Quantum Designer Physics

The spin-momentum-locked surface states of topological insulators [1] provide a fertile ground for novel quantum physics including topological superconductivity and associated Majorana fermions [2, 3]. In this talk, I will present our recent experiments to utilize state-of-the-art devices based on bulk-insulating topological insulators and discuss such physics as planar Hall effect [4], nanowire quantum transport, and proximity-induced superconductivity.

References:
[1] Y. Ando, Topological Insulator Materials, J. Phys. Soc. Jpn. 82, 102001 (2013).
[2] Y. Ando and L. Fu, Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials, Annu. Rev. Condens. Matter Phys. 6, 361 (2015).
[3] M. Sato and Y. Ando, Topological superconductors: a review, Rep. Prog. Phys. 80, 076501 (2017).
[4] A. A. Taskin, H. F. Legg, F. Yang, S. Sasaki, Y. Kanai, K. Matsumoto, A. Rosch, and Y. Ando, Planar Hall effect from the surface of topological insulators, Nature Commun. 8, 1340 (2017).

The possibility to induce and control superconductivity at the surface of insulating materials by means of electrostatic gating is a breakthrough development that has taken place during the last decade. Probing the nature of the gate-induced superconducting state is however extremely difficult, because the superconducting surface –buried between the gate electrode and the insulating material itself– is difficult to access with most experimental probes. This is why, until now, the superconducting properties of these systems have been studied almost exclusively by means of transport measurements. Here, I will discuss our work on gate induced superconductivity on exfoliated MoS2 crystals. I will first show that superconductivity survives down to the ultimate level of an individual monolayer. I will then discuss tunneling spectroscopy measurements in the gate-induced superconducting state that we succeeded in doing using suitably nano-fabricated devices. The measurements allow us to determine the density of states in the superconducting regime as a function of carrier density, and demonstrate that the superconducting state is not fully gapped. We find that throughout the carrier density range investigated, a finite sub-gap density of states vanishing linearly at low energy is present, indicative of unconventional superconductivity. I will point to different aspects of the measurements and discuss which indications they provide as to the nature of the superconducting state.

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, I will show that 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. The easy accessibility of the flat bands, the electrical tunability, and the bandwidth tunability though twist angle may pave the way towards more exotic correlated systems, such as quantum spin liquids or correlated topological insulators.

Due to the charge neutral and localized nature of surface Majorana modes, detection schemes rely mostly on local spectroscopy or interference through the Josephson effect. In this work we consider surface corrections to the orbital magnetization in the superconducting state and study the orbital magnetic response of a two-dimensional Majorana cone localized at the surface of a class DIII Topological Superconductors. For a field parallel to the surface we find that the field tilts the Majorana bands and an additional diamagnetic current appears beyond a critical threshold field $H^*$, that leads to a jump in the magnetization. The value of $H^*$ is expected to fall in the Meissner phase for highly doped small band gap Dirac insulators with odd-parity superconductivity. In a spherical configuration Majorana modes always show a finite coupling to arbitrary small applied fields. Beside the tilting, a curvature induced coupling appears between occupied and empty levels that leads to a finite response. Meissner screening results in an excess diamagnetic zero-field susceptibility $propto 1/H^*$ , that acquires a universal character in finite systems that are topologically equivalent to a sphere.

Triggered by the large number of experiments on superconductivity in the presence of spin-dependent fields we have developed a quasiclassical framework for studying transport properties in these systems. In this talk I will focus on both, ballistic and diffusive systems and discuss effects related to the interplay between superconductivity, intrinsic spin-orbit coupling (SOC) and spin-splitting fields. I will demonstrate that these spin-dependent fields convert singlet pair correlations into triplet ones. This conversion manifests itself through magneto-electric effects, in full analogy with the charge/spin coupling in normal systems. In diffusive systems, I will discuss the superconducting counterparts of the Spin-Hall (SHE) and the Edelstein (EE) effects, which are at the basis of the anomalous phase shift φ₀ in the current-phase relation of Josephson junctions with SOC.

I will also discuss spectral and transport properties of ballistic Josephson junctixnsand show that within the semiclassical approach all sub-gap, spectral and transport, properties depends only on two parameters, namely, a magnetic phase shift and a local precession axis for the spin. In particular these two parameters determine the topological state of the junction.

We study Cooper-pair and single-electron tunneling across a Josephson junction in a hybrid nanowire-based double quantum dot. Under microwave irradiation photon assisted tunneling is observed both in absence and presence of an axial magnetic field. Applying field demonstrates a transition from 2e to 1e periodic Coulomb blockade. The respective energy splittings at charge state degeneracies are extracted following the positions of microwave-induced transitions as a function of frequency. Corresponding quantum transport at finite field shows an extended zero bias conductance peak in gate voltage. Results are consistent with single-electron tunneling between two zero energy modes residing on each side of the junction.

