Low-energy spin excitations in any long-range ordered magnetic system in the absence of magnetocrystalline anisotropy are gapless Goldstone modes emanating from the ordering wave vectors. In helimagnets, these modes hybridize into the so-called helimagnon excitations. We employ neutron spectroscopy supported by theoretical calculations to investigate the magnetic excitation spectrum of the isotropic Heisenberg helimagnet ZnCr₂Se₄ with a cubic spinel structure, in which spin-3/2 magnetic Cr³⁺ ions are arranged in a geometrically frustrated pyrochlore sublattice. Apart from the conventional Goldstone mode emanating from the (0,0,qh) ordering vector, low-energy magnetic excitations in the single-domain spiral phase show soft helimagnon modes with a small energy gap of ∼ 0.17 meV, emerging from two orthogonal wave vectors (qh,0,0) and (0,qh,0) where no magnetic Bragg peaks are present. We term them pseudo-Goldstone magnons, as they appear gapless within linear spin-wave theory and only acquire a finite gap due to higher-order quantum-fluctuation corrections. To further investigate anisotropic low-temperature properties of the cubic spinel helimagnet ZnCr₂Se₄ we combined neutron scattering, thermal conductivity, ultrasound velocity, and dilatometry measurements. In an applied magnetic field, neutron spectroscopy shows a complex and non-monotonic evolution of the spin-wave spectrum across the quantum-critical point that separates the spin-spiral phase from the field-polarized ferromagnetic phase at high fields. A pseudo-Goldstone spin gap vanishes at this quantum critical point, restoring the cubic symmetry in the magnetic subsystem. The anisotropy imposed by the spin helix has only a minor influence on the lattice structure and sound velocity but has a much stronger effect on the heat conductivities measured parallel and perpendicular to the magnetic propagation vector. The thermal transport is anisotropic at T = 2 K, highly sensitive to an external magnetic field, and likely results directly from magnonic heat conduction. We also report long-time thermal relaxation phenomena, revealed by capacitive dilatometry, which are due to magnetic domain motion related to the destruction of the single-domain magnetic state, initially stabilized in the sample by the application and removal of magnetic field. Our results are likely universal for a broad class of helimagnetic materials in which a discrete lattice symmetry is spontaneously broken by the magnetic order.

In the first part of this talk a protocol is discussed for preparing a spin chain in a generic many-body state in the asymptotic limit of tailored nonunitary dynamics. The dynamics require the spectral resolution of the target state, optimized coherent pulses, engineered dissipation, and feedback. As an example, we discuss the preparation of an entangled antiferromagnetic state, and argue that the procedure can be applied to chains of trapped ions or Rydberg atoms. In the second part we propose a protocol which achieves fast adiabatic dynamics in a Landau-Zener problem by implementing a quantum-non-demolition (QND) measurement of the spin. In the limit where the effective dynamics can be described by a Born-Markov master equation, the QND measurement induces an effective dephasing and dissipative dynamics which enforce adiabaticity. We show that the resulting fidelity of the adiabatic transfer significantly increases with the strength of the QND coupling. We then discuss perspectives of applying these dynamics for quantum annealers.

Nuclear magnetic resonance (NMR) is successfully applied in many fields such as biology, chemistry, and condensed matter physics. The technique is non-invasive and reveals rich information about the underlying structure of the sample. However, due to NMR's limited sensitivity, the samples typically must be macrosco-pic in size, preventing the detection of single molecules or of two-dimensional materials. This limitation calls for a new approach.
Nitrogen-vacancy (NV) centers in diamond can be applied as quantum sensors and present an alternative path to magnetic resonance on the nanoscale. They are optically addressable and possess exceptionally long coherence times, even at ambient conditions. With the creation of shallow NV centers, it is now possible to detect the NMR signal on the nanoscale [1,2]. The measurement of a single proton spin [3] and of a monolayer of a two-dimensional material [4] shows the impressive sensitivity of the method. Nevertheless, the technique is still in its infancy and several challenges, such as low spectral resolution and the lack of colocalization between sample and sensor, need to be addressed.
In my presentation I will discuss how these limitations can be overcome by designing the quantum sensor system. Particularly I will describe the use of long-lived quantum memories based on single nuclear spins in diamond. Combining these quantum memories with the quantum sensors enables us to improve the spectral resolution by four orders of magnitude. This leads to the chemical shift detection and thereby identification of molecules on the nanoscale [5]. Another crucial aspect is the colocalization of sample and sensor spins, which we are addressing by nanofabricating the diamond surface.
In the talk I will also present our efforts to couple the quantum sensors to magnetic molecules and to two-dimensional metal-organic frameworks (MOF). These chemically tunable systems can be employed as sen-sor spins. Due to the reduced sample to sensor distance a significantly enhanced sensitivity can be expected.
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[3] A.Sushkov et al. PRL 113 (2014) 197601
[4] I. Lovchinsky et al. Science 355 (2017) 6324
[5] N. Aslam et al. Science 357 (2017) 67

