In my talk, I will argue that nanowire-based hybrid superconductor-semiconductor Josephson junctions are extremely useful platforms to study Majorana physics beyond local transport spectroscopy experiments (“zero bias anomalies”). Physical quantities that provide relevant information about Majorana zero modes in such junctions include ac Josephson currents [1], multiple Andreev reflection [2], critical current measurements [3] and ac susceptibility [4]. Nanowire-based Josephson junctions [5] with sizable charging energy are another novel platform where the physics of standard superconducting qubits in the so-called transmon regime acquires a new twist owing to the presence of Majorana zero modes and low-energy quasiparticle excitations in the junction [6]. In particular, I will discuss how the presence of low-energy quasiparticles and Majoranas affects the spectrum of the transmon qubit.

References:
[1] P. San-Jose, E. Prada and R. Aguado, PRL 108, 257001 (2012).
[2] P. San-Jose, J. Cayao, E. Prada, R. Aguado, New Journal of Physics 15 (7), 075019 (2013).
[3] J. Cayao, P. San-Jose, A.M. Black-Schaffer, R. Aguado, E Prada, PRB 96, 205425 (2017); Jonna Tiira et al, Nature Communications, 8, 14984 (2017); P San-Jose, E Prada, R Aguado, PRL 112, 137001 (2014).
[4] M Trif, O Dmytruk, H Bouchiat, R Aguado, P Simon, PRB 97, 041415 (2018).
[5] T. W. Larsen, et al, PRL, 115, 127001 (2015); G. de Lange, et al, PRL, 115, 127002 (2015).
[6] E. Ginossar and E. Grosfeld, Nature Communications 5, 4772 (2014); A. Kesselman et al, arXiv:1905.03275 ; J. Avila, E. Prada, P. San-Jose and R. Aguado, in preparation (2019).

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 spin-orbit 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.

In my talk, I will discuss low-dimensional condensed matter systems, in which topological properties could be engineered per demand. Majorana fermions can emerge in hybrid systems with proximity-induced superconducting pairing.  I will present our numerical and analytical studies of such geometries with proximity effects [1-3]. In the second part of the talk, I will discuss an analytical model of a Rashba nanowire that is partially covered by and coupled to a thin superconducting layer, where the uncovered region of the nanowire forms a quantum dot [4,5]. Even if there is no topological superconducting phase possible, there is a trivial Andreev bound state that becomes pinned exponentially close to zero energy as a function of magnetic field strength when the length of the quantum dot is tuned with respect to its spin-orbit length such that a resonance condition of Fabry-Perot type is satisfied. In this case, the Andreev bound state remains pinned near zero energy for Zeeman energies that exceed the characteristic spacing between Andreev bound state levels but that are smaller than the spin-orbit energy of the quantum dot. Importantly, as the pinning of the Andreev bound state depends only on properties of the quantum dot, this behavior is unrelated to topological superconductivity.

References:
1. C. Reeg, D. Loss, and J. Klinovaja, Phys. Rev. B 97, 165425 (2018).
2. C. Reeg, D. Loss, and J. Klinovaja, Phys. Rev. B 96, 125426 (2017).
3. C. Reeg, J. Klinovaja, and D. Loss, Phys. Rev. B 96, 081301 (2017).
4. C. Reeg, O. Dmytruk, D. Chevallier, D. Loss, and J. Klinovaja, Phys. Rev. B 98, 245407 (2018).
5. O. Dmytruk, D. Chevallier, D. Loss, and J. Klinovaja, Phys. Rev. B 98, 165403 (2018). 

Strong Coulomb interactions may induce a phase transition between a topological superconductor and an insulator. We find that there are several possible insulating phases of topological superconductors, dual (equivalent) to certain spin liquid phases. They include phases with non Abelian particles that may support universal quantum computation. We will discuss possible way to stabilize these exotic phases by interactions between Majorana-zero modes in a Cooper box. In particular we will show how a critical super-symmetric state emerges.

We consider a system of weakly coupled Rashba nanowires in the strong spin-orbit interaction (SOI) regime. The nanowires are arranged into two tunnel-coupled layers proximitized by a top and bottom superconductor such that the superconducting phase difference between them is π. We show that in such a system strong electron-electron interactions can stabilize a helical topological superconducting phase hosting Kramers partners of Z_2m parafermion edge modes, where m is an odd integer determined by the position of the chemical potential. Furthermore, upon turning on a weak in-plane magnetic field, the system is driven into a second-order topological superconducting phase hosting zero-energy Z_2m parafermion bound states localized at two opposite corners of a rectangular sample. As a special case, zero-energy Majorana corner states emerge in the non-interacting limit m = 1, where the chemical potential is tuned to the SOI energy of the single nanowires.