Coupling a semiconductor with strong spin-orbit interaction to a superconductor enables the creation of Majorana zero modes (MZMs), the fundamental building blocks of topological quantum bits (qubits). Using a two-dimensional electron gas (2DEG) as the semiconducting material offers the possibility to create complex networks that are required for the proposed qubit schemes. Among the 2DEG candidates, InSb is particularly promising due to a large Landé g-factor, strong spin-orbit interaction and a high mobility. Studying the normal state properties of these InSb 2DEGs, we find peak mobilities of 180,000 cm²/Vs, a spin-orbit length of ̴200 nm, and phase coherent transport across long distances (> 10 um). We couple these high-quality 2DEGs to a superconductor (NbTiN) to create Josephson junctions (JJs) and thus provide the first demonstration of induced superconductivity in InSb 2DEGs. We find that the supercurrent in these JJs is gate-tuneable and can be carried over distances of several microns. Measurements of multiple Andreev reflections and excess current indicate a large induced superconducting gap ( ̴1meV) along with reasonably high transparency (0.7-0.8). The application of a large magnetic field in the plane of the sample results first in a reduction and then in a re-entrance of the supercurrent, compatible with a Zeeman-induced 0-π transition in the JJs. These results are an important step forward in using InSb 2DEGs for Majorana physics, especially in light of recent proposals for the generation of phase-controllable MZMs in planar JJs.

Andreev bound states (ABSs) in hybrid semiconductor-superconductor nanowires can have near-zero energy in parameter regions where band topology predicts trivial phases. This surprising fact has been used to challenge the interpretation of a number of transport experiments in terms of non-trivial topology with Majorana zero modes (MZMs). I will discuss how this ongoing ABS versus MZM controversy is fully clarified when framed in the language of non-Hermitian topology, the natural description for open quantum systems. This change of paradigm allows us to understand topological transitions and the emergence of pairs of zero modes more broadly, in terms of exceptional point (EP) bifurcations of system eigenvalue pairs in the complex plane. Within this framework, I will argue that some zero energy ABSs are actually non-trivial, and share all the properties of conventional MZMs, such as the recently observed 2e²/h conductance quantization. From this point of view, any distinction between such ABS zero modes and conventional MZMs becomes artificial. The key feature that underlies their common non-trivial properties is an asymmetric coupling of Majorana components to the reservoir, which triggers the EP bifurcation.

Ge/Si core/shell nanowires are proposed candidates for observing Majorana fermions where a hard superconducting gap is essential for topological protection at zero energy. In double quantum dots, we observe shell filling of new orbitals and corresponding Pauli spin blockade. In nanowires with superconducting Al leads we create a Josephson junction via proximity-induced superconductivity. A gate-tuneable supercurrent is observed with a maximum of ~60 nA. We identify two different regimes: Cooper pair tunnelling via multiple subbands in the open regime, while near depletion a supercurrent is carried by single-particle levels of a quantum dot operating in the few-hole regime.

Secondly, we create ambipolar quantum dots in silicon nanoMOSFETs. In recent devices, we have investigated the conformity of aluminium, titanium and palladium nanoscale gates by means of transmission electron microscopy (TEM). Subsequently, we have defined low-disorder quantum dots with Pd gates. Finally, we have made depletion-mode hole quantum dots in undoped silicon. We use fixed charge in a SiO₂/Al₂O₃ dielectric stack to induce a 2DHG at the Si/SiO₂ interface. This depletion-mode design avoids complex multilayer architectures requiring precision alignment and allows directly adopting best practices already developed for depletion dots in other material systems.

Proximity-induced superconductivity is a core concept of expressing exotic superconducting properties. Furthermore, when combined with Cooper pair splitting (CPS), generalized Majorana fermion is predicted to emerge. Here we study the CPS proximity-induced superconductivity using an Al/InAs double nanowire/Al junction having two top gates. The normal conductance shows plateaus of quantized values as functions of two gate voltages, reflecting the conductance quantization of the respective nanowires. Measurement of supercurrent at various bias points of conductance plateaus reveals the switching current due to CPS to the two nanowires significantly larger than that due to local pair tunneling to the respective nanowires, indicating dominant contributions from the CPS superconductivity. Additionally, from the dependence on the number of nanowire channels, the observed CPS is assigned to electron-electron interactions or Tomonaga-Luttinger liquid effects, not electrostatic energy. These results may expand the flexibility in engineering proximity-induced superconductivity and help to realize Majorana Fermions and parafermions without magnetic fields.