Excitonic insulator is a quantum coherent phase resulting from the formation of a macroscopic population of electron-hole pairs. Because crystal structural symmetries are broken at the transition temperature T_c, it is difficult to determine whether a particular transition is of excitonic or structural origin. The nature of transition for the candidate material Ta₂NiSe₅ (T_c = 328K) is currently under debate, with both excitonic [1] and structural [2] explanations proposed. We report Raman-scattering results on Ta₂NiSe₅ to explore its critical excitonic fluctuations above T_c and emergent coherence below T_c [3]. The overdamped excitonic mode in the quadrupolar symmetry channel softens above T_c, while the optical phonon modes show no softening behavior. Moreover, the softening of the acoustic phonon mode [4] can be accounted for by its coupling to the excitonic mode, i.e. intrinsic ferroelastic instability is absent. On cooling, coherent superposition of band states at the gap edge gradually emerges. From these results, we demonstrate that the phase transition of Ta₂NiSe₅ is of excitonic nature. We further show that sulfur doping suppresses the excitonic contribution to ordering [5].
For Ta₂NiS₅, we identify a phase transition induced by ferroelastic instability at 120K, and a sharp in-gap exciton mode.
[1] Y. Wakisaka et al., Phys. Rev. Lett. 103, 026402 (2009); Y. F. Lu et al., Nat. Commun. 8, 14408 (2017)
[2] E. Baldini et al., arXiv: 2007.02909; A. Subedi, Phys. Rev. Materials 4, 083601 (2020)
[3] M. Ye et al., arXiv: 2102.07912 (2021); P. A. Volkov et al., arXiv: 2007.07344 (2020)
[4] A. Nakano et al., Phys. Rev. B 98, 045139 (2018)
[5] P. A. Volkov et al., arXiv: 2104.07032 (2021)

Topological solitons in condensed matter are stable excitations characterised by a non-zero “winding number” or topological charge. Their particle-like dynamics render them ideal for information-handling applications, including cryogenic memory and synaptic logic devices. Recently, combining topological solitons in chiral magnets (skyrmions) and superconductors (vortices) has attracted considerable theoretical attention, largely due to the possibility of creating a topological superconductor by imprinting the non-collinear exchange field from skyrmions onto s-wave Cooper pairs. Vortex cores in the resultant p_x + i p_y superconducting phase would harbour the Majorana fermions which have been so keenly sought for building quantum computers with increased resilience to environmental decoherence. However, it has so far proven extremely challenging to develop materials which simultaneously exhibit superconductivity and topological spin textures at low temperature.
I will outline the design principles for a new class of “hybrid” multilayer materials, which superpose a thin superconducting film onto a chiral magnetic layer. In such heterostructures, the characteristic length scales of both superconducting and magnetic orders may be tuned via the multilayer geometry and an applied magnetic field. Following the hierarchy ξ < r_sk < λ (where ξ, r_sk, and λ are the coherence length, skyrmion radius, and penetration depth, respectively), we stabilise skyrmions with r_sk ≈ 50nm in a IrFeCoPt multilayer and demonstrate that their stray field nucleates antivortices in a neighbouring 25nm Nb film. The antivortices principally reveal themselves via an emergent magnetic moment antiparallel to the external field, but also influence the bulk flux dynamics in an applied current or field gradient. Although the stray field dominates the interaction between chiral magnet and superconductor in our films, we additionally detect a weak Rashba-Edelstein coupling in exchange-coupled heterostructures which enhances antivortex formation.
I will discuss methods to further optimise the skyrmion-(anti)vortex coupling in such multilayers, with a view towards eventual quantum computational applications. Beyond the skyrmion-vortex example described here, the general concept of linking topological solitons from distinct quantum phases promises to facilitate spatially heterogeneous magnetoelectric coupling at nanometer length scales, with fascinating consequences for the hybrid soliton dynamics and functionality.

The compounds Sr₃Cr₂O₈ and Ba₃Cr₂O₈ are insulating dimerized antiferromagnets with Cr⁵⁺ magnetic ions. These spin-1/2 ions form hexagonal bilayers with a strong intradimer antiferromagnetic interaction that leads to a singlet ground state and gapped triplet states. The Cr⁵⁺ ions surrounded by oxygen ions in a tetrahedral coordination are Jahn-Teller active. I will discuss the effect on the structural and magnetic properties of Sr₃Cr₂O₈ by introducing chemical disorder upon replacing Sr by Ba. Mixed compounds Ba_3-xSr_xCr₂O₈ with x = 2.9 and x = 2.8 were grown in a four-mirror-type optical floating-zone furnace. There is a distinct suppression of the orbital-lattice fluctuation regime with increasing Ba content. This stands in contrast to the linear behavior exhibited by unit cell volumes, atomic positions, and intradimer spin-spin exchange interactions. The magnetic properties of these compounds were studied by magnetization measurements. Inelastic neutron-scattering measurements on Ba_0.1Sr_2.9Cr₂O₈ were performed in order to determine the interaction constants and the spin gap for x = 2.9. The intradimer interaction constant is found to be about 4% smaller than that of pure Sr₃Cr₂O₈, whereas the interdimer exchange interaction is smaller by 7%. These results indicate a noticeable change in the magnetic properties by a random substitution effect.