Parafermions are generalizations of Majorana fermions that emerge in interacting topological systems. They are known to be powerful building blocks of topological quantum computers. Existing proposals for realizations of parafermions typically rely on strong electronic correlations which are difficult to achieve in the laboratory. We identify a novel physical system in which parafermions develop. It is based on a quantum point contact (QPC) formed by the helical edge states of a quantum spin Hall insulator (QSHI) in vicinity to an ordinary s-wave superconductor. Interestingly, our analysis suggests that Z4 parafermions are emerging bound states in this setup even in the weakly interacting regime. Furthermore, we identify conditions under which parafermions and Majorana fermions coexist [1]. Additionally, we present recent transport measurements through a QPC formed in a QSHI. An intriguing conductance quantization is observed which indicates spontaneous breaking of time-reversal symmetry by electronic correlations [2].

References:
[1] C. Fleckenstein, N. Traverso Ziani, and B. Trauzettel, Phys. Rev. Lett. 122, 066801 (2019).
[2] J. Strunz, J. Wiedenmann, C. Fleckenstein, L. Lunczer, W. Beugeling, V. Müller, P. Shekhar, N. Traverso Ziani, S. Shamim, J. Kleinlein, H. Buhmann, B. Trauzettel, and L.W. Molenkamp, arXiv:1905.08175 (2019).

Tailoring electron scattering at surfaces is of key importance to develop topological materials for spintronics. For example, spin-polarized currents could be sustained at the surface through Rashba-split states, since these are topologically protected against backscattering at surface defects, such as atomic steps. In this context, we aim at probing electron scattering at steps by combining curved crystal surfaces and Angle Resolved Photoemission. By employing curved crystals with selected azimuthal direction we achieve tunable arrays of monoatomic steps with different morphology and orientations. Scanning the ultraviolet light beam on the curved surface during angle-resolved photoemission experiments we unveil the scattering behavior of surface states. The fundamental ideas are tested with noble metal surfaces and Shockley states, which exhibit a variable scattering strength and exotic charge-density-wave-like electronic/structural interplays. Finally, I will present the first realization of periodic step arrays on the BiAg2 atom-thick surface alloy, with unprecedented atomic precision, and demonstrate their potential for tuning helical Rashba states.

The understanding of strongly-correlated quantum matter has challenged physicists for decades. Such difficulties have stimulated new research paradigms, such as ultra-cold atom lattices for simulating quantum materials. In this talk I will present a new platform to investigate strongly correlated physics, based on graphene moiré superlattices. In particular, when two graphene sheets are twisted by an angle close to the theoretically predicted ‘magic angle’, the resulting flat band structure near the Dirac point gives rise to a strongly-correlated electronic system. These flat bands exhibit half-filling insulating phases at zero magnetic field, which we show to be a correlated insulator arising from electrons localized in the moiré superlattice. Moreover, upon doping, we find electrically tunable superconductivity in this system, with many characteristics similar to high-temperature cuprates superconductivity. These unique properties of magic-angle twisted bilayer graphene open up a new playground for exotic many-body quantum phases in a 2D platform made of pure carbon and without magnetic field. Since these discoveries, a large number of theoretical models have been proposed based on the magic-angle graphene superlattices and beyond. I will also discuss our data demonstrating nematicity in the superconducting state, strange metal behavior at correlated fillings with near Planckian dissipation as well as correlated states in other types of graphene superlattices. The easy accessibility of the flat bands, the electrical tunability, and the bandwidth tunability through twist angle may pave the way towards more exotic correlated systems, such as quantum spin liquids.

In this talk I will discuss the behaviour of twisted bilayer graphene, and particularly its lattice relaxation and the effect on its electronic structure. Based on a tight binding model, we develop a generic approach to the construction of continuum models. Due to the small local deformation of the graphene lattice, we find that this approach can be applied for any sensible model of the inter-layer hopping, and reproduce the result of rather expensive tight-binding calculations. We study the effects on near magic-angle bilayers (in the order of 1 degree of twist), and marginal angles, where networks of one-dimensional channels emerge.

We report a spontaneous spin-polarisation in a two-dimensional electron gas in monolayer MoS₂ [1].