Semiconducting quantum wires defined within two-dimensional electron gases and strongly coupled to thin superconducting layers have been extensively explored in recent experiments as promising platforms to host Majorana bound states. We study numerically such a geometry, consisting of a quasi-one-dimensional wire coupled to a disordered three-dimensional superconducting layer [1-5]. In the strong-coupling limit of a sizable proximity-induced superconducting gap, all transverse subbands of the wire are significantly shifted in energy relative to the chemical potential of the wire. For the lowest subband, this band shift is comparable in magnitude to the spacing between quantized levels that arise due to the finite thickness of the superconductor (which typically is ~500 meV for a 10-nm thick layer of Aluminum); in higher subbands, the band shift is much larger. Additionally, the width of the system, which is usually much larger than the thickness, and moderate disorder within the superconductor have almost no impact on the induced gap or band shift. We provided a detailed discussion of the ramifications of our results, arguing that a huge band shift and significant renormalization of semiconducting material parameters in the strong-coupling limit make it challenging to realize a topological phase in such a setup, as the strong coupling to the superconductor essentially metallizes the semiconductor. This metallization of the semiconductor can be tested experimentally through the measurement of the band shift.

References:
[1] C. Reeg, D. Loss, and J. Klinovaja, Phys. Rev. B 96, 125426 (2017).
[2] C. Reeg, J. Klinovaja, and D. Loss, Phys. Rev. B 96, 081301 (2017).
[3] C. Reeg, C.Schrade, J. Klinovaja, and D. Loss, Phys. Rev. B 96, 081301 (2017).
[4] C. Reeg, D. Loss, and J. Klinovaja, Phys. Rev. B 97, 165425 (2018).
[5] C. Reeg, D. Loss, and J. Klinovaja, Beilstein Journal of Nanotechnology 9, 1263 (2018).

In this talk, I present a unified framework for Majorana-based fault-tolerant quantum computation with Majorana surface codes. All logical Clifford gates are implemented with zero-time overhead. This is done by introducing a protocol for Pauli product measurements with tetrons and hexons which only requires local four-Majorana parity measurements. An analogous protocol is used in the fault-tolerant setting, where tetrons and hexons are replaced by Majorana surface code patches, and parity measurements are replaced by lattice surgery, still only requiring local few-Majorana parity measurements. To this end, we discuss twist defects in Majorana fermion surface codes and adapt the technique of twist-based lattice surgery to fermionic codes. Majorana surface codes can be used to decrease the space overhead and stabilizer weight compared to their bosonic counterparts.

Numerous signatures of possible Majorana zero modes in nanowire devices have now been observed in different labs in the form of zero-bias transport anomalies. Their interpretation, however, remains under debate. The core of the issue lies in determining whether the anomalies are associated to zero modes with a high degree of non-locality, characteristic of Majorana zero modes of topological origin. Determining the degree of wave function overlap is a hard experimental problem. Here we discuss the physically relevant measure of non-locality, and show how it can be faithfully estimated using a local measurement on one end of the nanowire. The precision of the estimator is quantified for homogeneous and inhomogeneous nanowires, with sharp and smooth potential and pairing profiles. The latter has been argued to host so-called trivial zero modes. We show that even for these states the estimator is useful, and provides bounds to their degree of non-locality.

Illumination of three level atoms (λ-systems) by detuned lasers can pump electrons into a coherent superposition of hyperfine-split levels which can no longer absorb light. Because fluorescent light emission is then suppressed, the coherent superposition is known as a dark state. We report an all-electric analogue of this destructive interference effect in a carbon nanotube quantum dot. A dark state is in this case a coherent superposition of states with opposite angular momentum which is fully decoupled from either the drain or the source leads. The emergence of dark states impacts the current-voltage characteristics, where missing current steps are observed depending on the sign of the applied source-drain bias. Our results demonstrate for the first time coherent-population trapping by all-electric means in an artificial atom. The existence of the dark states relies on the (quasi) valley degeneracy of the CNT and on the particular coupling to the metallic leads. The difference between the tunneling phases to the two electrodes is the most relevant parameter of the theory. Besides characterizing the dark states, this phase difference determines also the precession dynamics of the pseudospin associated to the orbital degeneracy. This theory predicts current suppression with a specific gate and bias dependence which accurately matches the experimental results.

Spins in semiconductors offer themselves for spintronics and are leading candidates for quantum computing. The spin relaxation time T₁ sets a fundamental upper bound for the coherence time and e.g. the spin readout fidelity. More than 15 years ago, it was predicted that at low magnetic fields, the dominant mechanism is the coupling to the nuclear spins, where the relaxation becomes isotropic and the scaling changes to T₁ ∝ B^-3. We establish these predictions in a GaAs quantum dot [1], by measuring T₁ over a large range of fields – made possible by lower temperature and control of the field direction – and report a T₁ = 57 ± 15 s, setting a record for the spin lifetime in a nanostructure.