Molecule-based switching and light-addressable systems have been in focus to harness spintronics and quantum technology applications. Spin-crossover (SCO) complexes featuring spin-state-dependent physical property variations are one of the pillars of molecular magnetism and a prominent example of spin-switchable material. Such complexes exhibiting bistable spin-state switching characteristics in the bulk and spin-state dependent conductance switching at the single-molecule level are desirable for developing molecule-based memory and spintronics, respectively, applications [1,2]. In the first part, a concise and systematic overview of - from the bulk-state to single-molecule level - functional SCO complexes studied for device applications will be presented [3,4]. In the second part, proposals to develop luminescent lanthanoid (Ln(III)) complexes as light-addressable systems for quantum technology applications will be presented. Lanthanoid complexes feature sharp inter-configurational f-f electronic transitions, which are well isolated from the environment by the outer 5d and 6s orbitals, and nuclear spin-levels with long-lived spin lifetimes. These features combined with the possible physical property tuning via molecular engineering approaches render lanthanoid complexes suitable for implementing quantum information processing (QIP) schemes. While lanthanoid molecule-based qubits and qdits have been reported in the literature [5,6] direct optical addressing of nuclear spin-based hyperfine qbits of lanthanoid complexes are yet to be reported. To begin with, we have prepared a series of Eu(III) complexes and shown optical polarisation of nuclear spin-levels in them and obtained optical coherence lifetime (T_2,opt) in the μs range. To progress further, we propose to synthesize isotopically enriched Ln(III) complexes following isotopologues chemistry [7]. This will enable us to precisely engineer the hyperfine splitting of nuclear spin-levels (¹⁵¹Eu vs. ¹⁵³Eu), tune the optical properties - for example, emission wavelength and lifetime - and improve the coherence lifetime by reducing the environmental fluctuations arising from phonon and spin baths. We also propose to study the optically addressable Ln(III) molecular systems on the surface and in resonant cavities to harness the utility of the systems as qbits and quantum memories [8,9] and use two-color laser pulses as the excitation source of Ln(III)-based f-f transitions to eliminate detection issues arising from light scattering [10]. Overall, we propose to develop a new and unexplored field of light-addressable Ln(III) molecular systems [11] as hyperfine qbits and qdits for quantum technology applications.
[1] K. S. Kumar and M. Ruben, Coord. Chem. Rev. 2017, 346(1), 176-205.
[2] K. S. Kumar and M. Ruben, Angew. Chem. Int. Ed. 2020, DOI: 10.1002/anie.201911256.
[3] K. S. Kumar, M. Studniarek, B. Heinrich, J. Arabski, G. Schmerber, M. Bowen, S. Boukari, E. Beaurepaire, J. Dreiser, and M. Ruben, Adv. Mater. 2018, 30(11), 1705416.
[4]. E. Burzuri, A. Garcia-Fuente, V. Garcia-Suarez, K. S. Kumar, M. Ruben, J. Ferrer, and HSJ Van Der Zant, Nanoscale, 2018, 10, 7905-7911.
[5] C. Godfrin, A. Ferhat, R. Ballou, S. Klayatskaya, M. Ruben, W. Wernsdorfer, and F. Balestro, Phy. Rev. Lett. 2017, 119, 187702.
[6] A. Gaita-Arino, F. Luis, S. Hill, and E. Coronado, Nat. Chem. 2019, 11, 301-309.
[7] W. Wernsdorfer and M. Ruben, Adv. Mater. 2019, 31, 1806687.
[8] D. D. Awschalom, R. Hanson, J. Wrachtrup, and B. B. Zhou, Nat. Phot. 2018, 12, 516-527.
[9] A. I. Lvovsky, B. C. Sanders, and W. Tittel, Nat. Phot. 2009, 3, 706-714.
[10] Y-M. He et al. Nat. Phy. 2019, 15, 941-946.
[11] K. S. Kumar, D. Serrano, A. Nonat, B. Heinrich, L. Karmazin, L. Charbonniere, P. Goldner and M. Ruben, Nat. Commun. (Revised final version submitted) arXiv:2006.09831.

Although the normal-state electronic structure of Sr₂RuO₄ is known with exceptional precision, even after two decades of research, the symmetry of its certainly unconventional superconducting state is under strong debate, e.g., the long-time favoured spin-triplet p_x ± i p_y state is ruled out by recent NMR experiments [1]. However, in general time-reversal-symmetry breaking (TRSB) superconductivity indicates complex two-component order parameters. Probing Sr₂RuO₄ under uniaxial stress offers the possibility to lift the degeneracy between such components [2]. One key prediction for Sr₂RuO₄, a splitting of the superconducting and TRSB transitions under uniaxial stress has not been observed so far. I will show results of muon spin relaxation (μSR) measurements on Sr₂RuO₄ placed under uniaxial stress, wherein a large stress-induced splitting between the onset temperatures of superconductivity and TRSB was observed [3]. Moreover, at high stress beyond the Van Hove singularity, a new spin density wave ordered phase was detected for the first time. In order to perform μSR measurements under uniaxial stress, a custom piezoelectric based pressure cell was developed [4]. This cell is going to be useful for a range of other materials, in which the Fermi surface or magnetic interaction strengths can be tuned leading to strong modifications of the electronic state.
[1] A. Pustogow, et al., Nature 574, 72 (2019); K. Ishida et al., J. Phys. Soc. Jpn. 89, 034712 (2020)
[2] C. Hicks, et al., Science 344, 283 (2014)
[3] V. Grinenko, S. Ghosh et al., arXiv:2001.08152, accepted in Nature Physics
[4] S. Ghosh et al., Review of Scientific Instruments 91, 103902 (2020)

A wave function exposed to measurements undergoes pure state dynamics, with deterministic unitary and probabilistic measurement induced state updates, defining a quantum trajectory. For many-particle systems, the competition of these different elements of dynamics can give rise to a scenario similar to quantum phase transitions. However, due to the stochastic nature of the wave function this type of phase transition does not manifest itself in common observable averages, obtained from the statistically averaged density matrix, and have instead mainly been observed in the dynamics entanglement. Hence, they are often termed entanglement transitions.
Here we establish a novel type of entanglement transition between a regime of logarithmic entanglement growth, and a quantum Zeno regime obeying an area law, in continuously monitored fermion dynamics. We analyze the phase transition from to different perspectives:
(i) numerical simulations of monitored lattice fermions and
(ii) an analytical field theory for monitored Dirac fermions, interpolating between the microscopic measurement dynamics and the macroscopic observables.
We identify the relevant degrees of freedom for describing the phase transition and show that their dynamics is governed by a non-Hermitian quantum Sine-Gordon model. This yields a physical picture for the phase transition in terms of a depinning from the measurement operator eigenstates induced by unitary dynamics, and places it into the BKT universality class.