In a two-dimensional electron gas (2DEG), Coulomb effects dominate over single-particle effects in the limit of low electron-density. In this regime, the average inter-electron distance is larger than the Bohr radius in the host material. In gallium arsenide and silicon 2DEGs, electrons are localized at these low electron densities such that Coulomb effects tend to be obscured. New opportunities arise in transition-metal dichalcogenides (TMDs). A TMD represents a natural realization of a 2DEG. Significantly, the extremely small Bohr radius in a TMD suggests that Coulomb effects play an important role at experimentally relevant electron-densities.

We probe the electronic ground-state of a gated monolayer of MoS₂ at various electron densities using optical absorption, a local, non-invasive, spin- and valley-resolved tool. In a single-particle picture, we expect the ground-state to be formed by a close-to-equal filling of the four available conduction bands. Our experiment overturns this single-particle picture: only two of the four bands are occupied – the two with the same spin but at different valleys. This is a striking result: the creation of a spontaneous spin-polarisation in a 2DEG.

We propose that inter-valley electron-electron exchange is responsible for the creation of a spin- polarised ground-state in electron-doped monolayer MoS2. Even though the K and K ́ points are far apart in phase-space, the Bohr radius is so small that inter-valley Coulomb scattering is significant.

This work was carried out in the Nano-Photonics Group in the Department of Physics, University of Basel, together with Jonas G. Roch, Guillaume Froehlicher and Nadine Leisgang. Complementary theoretical work was carried out by Dmitry Miserev, Jelena Klinovaja, and Daniel Loss [2].

References:
[1] Jonas G. Roch, Guillaume Froehlicher, Nadine Leisgang, Peter Makk, Kenji Watanabe, Takashi Taniguchi, Richard J. Warburton, Nature Nanotechnology 14, 432 (2019)
[2] Dmitry Miserev, Jelena Klinovaja, and Daniel Loss, arXiv:1902.07961 (2019)

Atomically thin layers of transition metal dichalcogenides (TMDs) such as MoS2 are two-valley materials that attract more and more attention as a promising candidates for valleytronics. Relatively large spin-orbit interaction provides valley-dependent selection rules for optical experiments allowing the optical control of the valley polarization of 2D electron gas at small densities. However, the single- particle picture is not always true. Here we present our work where we predict the first order Ising ferromagnetic phase transition coming from the electron-electron interaction. We show that the spontaneous valley and spin-valley polarization cannot develop due to the effect of the exchange inter- valley scattering which is strong in TMDs. The first order nature of the ferromagnetic phase transition comes from the non-analytic cubic terms in the thermodynamic potential. The spin-orbit interaction breaks the O(3) symmetry of the ferromagnet resulting in the Ising order. Our prediction is consistent with the recent optical experiment [J. G. Roch et al., published on-line in Nature Nanotech. (2019), arXiv:1807.06636] where the Ising ferromagnetic phase has been detected.

Recently it has become possible to look more closely thermodynamics in the single electron tunneling process because the devices of study hold improved capability of controlling and detecting the electron tunneling events and therefore the charge transport dynamics can be traced in real time. Then the fundamental statistics of the electrons has been revealed and thermodynamics rules such as the fluctuation theorem has been demonstrated. However, to date most of the experimental studies have concentrated on the charge degree of freedom but not the spin degree of freedom. On the other hand, spin measurement techniques have been well improved for electrons in quantum dots, and can apply for study on the fundamental statistics. Indeed various spin-related phenomena have been unveiled for the Pauli spin blockade (PSB) effect in quantum dots, including the peculiar time traces associated with lifting PSB, the spin-flip tunnel rates and the microscopic mechanism of the spin-flip events. Here we report on a theoretical and experimental study of the full counting statistics (FCS) for electron spins in the PSB on a GaAs gate-defined double quantum dot. The FCS is a probability density as a function of the charge transition number, and can provide important information about the statistics of the dynamics because it contains a lot of statistical information such as all-order of the cumulants. First, we evaluated all of the necessary tunnel rates to construct the FCS from the time traces and then constructed the FCS and compared it to our theoretical result. We found that there are two peculiar features, the asymmetric shape of the probability density and the parity effect about the transition number. We will discuss these origins using our theoretical model. These results are the first experimental results of the FCS for the spin-related phenomenon and provide a useful tool for revealing the dynamics of spins in the multiple quantum dots.