It is tempting and elegant to think of the spin alone as the carrier of quantum information. However, the spin is hosted by an electron with charge and quantum orbitals. The spin-orbit and hyperfine interactions depend on these orbitals, and this can be exploited to control spin relaxation and electric-dipole spin resonance for coherent manipulation. We present a non-invasive technique [2] which delivers the orientation angle of the orbitals in the plane as well the z-confinement, based on a model of flux threading of a 3D dot [3] and measurements of the xy-orbital spectrum in an in-plane magnetic field of varying magnitude and direction.

From the extracted z-confimenent and z-electric field, we can calculate the Rashba and Dresselhaus spin-orbit strengths. This gives good agreement with values from the T₁ anisotropy as well as independent experiments [4], where we demonstrated how the persistent spin helix can be stretched with top and back gate voltages. Further, the spin helix symmetry can be exploited to derive a closed-form expression for the weak localization magnetoconductivity [5] – the paradigmatic signature of spin-orbit coupling. We present a reliable method to extract all parameters from fits to the new expression, obtaining very good agreement with other experiments. This provides experimental confirmation of the new theory, and advances spin-orbit coupling as powerful resource in emerging quantum technologies.

References:
[1] Hyperfine-phonon spin relaxation in a single-electron GaAs quantum dot, L. C. Camenzind, L. Yu, P. Stano, J. Zimmermann, A. C. Gossard, D. Loss and D. M. Zumbühl, arXiv:1711.01474.
[2] Spectroscopy of Quantum-Dot Orbitals with In-Plane Magnetic Fields, L. C. Camenzind, L. Yu, P. Stano, J. Zimmermann, A. C. Gossard, D. Loss and D. M. Zumbühl, arxiv:1804.00162.
[3] Gate-defined quantum dot in a strong in-plane magnetic field: orbital effects, P. Stano, C.-H. Hsu, L. C. Camenzind, L. Yu, D. M. Zumbühl and D. Loss, arXiv:1804.00128.
[4] Stretchable persistent spin helices in GaAs quantum wells, F. Dettwiler, J. Fu, S. Mack, P. J. Weigele, J. C. Egues, D. D. Awschalom and D. M. Zumbühl, Phys. Rev. X 7, 031010 (2017).
[5] Symmetry Breaking of the Persistent Spin Helix in Quantum Transport, P. J. Weigele, D. C. Marinescu, F. Dettwiler, J. Fu, S. Mack, J. C. Egues, D. D. Awschalom,and D. M. Zumbühl, arxiv:1801.05657.

The interest in holes as potential spin qubits has strongly increased in the past few years. Due to the intrinsically large spin orbit coupling, hole spin qubits should be electrically tunable and show high Rabi frequencies. Indeed in 2016, the first hole spin qubit with Rabi frequencies as high as 70MHz was demonstrated [1]. Here we present the first Ge hole spin qubit. The qubit is formed in a Ge hut-wire [2] double quantum dot. Presumably due to the even stronger spin orbit coupling in Ge, Rabi-frequencies of 140 MHz were reached [3]. Ramsey experiments revealed dephasing times exceeding 130 ns. Finally, by measuring the spin relaxation time of holes in Ge hut wires an upper bound for the coherence time could be extracted [4].

References:
[1] R. Maurand et al., Nature Communications 7, 13575 (2016).
[2] J. J. Zhang et al., Phys. Rev. Lett. 109, 085502 (2012).
[3] H. Watzinger et al., arXiv:1802.00395.
[4] L. Vukušić et al., arXiv:1803.01775.

Electron spins are excellent candidates for solid state quantum computing due to their exceptionally long quantum coherence times, which is a result of weak coupling to environmental degrees of freedom. However, this isolation comes with a cost, as it is difficult to coherently couple two spins in the solid state, especially when they are separated by a large distance. Here we combine a large electric-dipole interaction with spin-orbit coupling to achieve spin-photon coupling [1]. Vacuum Rabi splitting is observed in the cavity transmission as the Zeeman splitting of a single spin is tuned into resonance with the cavity photon. We achieve a spin-photon coupling rate as large as g_s/2π = 10 MHz, which exceeds both the cavity decay rate κ/2π = 1.8 MHz and spin dephasing rate γ/2π = 2.4 MHz, firmly anchoring our system in the strong-coupling regime [2]. Moreover, the spin-photon coupling mechanism can be turned off by localizing the spin in one side of the double quantum dot. These developments in quantum dot cQED, combined with recent demonstrations of high-fidelity two-qubit gates in Si, firmly anchor Si as a leading material system in the worldwide race to develop a scalable quantum computer [3].

References:
1. Mi et al., Science 355, 156 (2017).
2. Mi et al., Nature 555, 599 (2018).
3. Zajac et al., Science 359, 439 (2018).