The success of superconducting quantum computing (SQC) has so far been largely built upon the transmon qubit. Finding an alternative qubit that drastically outperforms transmon represents one of the most fundamental and exciting frontiers of SQC. The fluxonium qubit stands out as a promising candidate, due to its long coherence times and large anharmonicity. Furthermore, fluxonium can be directly integrated into the existing circuit-QED schemes for scaling. For these reasons, fluxonium is our qubit platform of choice at Alibaba Quantum Laboratory.
In this talk, I will present our design and experiments of a 2D fluxonium circuit, which exhibits high coherence, high tunability and strong coupling. With T₁ > 200 μs at around the sweet spot, we achieve a dielectric loss tangent as low as 1.3 10^-6, and an estimated 1/f flux noise amplitude at best 1.4 μΦ₀/√Hz, both numbers approaching the state of the art. Using a high-bandwidth flux bias, we demonstrate robust qubit reset and readout, together with fast one- and two-qubit gates, thus paving the path toward a fluxonium-based, ultra-high-fidelity multi-qubit processor.

The scanning tunneling microscope (STM), relying on the overlap of wavefunctions of a sharp tip and a conductive sample, has proven to be an ideal tool for both measurement and manipulation of objects on the nanoscale. I will present an overview of our experimental techniques to control and read out the state of nano-objects with a low-temperature STM and their application to single molecule junctions [1]. We have extended the possibilities of conventional STM and built up an STM with a highly efficient light collection setup, which enables us to control and detect electron photon interaction on the nanoscale [2]. Recently, we have provided first evidence of sharp emission lines from individual self-decoupled molecules, avoiding non-radiative processes and quenching by the underlying metal substrate. I will present possibilities of how to further boost the quantum efficiency of electroluminescence of individual quantum objects. In the near future, our already record high external quantum yields will allow us to study statistics of photons emitted from single molecules, i.e. single-photon or entangled photon nature of the emitted light, with the help of a coincidence setup that is currently being finished. Medium-term plans include reversing the path of light, which opens up access to time-dependent processes in individual quantum objects.
[1] Gerhard, L. et al. An electrically actuated molecular toggle switch. Nature Communications 8, 14672 (2017).
[2] Rai, V. et al. Boosting Light Emission from Single Hydrogen Phthalocyanine Molecules by Charging. Nano Lett. 20, 7600-7605 (2020).

Understanding and controlling quantum spins in solids is an exciting scientific endeavor. Besides fundamental interest in non-equilibrium many-spin dynamics, this research is needed for applications in nanomagnetism, spintronics, quantum information, and advanced sensing at nanoscale. The nitrogen-vacancy (NV) centers in diamond constitute a particularly promising platform for many solid-state quantum technologies. I will overview the effort, and present our work on quantum spin dynamics and control of individual electronic and nuclear spins associated with NV centers. I will discuss how controlling and protecting the coherent dynamics of coupled spins enables accurate quantum gates on spin qubits in diamond, and how such gates allow development of the quantum registers with solid-state spin qubits [1]. I will talk about extending this approach into the area of nanoscience, which results in very sensitive nanoscale tomography with single-spin resolution [2], and about using these advances for implementing small/medium-scale quantum registers in diamond [3,4].
[1] T. van der Sar et al., Nature 484, 82 (2012).
[2] T. H. Taminiau et al., Phys. Rev. Lett. 109, 137602 (2012).
[3] T. H. Taminiau et al., Nature Nano. 9, 171 (2014).
[4] M. H. Abobeih et al., Nature 576, 411 (2019).

Many superconducting materials show an interplay of superconductivity, charge density waves and structural phases which can be tuned by chemical doping and hydrostatic pressure. Understanding this interplay is crucial in revealing the microscopic origin of these different phases. In the superconductor BaNi₂As₂ tetragonal, orthorhombic and triclinic structural phases as well as an incommensurate (IC-CDW) and a commensurate charge density wave (C-CDW) are reported. In this study, high quality phosphorus doped BaNi₂(As_1-xP_x)₂ crystals were synthesized with a flux method to apply chemical pressure to the crystals. The crystals were characterized by different experimental methods. In addition, x-ray diffraction (XRD) experiments using a four circle diffractometer were performed to investigate the different electronic and structural phases of BaNi₂(As_1-xP_x)₂. High pressure XRD studies were performed in order to compare the effect of chemical pressure due to phosphorus doping with the effect of hydrostatic pressure. The x-ray investigations confirm the existence of a Immm orthorhombic phase as proposed by Merz et al. [1] by means of the orthorhombic splitting of the (800) Bragg peak. The observed splitting is small (δ ∼ 10^-4) and increases linearly on cooling. The XRD measurements show strengthening of the IC-CDW and orthorhombic phase under phosphorus doping due to the larger temperature window of the phases. In addition, the IC-CDW was found at temperatures higher than the orthorhombic phase with relevant diffuse scattering signal observable up to room temperature. We verified the suppression of the triclinic/commensurable CDW (C-CDW) phase under phosphorus doping as reported by Kudo et al. [2]. However, under hydrostatic pressure BaNi₂As₂ showed a different behavior: The triclinic phase was only slightly suppressed and the initial C-CDW is totally suppressed. In addition, above 7.5 GPa the beginning IC-CDW in the tetragonal/orthorhombic phase is suppressed and a cascade of new superstructures appeared. Under a pressure of 10 GPa, new and much more complicated superstructures emerge.
[1] M. Merz et al., arXiv:2012.05024
[2] K. Kudo et al., PRL 109 (2012) 097002

