Strunz, J. Wiedenmann, C. Fleckenstein, L. Lunczer, W. Beugeling, V. Shekhar, N. Traverso Ziani, S. Shamim, J. Kleinlein, H. Buhmann, B. Trauzettel, and L. Molenkamp, arXiv 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. 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. 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 MoS 2 [1].

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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. 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 MoS 2 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.

Roch, Guillaume Froehlicher and Nadine Leisgang. References: [1] Jonas G. 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. Roch et al. 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.

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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. 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 Edelberg et al.

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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 []. In the presence of ac driving the transfer of electrons between distant dots takes place by means of photo-assisted virtual transitions [].

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[]. References: [1] M. Busl et al.

## Topological Insulators and Topological Superconductors | Princeton University Press

Lett, , Braakman et al. Stano, et al. B 92, Gallego-Marcos, et al. B 93, ; F. Gallego-Marcos et al. B, 99, Greentree et al. B, 70, Ban et al. Niklas et al. 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 [].

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. Steinbrecher et al. Khajetoorians et al. Kim et al. Krause and R. Wiesendanger, in: Atomic- and Nano-Scale Magnetism, ed. Hermenau et al. 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.

## Topological insulators and topological superconductors

Abulizi, A. Baumgartner, D. Chevallier, R. Delagrange, K. Dick, O. Faist, G. Haller, C. Lehmann, M. Nilsson, A. Pally, J. Ridderbos, L. Sorba, T. Taniguchi, C.

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Thelander, J. Ungerer, K. Watanabe and V. I am very grateful to them! 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. Mapping the orbital structure of impurity bound states in a superconductor. 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. In this talk I will show how the principle of additivity of interfacial DMI breaks down in the limit of ultrathin films.

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. Moreau-Luchaire, et al, Nat. Ajejas, et al. Heide, G. Bihlmayer, and S. Bluegel, Physica B, We develop the theory of quantum friction in two-dimensional topological materials. Tungsten ditelluride, which is one of the transition metal dichalcogenide materials, is classified as a semimetal and conducts electricity like metals in bulk form. An applied voltage drives the transition between these phases, which vary with temperature and electron concentration.

In superconducting materials, electrons flow without resistance generating no heat. Cava, a professor of chemistry at Princeton University. This edge current is governed by the spin of the electrons rather than by their charge, and electrons of opposite spin move in opposite directions. This topological property is always present in the material at cold temperatures.

This quantum spin Hall effect persisted up to a temperature of about kelvins Materials with these qualities are sought for spintronic and quantum computing devices. Although the topological insulating phenomenon was observed at up to kelvins, the superconducting behavior in the new work occurred at a much lower temperature of about 1K. This material has the advantage of entering the superconducting state with one of the lowest densities of electrons for any 2-D superconductor.

The MIT team built the experimental devices, carried out the electronic transport measurements at ultra-cold temperatures, and analyzed the data at the Institute. Jarillo-Herrero notes that this discovery that monolayer tungsten ditelluride can be tuned into a superconductor using standard semiconductor nanofabrication and electric field effect techniques was simultaneously realized by a competing group of collaborators, including Professor David Cobden at the University of Washington and Associate Professor Joshua Folk at the University of British Columbia.

These fermions have yet to be found as elementary particles in nature but can emerge in certain superconducting materials near absolute zero temperature. A magnetic gap is also needed for pinning the Majorana mode at a location. To this end, one can envision designing complex, dynamically tunable networks of superconducting quantum-spin-Hall edge states by electrostatic means. MIT News Office. Browse or. Browse Most Popular. Deploying drones to prepare for climate change Troy Van Voorhis named head of the Department of Chemistry A new way to corrosion-proof thin atomic sheets MIT Solve selects cohort of tech entrepreneurs Technology transfer award recognizes system that detects concealed objects on people A new act for opera Funding for sustainable concrete cemented for five more years An interdisciplinary approach to accelerating human-machine collaboration.

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