Complexity and Topology in Quantum Matter

Optically addressable spins in wide-bandgap semiconductors are a promising platform for exploring quantum phenomena. While colour centres in three-dimensional crystals such as diamond and silicon carbide were studied in detail, they were not observed experimentally in two-dimensional (2D) materials. Here, we report spin-dependent processes in the 2D material hexagonal boron nitride (hBN). We identify fluorescence lines associated with a particular defect, the negatively charged boron vacancy ([Formula: see text]), showing a triplet (S = 1) ground state and zero-field splitting of ~3.5 GHz. We establish that this centre exhibits optically detected magnetic resonance at room temperature and demonstrate its spin polarization under optical pumping, which leads to optically induced population inversion of the spin ground state-a prerequisite for coherent spin-manipulation schemes. Our results constitute a step forward in establishing 2D hBN as a prime platform for scalable quantum technologies, with potential for spin-based quantum information and sensing applications.

We introduce and study a novel class of sensors whose sensitivity grows exponentially with the size of the device. Remarkably, this drastic enhancement does not rely on any fine-tuning, but is found to be a stable phenomenon immune to local perturbations. Specifically, the physical mechanism behind this striking phenomenon is intimately connected to the anomalous sensitivity to boundary conditions observed in non-Hermitian topological systems. We outline concrete platforms for the practical implementation of these non-Hermitian topological sensors ranging from classical metamaterials to synthetic quantum materials.

Abstract Spin defects in solid-state materials are strong candidate systems for quantum information technology and sensing applications. Here we explore in details the recently discovered negatively charged boron vacancies (V B − ) in hexagonal boron nitride (hBN) and demonstrate their use as atomic scale sensors for temperature, magnetic fields and externally applied pressure. These applications are possible due to the high-spin triplet ground state and bright spin-dependent photoluminescence of the V B − . Specifically, we find that the frequency shift in optically detected magnetic resonance measurements is not only sensitive to static magnetic fields, but also to temperature and pressure changes which we relate to crystal lattice parameters. We show that spin-rich hBN films are potentially applicable as intrinsic sensors in heterostructures made of functionalized 2D materials.

The recent discovery of AV_{3}Sb_{5} (A=K,Rb,Cs) has uncovered an intriguing arena for exotic Fermi surface instabilities in a kagome metal. Among them, superconductivity is found in the vicinity of multiple van Hove singularities, exhibiting indications of unconventional pairing. We show that the sublattice interference mechanism is central to understanding the formation of superconductivity in a kagome metal. Starting from an appropriately chosen minimal tight-binding model with multiple van Hove singularities close to the Fermi level for AV_{3}Sb_{5}, we provide a random phase approximation analysis of superconducting instabilities. Nonlocal Coulomb repulsion, the sublattice profile of the van Hove bands, and the interaction strength turn out to be the crucial parameters to determine the preferred pairing symmetry. Implications for potentially topological surface states are discussed, along with a proposal for additional measurements to pin down the nature of superconductivity in AV_{3}Sb_{5}.

Optically active spin defects are promising candidates for solid-state quantum information and sensing applications. To use these defects in quantum applications coherent manipulation of their spin state is required. Here, we realize coherent control of ensembles of boron vacancy centers in hexagonal boron nitride (hBN). Specifically, by applying pulsed spin resonance protocols, we measure a spin-lattice relaxation time of 18 microseconds and a spin coherence time of 2 microseconds at room temperature. The spin-lattice relaxation time increases by three orders of magnitude at cryogenic temperature. By applying a method to decouple the spin state from its inhomogeneous nuclear environment the optically detected magnetic resonance linewidth is substantially reduced to several tens of kilohertz. Our results are important for the employment of van der Waals materials for quantum technologies, specifically in the context of high resolution quantum sensing of two-dimensional heterostructures, nanoscale devices, and emerging atomically thin magnets.