Electron transfer plays a crucial role in many chemical processes, from photosynthesis to combustion and corrosion. For instance, light-driven charge transfer can be exploited to drive carbon dioxide conversion into chemical fuels, being of enormous relevance to steer a carbon-free energy cycle. However, the effect of electron transfer on the electronic structure of organic molecules and light-harvesting interfaces remains largely unclear, limiting our current understanding of the mechanisms lying at the heart of sunlight-driven chemical transformations. Unveiling these fundamental aspects requires the development of experimental tools allowing the observation of (light-induced) electron transfer down to the single molecule level.
In this talk, I will present a novel imaging approach, based on atomic force microscopy (AFM), allowing mapping the orbital structure of single molecules upon electron transfer. In this way, we unveiled the effects of electron transfer and polaron formation on the single-orbital scale [1]. To understand the light-induced charge transfer process, we introduced a second microscopy technique, which combines an AFM setup with a visible-light source, allowing for the imaging of excitonic wavefunctions with angstrom resolution. Finally, I will show how this novel experimental approach opens for the study of photoexcited states in two-dimensional quantum materials.
[1] L. L. Patera, F. Queck, P. Scheuerer and J. Repp, Nature 566, 245-248 (2019)

The reduction of the dimensions of crystals to the nanometer length scale induces significant deviations in the phonon dispersions and the phonon density of states of nanostructures compared to their bulk counterparts and novel vibrational phenomena emerge. Due to the inherently small scattering volume of nanostructures, however, the determination of their lattice dynamics remains a challenge.
In this talk, I will present recent results on the lattice dynamics of α-phase FeSi₂ nanoislands [1] and nanowires [2], epitaxially grown on Si(111) and Si(110) surfaces, respectively. Iron silicides are a particularly interesting member of the technologically important class of transition metal silicides, since it is the only representative that forms metallic and semiconducting phases. The phonon density of states (PDOS) of the nanostructures was obtained by nuclear inelastic scattering, a technique based on the Mössbauer effect, which is uniquely suitable for the investigation of nanostructures. Additionally, the phonon dispersions and Phonon DOS of α-phase FeSi₂were determined by ab initio calculations. The experimental results reveal a distinct anisotropy of the atomic vibrations along and across the nanowires, which is not present in the nano islands. In both cases, the results can completely be understood by taking into account the specific orientation of the α-FeSi₂ unit cell on the Si surface. Furthermore, both kinds of nanostructures show a distinct damping of the PDOS features upon reduction of the characteristic sizes, which can be understood by modeling of the experimental results with the ab initio calculations.
[1] J. Kalt et al., Phys. Rev. B 101 (2020) 165406
[2] J. Kalt et al., Phys. Rev. B 102 (2020) 195414

The nickelate Pr₄Ni₃O₈ features quasi-two-dimensional layers consisting of three stacked square-planar NiO₂ planes, in a similar way to the well-known cuprate superconductors. Motivated by the discovery of possible superconductivity, herein we have synthesized Pr₄Ni₃O₈ by topotactic reduction of Pr₄Ni₃O₁₀, and report on measurements of powder-neutron diffraction, magnetization and muon-spin rotation (μSR). Although without detectable long-range magnetic order, we observe complex magnetic behaviours which should be intrinsic in Pr₄Ni₃O₈. Pr₄Ni₃O₈ exhibits typical spin-glass behaviour with a distinct magnetic memory effect in the temperature range from 2 to 300 K and a freezing temperature ≈ 68 K. Moreover, the analysis of μSR spectra indicates two magnetic processes characterized by remarkably different relaxation rates: a slowly relaxing signal, resulting from paramagnetic fluctuations of Pr/Ni ions, and a fast-relaxing signal, indicating the presence of short-range correlated interaction. This short-range interaction strengthens substantially below ≈ 70 K. We conclude a complicated spin-freezing process in Pr₄Ni₃O₈ governed by these multiple magnetic interactions. It is possible that the complex magnetism in Pr₄Ni₃O₈ is detrimental to the occurrence of superconductivity.

Strongly correlated electron systems are a natural host for spontaneous electronic symmetry breaking phenomena, which lead to emergent electronic phases often characterized by long-range order and collective behavior. Superconductivity and charge-density-waves are two prime examples of ordered electronic phases seeded by strong interactions, despite their very different macroscopic traits – the former exhibiting dissipationless conduction while in the latter charge motion is often hindered as a result of electrons freezing into a ‘supercrystal’. As in many other fields, our understanding of the mechanisms that promote these collective phenomena requires capturing their formation in the act, as the new phase emerges from a high-symmetry state (in this case, a correlated electron fluid).
In this talk, I will show how resonant soft X-ray scattering can be used to gain unprecedented sensitivity to the formation of charge-density-waves at an early stage. I will discuss two studies, one focused on charge order in the family of copper oxide high-temperature superconductors (cuprates), the other on charge-density-waves in quasi-1D material ZrTe₃.
In the cuprates, using X-ray scattering at the Cu L₃-resonance (~930 eV) we found an electronic ‘Wigner glass’ phase where electrons seemingly organize in a uncommon, ordered phase with broken-translational symmetry but full rotational symmetry. This state underscores the quantum nature of the electronic fluid in these materials and provides one of the missing links to understand the birth of an unconventional superconductor from a Mott insulating state [1].
In ZrTe₃, we used coherent X-ray scattering at the Te M-edge (~630 eV) to visualize the formation of the electronic superlattice and the precursor ‘seeds’ from which charge-density-waves develop into a long range ordered phase in quasi-1D systems. In the same study, we examined the dynamics of density-wave formation using photon correlation spectroscopy and proposed a connection between the mechanisms of CDW formation and the instabilities of the Fermi surface [2].
[1] M. Kang et al., Evolution of charge order topology across a magnetic phase transition in cuprate superconductors, Nature Physics 15 (2019) 335
[2] L. Yue et al., Distinction between pristine and disorder-perturbed charge density waves in ZrTe₃, Nature Communications 11 (2020) 98

