbit coupling has proved to be a versatile platform for engineering topological superconductivity predicted to host nonabelian excitations, Majorana zero modes (MZMs).
In this talk, I will focus on the theoretical analysis of magnetic skyrmions proximitized by conventional superconductors. I will show that a topological superconducting phase can emerge in these systems and uncover a whole flat band of these modes on the edge of the magnetic texture, in contrast to a previously reported MZM in the core of the skyrmion [1]. I will discuss in details the origin of these MZMs by relating this problem to the the extensivelystudied Rashba nanowire model. We have found that these modes are remarkably stable to electronic and geometric perturbations which we investigate by a combination of analytical arguments and numerical tightbinding calculations. Additionally, this analysis reveals that the number of MZMs on the edge scales linearly with its perimeter. I will then discuss possible experimental realizations and consequences of this phenomenon and argue that this system is suitable for the realization of the topological Kondo effect and of electron teleportation [2].
[1] G. Yang, P. Stano, J. Klinovaja & D. Loss, PRB 93, 224505 (2016).
[2] M. Garnier, A. Mesaros, P. Simon, submitted.

12:30  13:30

lunch

13:30  14:00

discussion


Jürgen König
(Bound states in Josephson spectroscopy)

14:00  14:30

Kasper GroveRasmussen
(University of Copenhagen)
YuShibaRusinov screening of spins in quantum dots coupled to a single superconducting lead
Recent progress in experiments and modelling has improved our understanding of subgap states in superconductorquantum dot systems. I will here present results on quantum states in hybrid superconductorsemiconductor (InAs) nanowire devices. When coupling a superconductor (S) to a quantum dot (QD) system, the confined electron spin may be screened by quasiparticles above the gap in the superconductor, similarly to the Kondo effect for QDs with normal electrodes. This screening results in socalled YuShibaRusinov (YSR) subgap states. We explore such states in bottomgated hybrid superconductornanowire single and double dot devices. The YSR states can be modelled by using a simple zeroband width approximation, which we compare to measurements on single [1] and double quantum dots (DQD) [2] coupled to a single superconductor, i.e. the NQDS and NDQDS configurations, respectively. In the latter case, the characteristic double dot honeycomb stability diagram is shown to be qualitatively different in the superconducting state.
[1] A. Jellinggaard, K. GroveRasmussen, M.H. Madsen, J. Nygård, “Tuning YuShibaRusinov states in a quantum dot”, Phys. Rev. B 94, 064520 (2016)
[2] K. GroveRasmussen, G. Steffensen, A. Jellinggaard, M. H. Madsen, R. Žitko, J. Paaske & J. Nygård, “YuShibaRusinov screening of spins in a double quantum dots”, Nat. Comm. 9:2376 (2018)

14:30  15:00

Richard Deblock
(ParisSud University and CNRS)
Josephson Effect in a Carbon Nanotube: 0$\pi$ Transitions and High Frequency Emission
We probed the currentphase relation in a clean carbon nanotube quantum dot, close to orbital degeneracy, in a regime of strong competition between local electronic correlations and superconducting proximity effect. We show experimentally that the 0pi transition can then be controlled by the superconducting phase [1] and that the nature of the transition depends crucially on the occupation and the width of the orbital levels [2]. When the transport of Cooper pairs takes place through only one of these levels, we find that the phase diagram of the phasedependent 0pi transition is a universal characteristic of a discontinuous levelcrossing quantum transition at zero temperature.
We have also measured the high frequency emission of a carbon nanotube junction due to the AC Josephson effect in the same regime of competition of the Kondo and superconducting proximity effect. We show that, strikingly, whereas the DC supercurrent is enhanced by the Kondo effect, the AC Josephson effect is not necessarily enhanced. This indicates possible signature of the dynamics of the Kondo screening.
[1] R. Delagrange, D. J. Luitz, R. Weil, A. Kasumov, V. Meden, H. Bouchiat, R. Deblock, Phys. Rev. B 91, 241401(R) (2015).
[2] R. Delagrange, R. Weil, A. Kasumov, M. Ferrier, H. Bouchiat and R. Deblock, Phys. Rev. B 93, 195437 (2016).

15:00  15:30

Volker Meden
(RWTH Aachen)
The Josephson current through a correlated quantum dot
An overview on the theoretical understanding of the equilibrium Josephson current through a correlated quantum dot is presented. Results obtained by elaborate manybody methods are compared to experiments. The quantitative agreement indicates that the experimental systems can be understood in terms of the simplified model.