Silicon and its close relative germanium form the core materials of the well-established microelectronics industry. Lately, they have enabled remarkable progress also in the raising field of quantum technologies, generating at the same time new fundamental questions and technological challenges. In fact, there is still a lot to know about these well-known semiconducting materials and their potential for quantum applications. In this talk, I will focus on hole-based systems made from silicon and silicon-germanium nanostructures. I will present recent experiments dealing with spin-related effects, and discuss their implications for hole-spin qubits and, more generically, quantum spintronic devices.

Majoranas in semiconductor nanowires can be probed via various electrical measurements. Tunnel spectroscopy have revealed zero-bias peaks in the differential conductance. When the existence of Majoranas is firmly established, the next challenge is to build Majorana qubits. We discuss the different qubit schemes and report on our first building blocks. The promise of Majorana qubits is that the error rate is very low yielding a relatively simple scalable architecture.

Recent papers:
Nature 556, 74 (2018), DOI: 10.1038/nature26142 (arxiv.org/pdf/1710.10701.pdf)
Nature Reviews Materials 3, 52 (2018), DOI: 10.1038/s41578-018-0003-1 (arxiv.org/pdf/1707.04899.pdf)

In this talk I will present recent results in the field of “quantum designer physics” using 2D van der Waals (vdW) heterostructures. The first result relates to proximity-induced spin-orbit interaction (SOI) in stacks of WSe2-graphene. The second to the role of edge relative to bulk current in graphene-hBN superlattices.

Large spin-orbital proximity effects have been predicted in graphene interfaced with a transition-metal dichalcogenide layer. Whereas clear evidence for an enhanced spin-orbit coupling has been found at large carrier densities, the type of SOI and its relaxation mechanism remained unknown. We have found an increased SOI close to the charge neutrality point (DP) in graphene, where topological states are expected to appear. Doping-dependent measurements have shown that the spin relaxation of the in-plane spins is largely dominated by a valley-Zeeman term and that the intrinsic spin-orbit coupling plays a minor role in spin relaxation.

In graphene devices, several reports have pointed to an unequal current distribution, which can be deduced from the so-called Fraunhofer pattern in graphene-based Josephson junctions. In particular, a large edge-current contribution appeared in some cases close to the DP, leading to the suggestion that a gap might open. We have recently looked into the current distribution using the same approach in devices that show a superlattice structure due to lattice mismatch between graphene and hBN. We also found an excess edge current not at the DP, but rather at the points where van Hove singularities (vHS) form. We argue that the effective transport time in the bulk increases at the vHSs, due to the suppression of the Fermi velocity, while the current continues to flow along the edges.

At the moment the two experiments discussed before are not directly connected. However, we aim to study Josephson junctions with proximity-induced spin-orbit interaction next.

Acknowledgment: This work has been done by the following list of contributors in alphabetic order: A. W. Cummings, R. Delagrange, J. H. Garcia, D. I. Indolese, M. Kedves, P. Makk, T. Taniguchi, J. Wallbanks, K. Watanabe, S . Zihlmann. I am very grateful to them! The work has financially been supported by the Swiss NSF, graphene flagship, ERC, SNF-QSIT, SNI and further organizations.

A pair of electron and hole across the interface of semiconductor heterostructure can form a bound quantum state of the interlayer exciton. In a coupled interface between atomically thin van der Waals layers, the Coulomb interaction of the interlayer exciton increases further. Coulomb drag effect is a mesoscopic effect which manifests many-body interactions between two low-dimensional systems, which has served an extremely useful probe the strong correlation in quantum systems. In this presentation, we will first discuss observing interlayer exciton formation in semiconducting transition metal dichalcogenide (TMDC) layers. Unlike conventional semiconductor heterostructures, charge transport in of the devices is found to critically depend on the interlayer charge transport, electron-hole recombination process mediated by tunneling across the interface. We demonstrate the enhanced electronic, optoelectronic performances in the vdW heterostructures, tuned by applying gate voltages, suggesting that these a few atom thick interfaces may provide a fundamental platform to realize novel physical phenomena. In addition, spatially confined quantum structures in TMDC can offer unique valley-spin features, holding the promises for novel mesoscopic systems, such as valley-spin qubits. In the second part of the presentation, we will discuss magneto-exciton condensation. In this electronic double layer subject to strong magnetic fields, filled Landau states in one layer bind with empty states of the other layer to form an exciton condensate. Driving current in one graphene layer generates a near-quantized Hall voltage in the other layer, resulting in coherent exciton transport. In our experiment, capitalizing strong Coulomb interaction across the atomically thin hBN separation layer, we realize a superfluid condensation of magnetic-field-induced excitons. For small magnetic fields (the BEC limit), the counter-flow resistance shows an activation behavior. On the contrary, for large magnetic fields limit where the inter-exciton separation decreases (the BCS limit), the counter-flow resistance exhibits sharp transitions in temperature showing characters of Berezinskii-Kosterlitz-Thouless (BKT) transition. Furthermore, complete experimental control of density, displacement and magnetic fields in our graphene double layer system enables us to explore the rich phase diagram of several superfluid exciton phases with the different internal quantum degrees of freedom.