The emergence of flat bands and of strongly correlated and superconducting phases in twisted bilayer graphene crucially depends on the interlayer twist angle upon approaching the magic angle. Utilizing a scanning nanoSQUID-on-tip, we attain tomographic imaging of the Landau levels and derive nanoscale high precision maps of the twist-angle disorder in high quality hBN encapsulated devices, which reveal substantial twist-angle gradients and a network of jumps [1]. We show that the twist-angle gradients generate large gate tunable in-plane electric fields, unscreened even in the metallic regions, which drastically alter the quantum Hall state by forming edge channels in the bulk of the samples. The correlated states are found to be particularly fragile with respect to twist-angle disorder. We establish the twist-angle disorder as a fundamentally new kind of disorder, which alters the local band structure and may significantly affect the correlated and superconducting states. The talk will also describe direct imaging of the QH edge states in monolayer graphene revealing their internal structure of counterpropagating equilibrium topological and nontopological currents [2].
[1] A. Uri, S. Grover, Y. Cao, J. A. Crosse, K. Bagani, D. Rodan-Legrain, Y. Myasoedov, K. Watanabe, T. Taniguchi, P. Moon, M. Koshino, P. Jarillo-Herrero, and E. Zeldov, Nature 581, 47 (2020).
[2] A. Uri, Y. Kim, K. Bagani, C. K. Lewandowski, S. Grover, N. Auerbach, E. O. Lachman, Y. Myasoedov, T. Taniguchi, K. Watanabe, J. Smet, and E. Zeldov, Nat. Physics 16, 164 (2020).

Nowadays we know of many gapless electronic phases with conical bands, such as graphene, Dirac semimetals, and Weyl semimetals. Their low-energy excitations resemble truly relativistic particles, creating an interesting analogy between the two branches of modern physics which were until now only loosely connected. This is how condensed matter physicists can now explore low-energy phenomena which were previously thought to occur only in high-energy physics. The key is understanding the physics at a milli-electron-volt scale. To access electronic structures at these low energies, we combine Landau level spectroscopy, infrared spectroscopy at zero magnetic field, and effective Hamiltonian models. Because of their inherent low energy scales, our materials are often easy to tune by external parameters such as temperature, high pressure and magnetic field, and have rich phase diagrams.
I will illustrate our approach for several Dirac and Weyl semimetals focusing on ZrTe₅.

Current quantum computers have relatively high error probabilities per operation. Therefore, any application has to use an extremely small number of operations and ideally be somewhat insensitive to the errors (e.g. decoherence). We discuss the number of operations needed for simulation of the electronic structure problem. We show that the number of operations and the mode of error accumulation seems somewhat favorable for lattice models. Given current limitations of quantum computers it is also important to compare to classical solvers like DMRG to understand at which point a quantum computer can really deliver a speed up of interest. We will also discuss our current work using DMRG and how it connects to our quantum computing goals.

Fully programmable quantum computing and simulation devices have hit several milestones over the past few years, with a massively growing involvement of industrial research from companies such as IBM, Google, and Microsoft. The emerging quantum computing technology promises to be useful for applications such as quantum machine learning, but notably also for intrinsically quantum-mechanical calculations that appear in material science, quantum chemistry, or quantum many-body physics. In this talk, I will show how state-of-the-art quantum hardware performs in this domain of quantum problems. Concretely, I focus on solving the ground state structure of a fermionic Hubbard model on a small cluster of sites and demonstrate that qualitatively and quantitatively accurate results can be obtained. This is enabled by exploiting the symmetries of the problem, employing a hybrid quantum-classical variational algorithm, and a Lanczos-based error mitigation scheme. I will introduce each of these steps in detail and discuss the potential of the general workflow for upscaling.

This lecture begins with the promise of idealised, error corrected, quantum algorithms. With this goal defined, we then outline the contemporary capacity of quantum enhanced processors. Increasing the control and capacity of quantum simulators has resulted in a new class of quantum devices, utilising an iterative classical-to-quantum feedback process. This so-called “variational” approach to quantum computation was formally proven (in the noise-free setting) to represent a universal model of quantum computation. An exciting global research effort to understand the variational model is redefining the field of quantum computation. While the ultimate capacity of variational algorithms remains unknown, these methods represent an attractive approach due to the ease at which these algorithms can be realized experimentally. Contrary to analog quantum simulation, the variational approach forgoes the requirement of realising the targeted Hamiltonian directly in the laboratory, thus allowing the study of a wide variety of previously intractable target models experimentally. This comes at the cost of increased measurements and classical pre- and postprocessing.
The talk should be accessible to graduate students in physics.
- J. Biamonte et al. , Quantum Machine Learning, Nature 549, 195 (2017)
- J. Biamonte, Universal Variational Quantum Computation, arXiv:1903.04500 (2019)
- J. V. Akshay et al. , Reachability Deficits in Quantum Approximate Optimization, Phys. Rev. Lett. 104, 090504 (2020)