Van der Waals materials are formed from weakly interacting and mechanically stiff atomic layers. Sliding and twisting these layers with respect to each other give rise to superstructures with emergent functionalities like, for example, the plethora of strongly correlated phenomena (superconductivity included) observed in twisted bilayer graphene. One of the most recent development on this front the observation of a remarkably large, linear in temperature (T) resistivity in the normal state. Some theories have attributed this behavior to electron-phonon scattering. In this talk, I will argue that the long-wavelength dynamics of these generically incommensurate structures are dominated by new collective modes, phasons [1]. These modes correspond to coherent superpositions of optical phonons describing the sliding motion of stacking solitons separating regions of partial commensuration. I will illustrate this physics with recent data acquired in MoSe2 multilayers [2], where scanning tunnel microscopy revealed the formation of stacking textures above some critical strain with distinct imprints in tunnel spectroscopy. I will also show that when interlayer forces are taken into account, transverse phason modes of twisted bilayer graphene dominate the interaction of electrons with the lattice. This coupling lifts the layer degeneracy of the reconstructed Dirac cones, which could explain the observed 4-fold (instead of 8-fold) Landau level degeneracy in magneto-transport. Electron-phason scattering gives rise to a linear-T contribution to the resistivity that increases with decreasing twist angle due to the reduced rigidity of the Moiré pattern. This contribution, however, seems to be insufficient to explain the rapid increase of the resistivity close to the magic angle condition. These results point to a different mechanism, possibly related to a Fermi-surface reconstruction linked to the correlated phenomena at lower temperatures.

References:
[1] H. Ochoa, arXiv:1905.10850.
[2] D. Edelberg et al., in preparation.

The effect of ac electric fields on the transport properties of low dimensional systems has been a topic of intense research in the last years. Applying ac electric fields to coupled quantum dots allows to transfer charge between them by means of photo-assisted transitions. Experiments in triple quantum dots unambiguously show direct electron transfer between the outer dots, without the participation of the intermediate region other than virtual, thus minimizing the effect of decoherence and relaxation [1-3]. In the presence of ac driving the transfer of electrons between distant dots takes place by means of photo-assisted virtual transitions [3-5].

A review on the theoretical models and experimental evidence of long range charge and quantum state transfer in ac driven quantum dot arrays will be provided. I will focus on a protocol for preparing a quantum state at the left edge of a triple quantum dot and directly transferring it to the right edge by means of ac gate voltages. I will show that by the controlled generation of dark states it is possible to increase the fidelity of the transfer protocol [6]. I will discuss as well other protocols which allow for long range charge transfer as coherent transfer by adiabatic passage (CTAP)[7]. Adiabatic protocols however, provide slow transfer prone to decoherence. I will show how these protocols can be speeded up by shortcuts of adiabaticity [8]. Furthermore, it allows for long range transfer of two electron entangled states in longer quantum dot arrays with high fidelity [11]. The proposed protocols offer an alternative and robust mechanism for quantum information processing.

Finally I will discuss how to implement the SSH model in a quantum dot array, the role of edge states in the electron dynamics and how the presence of an ac electric field allows to detect the topological phases by transport measurements[10-11].

References:
[1] M. Busl et al., Nature Nanotech, 8, 261 (2013).
[2] R. Sánchez et al., Phys. Rev. Lett, 112, 176803 (2014).
[3] F. Braakman et al., Nature Nanotech, 8, 432 (2013).
[4] P. Stano, et al., Phys. Rev. B 92, 075302 (2015).
[5] F. Gallego-Marcos, et al., Phys. Rev. B 93, 075424 (2016); F. Gallego-Marcos et al., J. Appl. Phys. 117, 112808 (2015).
[6] J. Picó-Cortés et al., Phys. Rev. B, 99, 155421 (2019).
[7] A. D. Greentree et al., Phys Rev. B, 70, 235317 (2004).
[8] Y. Ban et al., Nanotechnology, 29 505201 (2018).
[9] Y. Ban et al., submitted, arXiv, arXiv:1904.05694.
[10] M. Niklas et al., Nanotechnology, 27, 454002 (2016).
[11] B. Pérez-González et al., arXiv :1903.07678v1.

We show that in-plane magnetic-field-assisted spectroscopy allows extraction of the in-plane orientation and full 3D size parameters of the quantum mechanical orbitals of a single electron GaAs lateral quantum dot with subnanometer precision. The method is based on measuring the orbital energies in a magnetic field with various strengths and orientations in the plane of the 2D electron gas. From such data, we deduce the microscopic confinement potential landscape and quantify the degree by which it differs from a harmonic oscillator potential. The spectroscopy is used to validate shape manipulation with gate voltages, agreeing with expectations from the gate layout. Our measurements demonstrate a versatile tool for quantum dots with one dominant axis of strong confinement.