Graphene and other two-dimensional materials have rapidly established themselves as promising building blocks for spintronic applications. Due to weak spin-orbit coupling and a lack of hyperfine interaction with the predominant zero-spin isotope 12C, the spin lifetime in graphene was expected to be in the microsecond or even millisecond range. However, in contrast to these expectations, experiments have demonstrated spin lifetimes typically below 10 ns. In the first part of the talk, I will introduce the two main theoretical models that are currently being considered to explain such a fast spin relaxation. They are unique to graphene and involve either resonant scattering with magnetic centers or spin-pseudospin coupling and Rashba spin-orbit interaction [1]. I will then discuss recent experimental efforts aiming at highlighting their peculiarities; in particular, at verifying whether the spin relaxation is anisotropic, which would be the hallmark of the presence of a dominant spin orbit field [1,2]. These experimental efforts can also provide valuable information of spin-orbit proximity effects and spin Hall effects, allowing us to demonstrate highly anisotropic spin relaxation in graphene/transition-metal dichalcogenide heterostructures [3,4] and large spin-to-charge conversion in graphene/Pt devices [5]. In the second part of the talk, I will discuss the generation, propagation and detection of hot carriers in graphene using purely electrical means. I will show that because typical carrier cooling times can be similar to spin lifetimes, it is possible to implement nonlocal hot-carrier injection and detection methods analogous to those used for spin [6]. In addition, I will present evidence that the spin propagation can be reinforced (suppressed) by the presence of hot carriers [7].

References:
[1] W. Han et al Nature Nanotech. 9, 794–807 (2014).
[2] B. Raes et al., Nature Commun. 7, 11444 (2016); ibid, Phys. Rev. B 95, 085403 (2017).
[3] A. Cummings et al., Phys. Rev. Lett. 119, 206601 (2017).
[4] L. A. Benítez et al. Nature Phys. 14, 303 (2018).
[5] W. Savero-Torres, et al., 2D Mater. 4, 041008 (2017).
[6] J. F. Sierra et al., Nano Lett. 15, 4000 (2015).
[7] J. F. Sierra et al., Nature Nanotech.y 13, 107–111 (2018).

This talk reports on recent studies aimed at the implementation of robust magnetism and/or strong spin-orbit coupling (SOC) to graphene grown on metallic substrates. In the first part, we will discuss the observation of quasi-freestanding graphene with strong exchange and SO splittings achieved simultaneously (a so-called magneto-spin-orbit graphene). In Ref. [1], using spin- and angle-resolved photoemission spectroscopy (ARPES) it has been found that the Dirac state in the Au-intercalated graphene on Co(0001) experiences a giant spin splitting, while being by no means distorted due to interaction with the substrate. Scanning tunneling microscopy (STM) data suggest that the peculiar reconstruction of the Au/Co(0001) interface is responsible for the exchange field transfer to graphene. Calculations based on density functional theory (DFT) reveal the splitting to stem from the combined action of the Co thin film induced in-plane exchange field and Au-induced Rashba SOC.

The second part of the talk is devoted to a combined STM, (spin-)ARPES and DFT study of graphene/Pb/Ir(111), Ref [2]. Pb intercalation between graphene and Ir(111) reduces the coupling to the substrate in such a way that its corrugation becomes negligible and distortions of the linear dispersion largely disappear, as compared to graphene/Ir(111), while graphene's sublattice symmetry is maintained. Remarkably, the spin-orbit splittings induced by the proximity of the Ir(111) surface are preserved after Pb intercalation in a wide energy range. It is further shown that the Pb/Ir(111) surface induces a complex spin texture in graphene bands with both in-plane and out-of-plane components, that are fingerprints of the Rashba and Kane-Mele couplings, respectively.

References:
[1] A.G. Rybkin, A.A. Rybkina, M.M. Otrokov, O.Yu. Vilkov, I.I. Klimovskikh, A.E. Petukhov, M.V. Filianina, V.Yu. Voroshnin, I.P. Rusinov, A. Ernst, A. Arnau, E.V. Chulkov, A.M. Shikin. Nano Letters 18, 1564 (2018).
[2] M.M. Otrokov, I.I. Klimovskikh, F. Calleja, A.M. Shikin, O.Yu. Vilkov, A.G. Rybkin, D. Estyunin, S. Muff, H. Dil, A. L. Vázquez de Parga, R. Miranda, H. Ochoa, F. Guinea, J.I. Cerdá, E.V. Chulkov, A. Arnau. 2D Materials 5, 035029 (2018).