In multi-orbital Hubbard models including strong intra-atomic exchange a so-called "Hund's metal" phase is realized that shows, among other hallmarks, typically a strong differentiation in the degree of correlation of the conduction electrons based on their orbital character. This selective physics is also a key player in iron-based superconductors (FeSC), where a wealth of experimental evidences validates this theoretical picture. We will show that at the frontier between this Hund's metal phase and a conventional metal, the electronic compressibility is strongly enhanced or even divergent, and that the FeSC that have a high T_c are placed in our simulations on this frontier. This theoretical evidence of enhanced compressibility at the frontier between a phase with selective correlations and a more conventional metal is found in cuprates. We will outline the main indications for a common scenario of high-T_c superconductivity.

The divergent nematic susceptibility, obeying a simple Curie-Weiss power law over a large temperature interval, is empirically found to be a ubiquitous signature in several iron-based superconductors across their doping-temperature phase diagram. I will discuss the impact of nematicity in the optical response of selected iron pnictide and chalcogenide materials, over a broad spectral range, as a function of temperature and of tunable applied stress, which acts as an external symmetry breaking field. First, I will focus my attention on FeSe where we reveal an astonishing anisotropy of the optical response in the mid-infrared-to-visible spectral range. This bears testimony to an important polarization of the underlying electronic structure, due to an orbital-ordering mechanism, supplemented by orbital selective band renormalization. The far-infrared response of the charge dynamics in FeSe moreover allows establishing the link to the dc resistivity, emphasizing scenarios based on scattering by anisotropic spin-fluctuations. Second, I will offer a comprehensive optical investigation of the optimally hole-doped Ba_0.6K_0.4Fe₂As₂, for which we show that the stress-induced optical anisotropy in the infrared spectral range is reversible upon sweeping the applied stress and occurs only below the superconducting transition temperature. These findings demonstrate that there is a large electronic nematicity at optimal doping which extends right under the superconducting dome.

I will briefly explain the basics of Scanning Tunneling Spectroscopy (STS), focusing on techniques to study strongly correlated electron systems at dilution refrigeration temperatures. I will first report on the discovery of a one-dimensional charge density wave (1D-CDW) which is a Moiré pattern between the atomic lattice and a hot spot for electronic scattering in the bandstructure of the hidden order (HO) state of URu₂Si₂. The Moiré is produced by fracturing the crystal in presence of a dynamical spin mode at low temperatures and its presence suggests that charge interactions are among the most relevant features competing with HO in URu₂Si₂. Then, I will discuss the consequences of band hybridization in the local density of states which lead to new insight into the local density of states on small-sized atomically flat areas in URu₂Si₂. Finally, I will briefly present suprising results in feedback driven atomic size Josephson junctions, which lead to an AC Josephson signal that will likely improve Josephson Scanning Spectroscopy.

I will expose the concepts of quantum computing for physicists and from a physicist's point of view. I will go through the construction of quantum error corrections and point out the difficulties and physical limitations for implementing this framework. I will, in particular, address the surface code and the concept of correctable versus non-correctable errors. This presentation is intended to an audience of physicists that mostly know about what the qubits are but not how we are supposed to make a computer out of them.
After the main talk, there will be a more specialized discussion session "Is quantum supremacy real?" for those who are interested in details of the recent Google experiment on quantum supremacy.

So-called 1/f-type fluctuations are ubiquitous in nature, and can be found in such diverse contexts as light curves of quasars, the human heartbeat, earthquakes, road traffic or classical music. In this seminar, we aim to give a broad and pedagogical overview of such fluctuation phenomena in condensed-matter systems and discuss how 'noise can be turned into a signal' by the method of fluctuation spectroscopy. We first give an example where understanding the microscopic origin of the fluctuations in semiconductor-based Hall sensors helps to improve the signal-to-noise ratio and hence the device performance. In the main part of the talk we then will discuss recent results on the low-frequency dynamics of strongly correlated electrons in low-dimensional molecular metals, which may be considered model systems for studying the Mott metal-insulator transition, a key phenomenon in many-body physics. Our findings range from glassy structural dynamics, critical slowing down of charge fluctuations at the Mott transition, and recent results on the formation of polar nanoregions in charge-driven ferroelectrics.