The ability to construct nano-scale systems with atomic-level precision by using STM-based single-atom manipulation techniques has led to numerous outstanding examples of Quantum Designer Physics. In particular the combination of single-atom manipulation with spin- sensitive imaging and spectroscopy based on the spin-polarized STM technique [1] offers an exciting approach towards the design of specific properties of 1D spin chains [2] as well as 2D arrangements of tailored nanomagnets [3]. Investigating such artificially built spin arrays on superconductor surfaces has recently led to the observation of Majorana zero-energy modes in atomically well-defined magnet-superconductor hybrid systems [4]. Moreover, prototypes for all-spin atomic-scale spin logic devices could be demonstrated by a bottom-up fabrication technique [5].

In this talk, the focus will be on the tailoring of the spin dynamics of artificially built atomic arrangements on surfaces, such as few-atom clusters or 2D spin arrays. Making use of time- and spin-resolved STM techniques [6] we will show how the spin dynamics can be tuned by the choice of the substrate, the chemical identity and number of the adatoms as well as their geometric arrangement [7-9]. In particular it will be demonstrated that the symmetry of the adatom arrangements can have a decisive influence on the spin dynamics. This can be explained by the effect of anisotropic indirect exchange interactions which can lead to a destabilization of the spin system for atomic arrangements exhibiting a lower symmetry [9].

References:
[1] D. Serrate et al., Nature Nanotechnology 5, 350 (2010).
[2] M. Steinbrecher et al., Nature Commun. 9, 2853 (2018).
[3] A. A. Khajetoorians et al., Nature Physics 8, 497 (2012).
[4] H. Kim et al., Science Advances 4, eaar5251 (2018).
[5] A. A. Khajetoorians et al., Science 339, 55 (2013).
[6] S. Krause and R. Wiesendanger, in: Atomic- and Nano-Scale Magnetism, ed.: R. Wiesendanger, Springer Series in Nano Science and Technology, Springer Nature Switzerland (2018), p. 221.
[7] A. A. Khajetoorians et al., Science 332, 1062 (2011). [8] J. Hermenau et al., Nature Commun. 8, 41467 (2017).
[9] J. Hermenau et al., Nature Commun. (2019), in press.

We demonstrate that the interplay of Zeeman and spin-orbit coupling fields in a 1D wire leads to an equilibrium spin current that manifests itself in a spin accumulation at the wire ends with a polarization perpendicular to both fields. This is a universal property that occurs in the normal and superconducting state independently of the degree of disorder. We find that the edge spin polarization transverse to the Zeeman field is strongly enhanced in the superconducting state when the Zeeman energy is of the order of the superconducting gap. By calculating the space resolved magnetization response of the wire we demonstrate that the transverse component of the spin at the wire edges can be much larger than the one parallel to the field. This result generalizes the well established theory of the Knight-shift in superconductors to the case of finite systems.

In this presentation I will review our recent experiments on semiconducting nanowires (NWs) and carbon nanotubes (CNTs) in close proximity to one or two superconducting contacts. To perform well-controlled transport spectroscopy in such systems, we introduce two new device types, namely InAs NWs with atomically precise crystal phase engineered in-situ grown axial tunnel barriers, and CNTs fully encapsulated in hexagonal Boron Nitride, both contacted by bulk superconductors. In the latter devices we obtain very long and clean quantum dots, with multiple subgap states and a non-monotonic magnetic field dependence of the critical supercurrent. For the NW systems, we use the axial tunnel barriers to probe, for example, the formation of the superconducting proximity gap in a long NW segment, or the hybridization of Andreev-type bound states (ABSs) with quantum dot states. We also have studied the ABSs spectroscopically in magnetic field. We believe that these device architectures will be crucial for investigating and characterizing the large variety of new topologically trivial and non-trivial subgap states expected to form in such systems.

Acknowledgment: This work has been done by the following list of contributors in alphabetic order: G. Abulizi, A. Baumgartner, D. Chevallier, R. Delagrange, K. A. Dick, O. Faist, G. Fülöp, R. Haller, C. Jünger, S. Lehmann, M. Nilsson, A. Pally, J. Ridderbos, L. Sorba, T. Taniguchi, C. Thelander, J. Ungerer, K. Watanabe and V. Zannier. I am very grateful to them! The work has financially been supported by the Swiss NSF, SNF-QSIT, SNI, H2020 project QuantEra SuperTop and FET-open AndQC.