In crystalline materials that break inversion symmetry, light pulses can generate DC currents via photogalvanic effects. In this talk I will describe a surprising topological aspect of this effect that occurs when the light is circularly polarized: in chiral nodal semimetals, the magnitude of the current is exactly quantized in terms of fundamental constants only. This occurs because this response function measures the monopole Berry flux of the node, a rare example of quantization in a gapless system at finite frequency. I will discuss how to measure the effect both in chiral Weyl semimetals, as well as in more complex chiral multifold band crossings that have been recently predicted. I will also show how this quantized response can be distinguished from other circular intraband currents that are unavoidable in metallic systems.

Topology a mathematical concept became recently a hot topic in condensed matter physics and materials science. One important criteria for the identification of the topological material is in the language of chemistry the inert pair effect of the s-electrons in heavy elements and the symmetry of the crystal structure [1]. Beside of Weyl and Dirac new fermions can be identified compounds via linear and quadratic 3-, 6- and 8- band crossings stabilized by space group symmetries [2]. Binary phoshides are the ideal material class for a systematic study of Dirac and Weyl physics. Weyl points, a new class of topological phases was also predicted in NbP, NbAs. TaP, MoP and WP2. [3-7]. In magnetic materials the Berry curvature and the classical AHE helps to identify interesting candidates. Magnetic Heusler compounds were already identified as Weyl semimetals such as Co2YZ [8-10], in Mn3Sn [11,12] and Co3Sn2S2 [13].

The Anomalous Hall angle helps to identify even materials in which a QAHE should be possible in thin films. Besides this k-space Berry curvature, Heusler compounds with non-collinear magnetic structures also possess real-space topological states in the form of magnetic antiskyrmions, which have not yet been observed in other materials [14].

References:
[1] Bradlyn et al., Nature 547 298, (2017) arXiv:1703.02050.
[2] Bradlyn, et al., Science 353, aaf5037A (2016).
[3] Shekhar, et al., Nature Physics 11, 645 (2015).
[4] Liu, et al., Nature Materials 15, 27 (2016).
[5] Yang, et al., Nature Physics 11, 728 (2015).
[6] Shekhar, et al. preprint arXiv:1703.03736.
[7] Kumar, et al., Nature Com. , preprint arXiv:1703.04527.
[8] Kübler and Felser, Europhys. Lett. 114, 47005 (2016).
[9] Chang et al., Scientific Reports 6, 38839 (2016).
[10] Kübler and Felser, EPL 108 (2014) 67001 (2014).
[11] Nayak, et al., Science Advances 2 e1501870 (2016).
[12] Nakatsuji, Kiyohara and Higo, Nature 527 212 (2015).
[13] Liu, et al. preprint arXiv:1712.06722.
[14] Nayak, et al., Nature 548, 561 (2017).

We show that a conformal anomaly in Weyl/Dirac semimetals generates a bulk electric current perpendicular to a temperature gradient and the direction of a background magnetic field. The associated conductivity of this novel contribution to the Nernst effect is fixed by a beta function associated with the electric charge renormalization in the material.

Antiferromagnetic spintronics considers the active manipulation of the antiferromagnetic order parameter in spin-based devices. An additional concept that has emerged is that antiferromagnets provide a unifying platform for realizing synergies among three prominent fields of contemporary condensed matter physics: Dirac quasiparticles and topological phases. Here spintronic devices made of antiferromagnets with their unique symmetries will allow us to control the emergence and to study the properties of Dirac/Weyl fermion topological phases that are otherwise principally immune against external stimuli. In return, the resulting topological magneto-transport phenomena open the prospect of new, highly efficient means for operating the antiferromagnetic memory-logic devices. We discuss how these topological phases emerge and how their robustness depends on the relative orientation of the Neel order parameter that can be manipulated by Neel spin-orbit torques. Their natural excitations are in the THz but with the additional consideration that they can now be directly tuned.

Majorana states in atomic-scale magnet-superconductor hybrid systems have recently become of great interest because they can encode topological qubits and ultimately provide a new direction in topological quantum computation [1,2]. First, we will focus on artificially fabricated 1D atomic chains of magnetic Fe adatoms on a high spin-orbit coupled superconducting Re(0001) substrate using STM-based atom-manipulation techniques at T=350 mK. Spin-polarized STM measurements [3] reveal the presence of non-collinear spin textures, i.e. spin spiral ground states, stabilized by interfacial Dzyaloshinskii-Moriya interactions [4] as found earlier for self-assembled biatomic Fe chains on Ir(001) [5]. Tunneling spectra measured spatially resolved on the Fe-atom chain on Re(0001) reveal the evolution of the spatially and energetically resolved local density of states as well as the emergence of zero-energy bound states at the chain ends above a critical chain length. Based on the exact knowledge of the geometrical, electronic, and spin structure of the magnetic chain – superconductor hybrid system, the experimental results can be compared rigorously with ab-initio and model-type tight-binding calculations supporting the interpretation of the spectroscopic signatures at the ends of the chains as Majorana bound states [6].