Metal halide perovskites are the first solution processed semiconductors that can compete in their functionality with conventional semiconductors, such as silicon. Over the past several years, perovskite semiconductors have reported breakthroughs in various optoelectronic devices, such as solar cells, photodetectors, light emitting and memory devices, and so on. Until now, perovskite semiconductors face challenges regarding their stability, reproducibility, and toxicity. In this Roadmap, we combine the expertise of chemistry, physics, and device engineering from leading experts in the perovskite research community to focus on the fundamental material properties, the fabrication methods, characterization and photophysical properties, perovskite devices, and current challenges in this field. We develop a comprehensive overview of the current state-of-the-art and offer readers an informed perspective of where this field is heading and what challenges we have to overcome to get to successful commercialization.

Abstract Non-collinear antiferromagnets are revealing many unexpected phenomena and they became crucial for the field of antiferromagnetic spintronics. To visualize and prepare a well-defined domain structure is of key importance. The spatial magnetic contrast, however, remains extraordinarily difficult to be observed experimentally. Here, we demonstrate a magnetic imaging technique based on a laser induced local thermal gradient combined with detection of the anomalous Nernst effect. We employ this method in one the most actively studied representatives of this class of materials—Mn 3 Sn. We demonstrate that the observed contrast is of magnetic origin. We further show an algorithm to prepare a well-defined domain pattern at room temperature based on heat assisted recording principle. Our study opens up a prospect to study spintronics phenomena in non-collinear antiferromagnets with spatial resolution.

The layered van der Waals antiferromagnet MnBi${}_{2}$Te${}_{4}$ has been predicted previously to realize the first intrinsic magnetic topological insulator. Here, the authors report spin- and angle-resolved photoemission experiments for the MnBi${}_{2}$Te${}_{4}$(0001) surface, revealing a surface state in the bulk band gap and providing evidence for the interplay between magnetic exchange interaction and spin-orbit coupling in the surface electronic structure. MnBi${}_{2}$Te${}_{4}$ thus constitutes a promising candidate to exploit the interplay of topological states and magnetic order in spintronic device concepts.

High-quality single crystals of ${\mathrm{NaYbSe}}_{2}$, which resembles a perfect triangular-lattice antiferromagnet without intrinsic disorder, are investigated by magnetization and specific heat, as well as the local probe techniques nuclear magnetic resonance (NMR) and electron spin resonance. The low-field measurements confirm the absence of any spin freezing or long-range magnetic order down to 50 mK, which suggests a quantum spin liquid ground (QSL) state with gapless excitations. Instability of the QSL state is observed upon applying magnetic fields. For the $H\ensuremath{\perp}c$ direction, a field-induced magnetic phase transition is observed above 2 T from the ${C}_{\mathrm{p}}(T)$ data, agreeing with a clear $\frac{{M}_{s}}{3}$ plateau of $M(H)$, which is associated with an up-up-down spin arrangement. For the $H\ensuremath{\parallel}c$ direction, a field-induced transition could be evidenced at a much higher field range (9--21 T). The $^{23}\mathrm{Na}$ NMR measurements provide microscopic evidence of field-induced ordering for both directions. A reentrant behavior of ${T}_{\mathrm{N}}$, originating from the thermal and quantum spin fluctuations, is observed for both directions. The anisotropic exchange interactions ${J}_{\ensuremath{\perp}}\ensuremath{\simeq}4.7$ K and ${J}_{z}\ensuremath{\simeq}2.33$ K are extracted from the modified bond-dependent XXZ model for the spin-$\frac{1}{2}$ triangular-lattice antiferromagnet. The absence of magnetic long-range order at zero fields is assigned to the effect of strong bond frustration, arising from the complex spin-orbit entangled $4f$ ground state. Finally, we derive the highly anisotropic magnetic phase diagram, which is discussed in comparison with the existing theoretical models for spin-$\frac{1}{2}$ triangular-lattice antiferromagnets.

Abstract Phases with spontaneous time-reversal ( $${{{{{{{\mathcal{T}}}}}}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> </mml:math> ) symmetry breaking are sought after for their anomalous physical properties, low-dissipation electronic and spin responses, and information-technology applications. Recently predicted altermagnetic phase features an unconventional and attractive combination of a strong $${{{{{{{\mathcal{T}}}}}}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> </mml:math> -symmetry breaking in the electronic structure and a zero or only weak-relativistic magnetization. In this work, we experimentally observe the anomalous Hall effect, a prominent representative of the $${{{{{{{\mathcal{T}}}}}}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> </mml:math> -symmetry breaking responses, in the absence of an external magnetic field in epitaxial thin-film Mn 5 Si 3 with a vanishingly small net magnetic moment. By symmetry analysis and first-principles calculations we demonstrate that the unconventional d-wave altermagnetic phase is consistent with the experimental structural and magnetic characterization of the Mn 5 Si 3 epilayers, and that the theoretical anomalous Hall conductivity generated by the phase is sizable, in agreement with experiment. An analogy with unconventional d-wave superconductivity suggests that our identification of a candidate of unconventional d-wave altermagnetism points towards a new chapter of research and applications of magnetic phases.