Majorana bound states (MBSs) are non-Abelian quasiparticles in vortices of topological superconductors. They have been identified as building blocks for topologically protected qubits where quantum state evolution within a degenerate ground state manifold proceeds via braiding of distant MBSs. We present a theory of coherent time-dependent electron tunneling from a metal tip into a Corbino geometry topological Josephson junction where four MBSs rotate. The time averaged tunneling conductance exhibits, as a function of bias voltage between the tip and the Josephson junction, distinctive conductance peaks that are separated by h/(4TJ) (where TJ is the time period of the system Hamiltonian). This separation is a result of interference between processes where electron tunneling between the tip and the junction interrupts the rotation of the MBS after different number of round trips. The interference effect is shown to be a direct consequence of two non-commuting braiding operations---a rotation of the four MBSs along the Josephson junction and a tunneling assisted rotation---reflecting the non-Abelian nature of MBSs. This mechanism of non-Abelian state evolution actively utilizes electron tunneling that changes the fermion occupation number parity of the system rather than avoiding it while the MBSs are spatially decoupled from each other and hence are not fused physically. The proposed scheme would provide an alternative route for detecting non- Abelian statistics.

The coupling of lattice deformations to electronic properties in graphene -the most popular Dirac material- as gauge fields has given rise to a vast field of theoretical, experimental results and applications. In this talk we will review the situation in the novel 3D Dirac semimetals with especial focus on the interplay between strain and and the chiral and gravitational anomalies.

Recently, the introduction of impurity states in the superconducting gap has received a lot of attention. Indeed, the search of a new superconducting state called topological superconductivity is strongly based in the combination of doping classical (s-wave) superconductors with magnetic impurities that arrange spins in a chiral fashion. Magnetic adatoms can be considered as impurities that weaken the binding of superconducting Cooper pairs leading to impurity levels in the gap: so-called Yu- Shiba-Rusinov (YSR) states. By using scanning tunneling microscopy (STM), we study magnetic impurities on superconducting surfaces revealing the orbital properties of the YSR states associated with them [1]. We also present the first results of controlled single-atom manipulation to assemble a chain of Cr atoms on a Bi2Pd superconductor. The influence of the atoms on the superconducting electronic structure is revealed as well as the interactions at work. The dependence of the electronic structure on the interatomic distance between two Cr atoms is thoroughly explored revealing Cr-Cr interactions mediated by the superconductor for the first time [2]. Such magnetic impurities on different substrates allow us to explore many- body effects and exotic phenomena in different experimental spin systems giving an understanding on the parameters on each system.

References:
[1] Choi, D.-J. et al. Mapping the orbital structure of impurity bound states in a superconductor. Nat. Commun. 8, 15175 (2017).
[2] Choi, D.-J. et al. Influence of Magnetic Ordering between Cr Adatoms on the Yu-Shiba-Rusinov States of the β-Bi2Pd superconductor, Phys. Rev. Lett., 120(16), 167001 (2018).

The effective manipulation of antiferromagnets (AF), through the recently proposed and discovered Néel spin-orbit torque, has turned AFM into active elements of spintronic devices. This, coupled with the inherent topological properties of their band-structure, makes topological antiferromagnetic spintronics a fruitful area of exploration. A key remaining challenging aspect is the observation of the Néel order parameter. Here we show that the anomalous Hall effect can play a key role, which over a century, continue to play a central role in condensed matter research for their intriguing quantum-mechanical, relativistic, and topological nature. Here we introduce a microscopic mechanism whose key component is an asymmetric spin-orbit coupling originating from lowered symmetry positions of atoms in the crystal. Based on first-principles calculations, we demonstrate a pristine form of this crystal Hall effect in a room-temperature rutile antiferromagnet RuO2 whose Hall conductivity reaches 1000 S/cm. While a collinear antiferromagnetic order of magnetic moments alone would generate zero Hall response, the effect arises when combining it with the spin-orbit coupling due to non-magnetic atoms occupying non-centrosymmetric crystal positions. The crystal Hall effect can also explain recent measurements in a chiral antiferromagnet CoNb3S6, and we predict it in a broad family of collinear antiferromagnets.

The Dzyaloshinskii-Moriya interaction (DMI) has its origin in the spin-orbit correction of the Heisenberg exchange interactions. It is a rank-one first-order effect that favours canting of neighbouring spins and it is thus one of the interactions that govern long-range non-collinear spin textures. The DMI is behind the chirality of spin spirals that leads magnetic domain wall movement [1].

Since the DMI is forbidden by inversion symmetry, it often appears localized at surfaces and interfaces. Moreover, in multilayer heterostructures the interactions present at each interface are combined additively [2]. This property opens the door to controlling the chirality of domain wall displacement at selected buried interfaces by epitaxial growth. For example, experiments suggest that the strong DMI at a Pt/Co interface may be nearly halved if the Co film is (pseudomorphically) grown by intercalation between Pt and graphene [3].