In the second part, the atomic-scale design of more complex network structures for Majorana state manipulation, including braiding operations will be discussed. Moreover, we will also address recent experimental and theoretical studies of monolayer topological superconductivity and chiral Majorana edge modes in model-type 2D magnetic islands on elemental superconductors [7]. Finally, the prospects for studies of Majorana states in skyrmion – superconductor hybrid systems [8] will be highlighted.

References:
[1] J. Alicea et al., Nature Phys. 7, 412 (2011).
[2] S. Nadj-Perge et al., PRB 88, 20407 (2013); H.-Y. Hui et al., Sci. Rep.. 5, 8880 (2015).
[3] R. Wiesendanger, Rev. Mod. Phys. 81, 1495 (2009).
[4] A. A. Khajetoorians et al., Nature Commun. 7, 10620 (2016).
[5] M. Menzel et al., Phys. Rev. Lett. 108, 197204 (2012).
[6] H. Kim et al., Science Advances 4, eaar5251 (2018).
[7] A. Palacio-Morales et al. (2018), submitted.
[8] N. Romming et al., Science 341, 6146 (2013).

In recent years, a renewed interest in magnetic impurities in superconductors was driven by their potential as a new platform for topological superconductivity. Recent scanning tunneling spectroscopy measurements on a superconducting monolayer of lead (Pb) with nanoscale cobalt islands, have revealed puzzling quasiparticle in-gap states [1] which demand a better understanding of two-dimensional superconductivity in presence of spin-orbit coupling and magnetism. Tantalizingly, the quasiparticle states evoke general topologically protected states which haven't yet been explored in two-dimensional superconductors. Thus motivated, we theoretically study a model of two-dimensional s-wave superconductor with a fixed configuration of exchange field and spin-orbit coupling terms allowed by symmetry.

Using analytics and exact diagonalization of tight-binding models, we find that a vortex-like defect in the Rashba spin-orbit coupling binds a single Majorana zero-energy (mid-gap) state. Importantly, in contrast to the case of a superconducting vortex [2], our spin-orbit defect does not create a tower of in-gap excitation states. Our findings match the puzzling features observed in the experiment, particularly: (1) preservation of superconducting gap, and (2) short localization length of the zero-energy state compared to the superconductor coherence length [3]. Additionally, these properties indicate that the system realizes the coveted well-protected Majorana states, which is a key requirement for a potential realization of a topological qubit. We also discuss how the quasiparticle states of the defect relate to the states of superconductors on top of magnetic textures, such as skyrmions.

References:
1. G. Ménard et al., Nature Comm 11, 1013 (2017).
2. C. Caroli, P.G. de Gennes, and J. Matricon, Physics Letters 9, 307(1964).
3. G. Ménard, A. Mesaros et al., in preparation.

1T-TaS₂ is a charge density wave layered TMD material that was thoroughly studied in the early 1970's. It is unique among the 2D CDW materials in that it has an insulating ground state. It was understood as an example of a cluster Mott insulator: the lattice distortions create 13 Ta site "star of David" clusters which form a triangular lattice with one electron per cluster. Mott insulators are expected to from local moments which eventually order magnetically, but no sign of the local moment or magnetism has ever been found. We proposed that the local moments may have formed a quantum spin liquid, an exotic and elusive state proposed by Anderson in 1973. Recently this proposal received strong support by the observation of a linear T term in the thermal conductivity by Matsuda's group (arXiv 1803.06100), which we interpret as being due to a spinon Fermi surface in a charge insulator. We support this interpretation with DMRG calculations, showing peaks at 2k_F in the spin structure factor. We discuss the prospects of finding high temperature superconductor by doping monolayer samples by gating.

In this talk, I will describe two kinds of magnetic phenomena on the edge of topological systems. In the first part of the talk, I consider the properties of a localized magnetic impurity that is strongly coupled to a quantum spin Hall (QSHI) edge. It will be shown that the impurity can lead to anti-resonances in the transmission coefficient, which can have a dramatic effect on the transport properties of the edge channel. When the electrons at the Fermi energy of the edge channel are on resonance, interaction effects lead to a temperature dependent broadening of the anti-resonance for both repulsive and moderately attractive interactions in the channel. Consequences for QSHI in proximity to a superconductor (a system that is relevant for the search of Majorana bound states) will be also discussed , time permitting. In the second part of the talk, the spin excitations localized at the edge of a finite chain of half-integer spin magnetic adatoms are characterized using the time-dependent density matrix renormalization algorithm. It is argued that the understanding of such excitations allows to construct an effective low-energy model that can account for the spatial location of the Kondo resonances observed in recent experiments.