15:30  16:00

Tomáš Novotný
(Charles University of Prague)
Semianalytical theories for a correlated quantum dot attached to superconducting leads
I will present an overview of relatively simple theoretical approaches developed in our group in past several years and applied to the problem of description of correlated quantum dots attached to the BCS superconducting leads. As a thorough Quantum Monte Carlo analysis [1] of the experimental data [2] showed realistic experimental setups can be even quantitatively captured by the Single Impurity Anderson Model with superconducting leads. Pioneering semianalytical approaches have not matched the so far employed heavy numerical tools such as Numerical Renormalization Group and/or Quantum Monte Carlo in the ability of quantitatively predicting the properties of this model. However, we have shown recently that selfconsistent perturbation expansion up to the second order in the interaction strength [3,4] yields at zero temperature and for a wide range of other parameters excellent results for the position of the 0 − π impurity quantum phase transition boundary and the Josephson current as well as the energy of Andreev bound states in the 0phase. This method can be also extended to the threeterminal situation with an extra normal lead corresponding to the experimentally interesting STM setup [5], where it allows to study phasedependent Kondo physics. Furthermore, we have discovered exact identities connecting symmetric and asymmetric coupling situations which significantly reduce computational requirements in experimentally generic asymmetric setups [6] and provided simple approximate analytical formulas for the fitting of the phase boundaries from finitetemperature experimental data [7].
[1] David J. Luitz, Fakher F. Assaad, Tomáš Novotný, Christoph Karrasch, and Volker Meden, Understanding the Josephson current through a Kondocorrelated quantum dot, Phys. Rev. Lett. 108, 227001 (2012)
[2] H. Ingerslev Jørgensen, T. Novotný, K. GroveRasmussen, K. Flensberg, and P. E. Lindelof, Critical Current 0π Transition in Designed Josephson Quantum Dot Junctions, Nano Lett. 7 (8), 2441 (2007)
[3] M. Žonda, V. Pokorný, V. Janiš, and T. Novotný, Perturbation theory of a superconducting 0π impurity quantum phase transition, Scientific Reports 5, 8821; DOI:10.1038/srep08821 (2015)
[4] M. Žonda, V. Pokorný, V. Janiš, and T. Novotný, Perturbation theory for an Anderson quantum dot asymmetrically attached to two superconducting leads, Phys. Rev. B 93, 024523 (2016)
[5] T. Domański, M. Žonda, V. Pokorný, G. Górski, V. Janiš, and T. Novotný, Josephsonphasecontrolled interplay between correlation effects and electron pairing in a threeterminal nanostructure, Phys. Rev. B 95, 045104 (2017)
[6] Alžběta Kadlecová, Martin Žonda, and Tomáš Novotný, Quantum dot attached to superconducting leads: Relation between symmetric and asymmetric coupling, Phys. Rev. B 95, 195114 (2017)
[7] Alžběta Kadlecová, Martin Žonda, Vladislav Pokorný, and Tomáš Novotný, Practical Guide to Quantum Phase Transitions in Superconducting Quantum Dots, arXiv:1807.07017 (under review in Phys. Rev. Applied)

16:00  16:30

coffee break


Jesper Nygård
(chair)
Microwave spectroscopy of Andreev states

16:30  17:00

Hugues Pothier
(CEA Saclay)
spinorbit splitting of Andreev states revealed by microwave spectroscopy
Using a circuitQED setup, we measure the spectrum of excitations in an InAs nanowire connected to superconducting electrodes. Some transitions correspond to Andreev levels spinsplit by spinorbit interaction.

17:00  17:30

Wolfgang Belzig
(University of Konstanz)
Microwave spectroscopy reveals the quantum geometric tensor of topological Josephson matter
Topology is providing new insight into condensed matter physics problems. Concepts like Chern numbers and their relation to physical phenomena have become very familiar, but actually, key quantities like the quantum geometric tensor, which provides a much deeper information about quantum states, remain experimentally difficult to access. Recently it has been shown that multiterminal superconducting junctions constitute an ideal playground to mimic topological systems in a controlled manner. Here, we theoretically study the spectrum of Andreev bound states in topological Josephson matter and demonstrate that the full information of the quantum geometric tensor of the ground state manifold can be extracted with the help of microwave spectroscopy. In particular, we develop the concept of artificially polarized microwaves, which can be used to obtain both the quantum metric tensor and the Berry curvature. The quantized integrated absorption provides a direct evidence of topological quantum properties of the Andreev states.

17:30  18:00

Christoph Strunk
(University of Regensburg)
ACJosephson emission and microwave stimulated superconductivity in SNS weak links
We investigate the Josephson radiation of a voltagebiased diffusive normal metal bridge between two superconductors. The higher harmonics of the Josephson radiation strongly depend on the nonequilibrium population of Andreev bound states that is generated both by the dc and ac bias voltages. The combined effect of dcbias and microwave excitation leads to strong Josephson emission even at higher temperatures, where the equilibrium Josephson current is suppressed by thermal excitation.

19:30  22:30

workshop dinner