Topological insulator lasers are arrays of semiconductor lasers that exploit fundamental features of topology to force all emitters to act as a single coherent laser. In this study, we demonstrate a topological insulator vertical-cavity surface-emitting laser (VCSEL) array. Each VCSEL emits vertically, but the in-plane coupling between emitters in the topological-crystalline platform facilitates coherent emission of the whole array. Our topological VCSEL array emits at a single frequency and displays interference, highlighting that the emitters are mutually coherent. Our experiments exemplify the power of topological transport of light: The light spends most of its time oscillating vertically, but the small in-plane coupling is sufficient to force the array of individual emitters to act as a single laser.

Abstract Topological photonics seeks to control the behaviour of the light through the design of protected topological modes in photonic structures. While this approach originated from studying the behaviour of electrons in solid-state materials, it has since blossomed into a field that is at the very forefront of the search for new topological types of matter. This can have real implications for future technologies by harnessing the robustness of topological photonics for applications in photonics devices. This roadmap surveys some of the main emerging areas of research within topological photonics, with a special attention to questions in fundamental science, which photonics is in an ideal position to address. Each section provides an overview of the current and future challenges within a part of the field, highlighting the most exciting opportunities for future research and developments.

We construct a two-dimensional higher-order topological phase protected by a quasicrystalline eightfold rotation symmetry. Our tight-binding model describes a superconductor on the Ammann-Beenker tiling hosting localized Majorana zero modes at the corners of an octagonal sample. In order to analyze this model, we introduce Hamiltonians generated by a local rule, and use this concept to identify the bulk topological properties. We find a Z_{2} bulk topological invariant protecting the corner modes. Our work establishes that there exist topological phases protected by symmetries impossible in a crystal.

Non-symmorphic chiral topological crystals host exotic multifold fermions, and their associated Fermi arcs helically wrap around and expand throughout the Brillouin zone between the high-symmetry center and surface-corner momenta. However, Fermi-arc splitting and realization of the theoretically proposed maximal Chern number rely heavily on the spin-orbit coupling (SOC) strength. In the present work, we investigate the topological states of a new chiral crystal, PtGa, which has the strongest SOC among all chiral crystals reported to date. With a comprehensive investigation using high-resolution angle-resolved photoemission spectroscopy, quantum-oscillation measurements, and state-of-the-art ab initio calculations, we report a giant SOC-induced splitting of both Fermi arcs and bulk states. Consequently, this study experimentally confirms the realization of a maximal Chern number equal to ±4 in multifold fermionic systems, thereby providing a platform to observe large-quantized photogalvanic currents in optical experiments. © 2020, The Author(s).

Abstract The concept of chirality is of great relevance in nature, from chiral molecules such as sugar to parity transformations in particle physics. In condensed matter physics, recent studies have demonstrated chiral fermions and their relevance in emergent phenomena closely related to topology 1–3 . The experimental verification of chiral phonons (bosons) remains challenging, however, despite their expected strong impact on fundamental physical properties 4–6 . Here we show experimental proof of chiral phonons using resonant inelastic X-ray scattering with circularly polarized X-rays. Using the prototypical chiral material quartz, we demonstrate that circularly polarized X-rays, which are intrinsically chiral, couple to chiral phonons at specific positions in reciprocal space, allowing us to determine the chiral dispersion of the lattice modes. Our experimental proof of chiral phonons demonstrates a new degree of freedom in condensed matter that is both of fundamental importance and opens the door to exploration of new emergent phenomena based on chiral bosons.