In this talk I will show how the principle of additivity of interfacial DMI breaks down in the limit of ultrathin films. Taking the Pt/Co/Graphene heterostructure as case study, we have carried out DFT calculations of spin spirals [4] and obtained the interatomic DMI vectors, D, by fitting a model hamiltonian. We find that the in-plane component of D has a non-trivial oscillatory behaviour up to 3ML of Co, which is likely to modulate the Néel-type domain wall velocity. Interestingly, we find a significant out-of-plane component of D, compatible with a more complex chiral spin structure.

References:
[1] Z. Luo, et al., Science 363, 1435-1439 (2019)
[2] C. Moreau-Luchaire, et al, Nat. Nanotech. 11, 444 (2016)
[3] F. Ajejas, et al., Nano Lett. 18, 5364-5372 (2018)
[4] M. Heide, G. Bihlmayer, and S. Bluegel, Physica B, 404. 2678-2683 (2009)

We develop the theory of quantum friction in two-dimensional topological materials. The quantum drag force on a metallic nanoparticle moving above such systems is sensitive to the nontrivial topology of their electronic phases, shows a novel distance scaling law, and can be manipulated through doping or via the application of external fields. We use the developed framework to investigate quantum friction due to the quantum Hall effect in magnetic field biased graphene, and to topological phase transitions in the graphene family materials. It is shown that topologically nontrivial states in two-dimensional materials enable an increase of two orders of magnitude in the quantum drag force with respect to conventional neutral graphene systems.

Magnetic proximity effect at the interface between magnetic and topological insulators (MIs and TIs) is considered to have great potential in spintronics as, in principle, it allows realizing the quantum anomalous Hall and topological magneto-electric effects (QAHE and TME). Although an out-of-plane magnetization induced in a TI by the proximity effect was successfully probed in experiments, first-principles calculations reveal that a strong electrostatic potential mismatch at abrupt MI/TI interfaces creates harmful trivial states rendering both the QAHE and TME unfeasible in practice. Here on the basis of recent progress in formation of planar self-assembled single layer MI/TI heterostructure [1], we propose a conceptually new type of the MI/TI interfaces by means of density functional theory calculations [2]. By considering MnSe/Bi2Se3, MnTe/Bi2Te3, and EuS/Bi2Se3 we demonstrate that, instead of a sharp MI/TI interface clearly separating the two subsystems, it is energetically far more favorable to form a built-in interface via insertion of the MI film inside the TI’s surface quintuple layer (e.g., Se–Bi–Se–[MnSe]–Bi–Se) where it forms a bulk-like MI structure. This results in a smooth MI-to-TI connection that yields the interface electronic structure essentially free of trivial states. Our findings open a new direction in studies of the MI/TI interfaces and restore their potential for the QAHE and TME observation.

The supports by the Spanish Ministerio de Economia y Competitividad (FIS2016-75862-P), Academic D.I. Mendeleev Fund Program of Tomsk State University (8.1.01.2018), Saint Petersburg State University grant for scientific investigations (15.61.202.2015), and Fundamental Research Program of the State Academies of Sciences, line of research III.23 are acknowledged.

References:
[1] T. Hirahara et al. Nano Lett. 17, 3493 (2017).
[2] S.V. Eremeev, M.M. Otrokov, E.V. Chulkov, Nano Lett. 18, 6521 (2018).

We introduce and study a minimum two-orbital Hubbard model on a triangular lattice, which captures the key features of both the trilayer ABC-stacked graphene-boron nitride heterostructure and twisted transition metal dichalcogenides in a broad parameter range. Our model comprises first- and second-nearest neighbor hoppings with valley-contrasting flux that accounts for trigonal warping in the band structure. For the strong-coupling regime with one electron per site, we derive a spin-orbital exchange Hamiltonian and find the semiclassical ground state to be a spin-valley density wave. We show that a relatively small second-neighbor exchange interaction is sufficient to stabilize the ordered state against quantum fluctuations. Effects of spin- and valley Zeeman fields as well as thermal fluctuations are also examined.

The van-der-Waals fabrication method allows the realization of novel types of superconducting devices. In our work, we use van der Waals semiconductors as tunnel barriers separating the superconductor NbSe2 and normal counter electrodes. The devices exhibit a hard gap [1], which allows tracking sub-gap excitations such as vortex-bound states [2]. Van-der-Waals barriers often carry defects, which function as atomic-sized quantum dots. We find that in certain cases, a barrier defect may hybridize with the underlying superconductor, and form Andreev bound states (ABS), which are observed as sub-gap features in tunneling experiments, analogous to ABS observed in nanowires. We take advantage of the special properties of ultrathin NbSe2, where spin-orbit coupling keeps the superconducting gap stable upon application of parallel magnetic fields in the few Tesla regime. This gap stability allows the following of sub-gap features. These are found to split in energy, with a lower branch meeting at zero at a finite field. Such spectral evolution, associated with a singlet ground state, is consistent with a small charging energy. We further describe the observation of zero-energy states appearing at finite magnetic fields, and discuss their relation to the strong spin orbit term in the system [3].