In this talk I give an overview of our recent research on 2D and 3D topological superconducting materials. I will focus on the doped topological insulator Bi₂Se₃ and on heterostructures between a quantum anomalous Hall insulator and a superconductor. A nematic topological superconductor has an order parameter symmetry, which spontaneously breaks the crystalline symmetry in its superconducting state. This state can be observed, for example, by thermodynamic or upper critical field experiments in which a magnetic field is rotated with respect to the crystalline axes, but also directly from the anisotropic gap symmetry in scanning tunneling probe experiments. We present a study on the upper critical field of the Nb-doped Bi₂Se₃ for various magnetic field orientations parallel to the basal plane of the Bi2Se3 layers. The data clearly demonstrate a two-fold symmetry that breaks the three-fold crystal symmetry. This provides strong experimental evidence that Nb-doped Bi₂Se₃ is a nematic topological superconductor similar to the Cu- and Sr-doped Bi₂Se₃, and rules out earlier suggestions that the finite magnetic moment of the intercalated Nb ions could instead induce a chiral superconducting state. We then show that in doped Bi₂Se₃, the nematic order arises from a multicomponent order parameter where superconductivity is the primary order and the nematic order an intertwined secondary order. Such a state of matter with a multi-component order parameter can give rise to a vestigial order. In the vestigial phase, the primary order is only partially melted, leaving a remaining symmetry breaking behind, an effect driven by strong classical or quantum fluctuations. We present the observation of a partially melted superconductor in which pairing fluctuations condense at a separate phase transition and form a nematic state with broken Z₃ symmetry High-resolution thermal expansion, specific heat and magnetization measurements reveal that this symmetry breaking occurs at T_nem≈3.8 K above T_c≈3.25 K, along with an onset of superconducting fluctuations. Thus, before Cooper pairs establish long-range coherence at T_c, they fluctuate in a way that breaks the rotational invariance at Tnem and induces a distortion of the crystalline lattice. With the recent discovery of the quantum anomalous Hall insulator, which exhibits the conductive quantum Hall edge states without external magnetic field, it becomes possible to create a novel topological superconductor by introducing superconductivity into these edge states. In this case, two distinct topological superconducting phases with one or two dispersive chiral Majorana edge modes were theoretically predicted, characterized by Chern numbers (N) of 1 and 2, respectively. We present spectroscopic evidence from Andreev reflection experiments for the presence of chiral Majorana modes in a Nb / (Cr_0.12Bi_0.26Sb_0.62)₂Te₃ heterostructure with distinct signatures attributed to two different topological superconducting phases. The results are in qualitatively good agreement with the theoretical predictions.

When cooled down, most magnetic materials form long-ranged structures of the magnetic moments. The situation is markedly different when strong quantum fluctuations are present in low dimensional materials or lattices with highly frustrated networks of spins. Such systems collectively called quantum magnets may exhibit unconventional magnetism and even maintain a fluctuating quantum state down to the lowest temperatures.
Sometimes one of the best ways to reveal these new ground states and their excitations is by perturbing such systems. In this talk, I will present several ways to modify the quantum magnets using chemical substitution as well as application of high pressure. First, I will show how spectral modifications can be achieved by diluting low dimensional magnets and what effects the impurities have on magnetic ordering as well as the universal scaling properties [1]. I will then talk about a different way to perturb such systems: high pressure. In particular, I will discuss the search and discovery of new phases in bond-frustrated iridate and ruthenate magnets. The links between the exact modification of the lattice and the resulting magnetic phases will be demonstrated in some of Kitaev materials [2].
Finally, I will discuss arguably the most interesting perturbation - carrier doping. After an overview of previous efforts to dope a spin liquid, I will present our ongoing study of the interplay between the charge and magnetic degrees of freedom in an iridium-based geometrically frustrated hyperkagome lattice [3].
[1] Phys. Rev. Lett. 111, 067204 (2013); Phys. Rev. 95, 054409 (2017)
[2] Phys. Rev. B 98, 104421 (2018); Phys. Rev. Lett. 120, 237202 (2018)
[3] Phys. Rev. Lett. 99, 137207 (2007); Scientific Reports 4, 6818 (2014)

Scalar spin chirality is a pervasive concept in contemporary research on magnetism in condensed matter, especially as relates to the coupling between magnetic order and the conduction electrons. In metallic magnets, non-coplanar spin structures on the nanoscale can exert a giant emergent magnetic field on charge carriers, with potential applications in spintronics. The emergent magnetic field may also be harnessed in the future design of new types of correlated systems with protected surface modes. In this talk, I will outline our work on magnets with non-coplanar order on different length scales: (1) The canted ferromagnetic state in the correlated pyrochlore oxide Nd₂Mo₂O₇ is a representative example of non-coplanarity within a single crystallographic unit cell [1,2]. We discuss our experimental efforts of tuning the chemical potential in this material by chemical substitution, and new theoretical insight into the qualitatively different effects of scalar spin chirality and spin-orbit coupling on the electronic band structure [3]. (2) The metallic antiferromagnet Dy₃Ru₄Al₁₂ with breathing Kagome network of rare-earth sites serves as an example of an intermediate class (λ_mag ~ 1.5 nm): Its non-coplanar magnetic order (in zero field) can be described as antiferromagnetic stacking of strongly coupled spin-trimers with tilted all-in or all-out configuration [4]. We reveal high sensitivity of the trimer arrangement to external magnetic field, which leads to a large anomalous Hall effect when net scalar spin-chirality emerges above 1 Tesla. (3) Finally, I will discuss our recent work on the formation of nanometer-sized skyrmion spin-vortices in the centrosymmetric rare earth intermetallics Gd₂PdSi₃ [5] and Gd₃Ru₄Al₁₂ [6] with Heisenberg Gd3+ moments and modulation length λ_mag ~ 2.5-3 nm. In contrast to the more widely studied case of skyrmions in non-centrosymmetric material platforms such as bulk B20 compounds or magnetic interfaces (λ_mag ~ 5-200 nm), skyrmions emerge here in absence of the Dzyaloshinskii-Moriya interaction. We report the phase diagrams of these compounds, reveal their magnetic order using scattering and real space imaging techniques, and discuss their large topological Hall and Nernst responses [7].
[1] Y. Taguchi et al., Science 291, 2573
[2] Y. Taguchi et al., Physical Review Letters 90, 257202
[3] M. Hirschberger et al., manuscript in preparation
[4] S. Gao, M. Hirschberger et al., arXiv:1908.07728
[5] T. Kurumaji, T. Nakajima, M. Hirschberger, et al., Science 365, 914
[6] M. Hirschberger, T. Nakajima, et al., arXiv:1812.02553, accepted to Nat. Comms.
[7] M. Hirschberger, L. Spitz, et al., arXiv:1910.06027