Polymeric vesicles or polymersomes are one of the supramolecular entities at the leading edge of synthetic biology. These small compartments have shown to be feasible candidates as nanoreactors, especially for enzymatic reactions. Once cross-linked and equipped with a pH sensitive material, the reaction can be switched off (pH 8) and on (pH 6) in accordance with the increased permeability of the polymersome membranes under acidic conditions. Thus cross-linked and pH sensitive polymersomes provide a basis for pH controlled enzymatic reactions where no integrated transmembrane protein is needed for regulating the uptake and release of educts and products in the polymersome lumen. This pH-tunable working tool was further used to investigate their use in sequential enzymatic reactions (glucose oxidase and myoglobin) where enzymes are loaded in one common polymersome or in two different polymersomes. Crossing membranes and overcoming the space distance between polymersomes were shown successfully, meaning that educts and products can be exchanged between enzyme compartments for successful enzymatic cascade reactions. Moreover the stabilizing effect of polymersomes is also observable by single enzymatic reactions as well as a sequence. This study is directed to establish robust and controllable polymersome nanoreactors for enzymatic reactions, describing a switch between an off (pH 8) and on (pH 6) state of polymersome membrane permeability with no transmembrane protein needed for transmembrane exchange.

For the first time, experiments reveal a material with both an intrinsic net magnetization and a topological band inversion, a major advance in the search for materials with tunable topological properties.

A bstract Krylov complexity measures the spread of the wavefunction in the Krylov basis, which is constructed using the Hamiltonian and an initial state. We investigate the evolution of the maximally entangled state in the Krylov basis for both chaotic and non-chaotic systems. For this purpose, we derive an Ehrenfest theorem for the Krylov complexity, which reveals its close relation to the spectrum. Our findings suggest that neither the linear growth nor the saturation of Krylov complexity is necessarily associated with chaos. However, for chaotic systems, we observe a universal rise-slope-ramp-plateau behavior in the transition probability from the initial state to one of the Krylov basis states. Moreover, a long ramp in the transition probability is a signal for spectral rigidity, characterizing quantum chaos. Also, this ramp is directly responsible for the late-time peak of Krylov complexity observed in the literature. On the other hand, for non-chaotic systems, this long ramp is absent. Therefore, our results help to clarify which features of the wave function time evolution in Krylov space characterize chaos. We exemplify this by considering the Sachdev-Ye-Kitaev model with two-body or four-body interactions.

Magnetic skyrmions are stable topological solitons with complex non-coplanar spin structures. Their nanoscopic size and the low electric currents required to control their motion has opened a new field of research, skyrmionics, that aims for the usage of skyrmions as information carriers. Further advances in skyrmionics call for a thorough understanding of their three-dimensional (3D) spin texture, skyrmion-skyrmion interactions and the coupling to surfaces and interfaces, which crucially affect skyrmion stability and mobility. Here, we quantitatively reconstruct the 3D magnetic texture of Bloch skyrmions with sub-10-nanometre resolution using holographic vector-field electron tomography. The reconstructed textures reveal local deviations from a homogeneous Bloch character within the skyrmion tubes, details of the collapse of the skyrmion texture at surfaces and a correlated modulation of the skyrmion tubes in FeGe along their tube axes. Additionally, we confirm the fundamental principles of skyrmion formation through an evaluation of the 3D magnetic energy density across these magnetic solitons.

Abstract Altermagnets are a novel class of magnetic materials, where magnetic order is staggered both in coordinate and momentum space. The metallic rutile oxide RuO 2 , long believed to be a textbook Pauli paramagnet, recently emerged as a putative workhorse altermagnet when resonant X-ray and neutron scattering studies reported nonzero magnetic moments and long-range collinear order. While some experiments seem consistent with altermagnetism, magnetic order in RuO 2 remains controversial. We show that RuO 2 is nonmagnetic, both in bulk and thin film. Muon spectroscopy complemented by density-functional theory finds at most 1.14 × 10 −4 μ B /Ru in bulk and at most 7.5 × 10 −4 μ B /Ru in 11 nm epitaxial films, at our spectrometers’ detection limit, and dramatically smaller than previously reported neutron results that were used to rationalize altermagnetic behavior. Our own neutron diffraction measurements on RuO 2 single crystals identify multiple scattering as the source for the false signal in earlier studies.