References:
[1] T. Dvir, F. Massee, L. Attias, M. Khodas, M. Aprili, C. H. L. Quay, and H. Steinberg. Spectroscopy of bulk and few-layer superconducting NbSe2 with van der Waals tunnel junctions. Nature Communications 9, 598 (2018).
[2] T. Dvir, M. Aprili, C. H. L. Quay, and H. Steinberg. Tunneling into the Vortex State of NbSe2 with van der Waals Junctions. Nano Lett. 18, 7845-7850 (2018).
[3] T. Dvir, C. H. L. Quay, M. Aprili, and H. Steinberg. Singlet ground state of Andreev bound states in van der Waals heterostructures. In Preparation (2019).

A nanoscale gap between two metallic nanoparticles is an ideal platform to exploit the interplay between electron currents and photonic excitations. The capability of the metallic gap to enhance the amplitude of the induced plasmonic field produces a variety of non-linear effects [1] which can be exploited in different applications of optoelectronics, such as optical rectification, light emission driven by DC currents, or high-harmonic generation, among others. Furthermore, in ultranarrow gaps, tunneling of electrons at optical frequencies has been found to screen the plasmonic bonding gap resonance, and activate a new distribution of optical modes characterized by optical charge transfer [2].

Here we address the complex dynamics of photoelectrons driven by single-cycle optical pulses in nanoscale gaps. By solving Schrödinger equation within the framework of Time-Dependent Density Functional Theory (TDDFT), the currents of the electrons photoemitted across the gap can be monitored, identifying ultrafast electron bursts where electron quiver occurs when the amplitude of the induced field at the plasmonic gap is reversed within the optical cycle. The properties of the amplitude and carrier-envelope phase (CEP) of the incident pulse, together with the gap length determine the complex electron dynamics [3].

Experimental measurements of the current autocorrelations for pairs of such pulses with controlled relative delay between them, confirms the ultrafast dynamics of the photoelectrons in the gap and its complexity.

References:
[1] D.C. Marinica et al., "Quantum plasmonics: nonlinear effects in the field enhancement of a plasmonic dimer". Nano Lett. 12, 1333 (2012).
[2] K.J. Savage et al., "Revealing the quantum regime in tunneling plasmonics". Nature 491, 574 (2012).
[3] G. Aguirregabiria et al., "Dynamics of electron-emission currents in plasmonic gaps induced by strong fields". Faraday Discussions DOI: 10.1039/c8fd00158h (2019).

We revisit the problem of an interacting quantum wire subject to spin-orbit interaction and transverse magnetic field. Previous studies showed that the spin sector of the model is equivalent to that of a spin chain with uniform DM interaction (D) in a transverse magnetic field (h), the ground state of which contains two ordered Ising phases and a critical Tomonaga-Luttinger liquid phase, depending on the ratio D/h. Importantly, the charge sector of the wire is a gapless Tomonaga-Luttinger liquid. We show that a quantum wire with an open boundary supports a zero-energy bound state localized at the edge, provided that the spin sector of the problem is massive. We argue that as long as the charge sector is gapless, the wire is in a topological phase and that the bound state is a Majorana zero mode, and discuss physical implications of this finding.

Higher-order topological insulators recently emerged as a new class of materials exhibiting topologically protected states in at least two dimensions below that of the bulk. In the important case of electronic 2D higher-order topological insulators, non-trivial 0D corner modes arise which can accommodate quasiparticles with a fraction of the electron charge. Charge fractionalization is well-known for the strongly-correlated electron systems in the fractional quantum Hall effect and Luttinger liquids. Here, we experimentally realize quasiparticles with fractional charge in the absence of electron-electron interactions. Specifically, by carefully tuning the design of an artificial electronic lattice in a scanning tunneling microscope, we create a higher-order topological insulator based on the 2D Su-Schrieffer-Heeger (SSH) lattice. Scanning tunneling spectroscopy and wavefunction mapping reveal protected corner modes that carry a fraction of the unit charge. Our results provide a first step to incorporate quasiparticles with fractional charge into electronic devices for quantum computation.