Chiral phonons in quartz probed by X-rays.

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 topology1-3. The experimental verification of chiral phonons (bosons) remains challenging, however, despite their expected strong impact on fundamental physical properties4-6. 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.

Berezinskii-Kosterlitz-Thouless Transition in the Type-I Weyl Semimetal PtBi2.

Symmetry breaking in topological matter has become in recent years a key concept in condensed matter physics to unveil novel electronic states. In this work, we predict that broken inversion symmetry and strong spin-orbit coupling in trigonal PtBi2 lead to a type-I Weyl semimetal band structure. Transport measurements show an unusually robust low dimensional superconductivity in thin exfoliated flakes up to 126 nm in thickness (with Tc ∼ 275-400 mK), which constitutes the first report and study of unambiguous superconductivity in a type-I Weyl semimetal. Remarkably, a Berezinskii-Kosterlitz-Thouless transition with TBKT ∼ 310 mK is revealed in up to 60 nm thick flakes, which is nearly an order of magnitude thicker than the rare examples of two-dimensional superconductors exhibiting such a transition. This makes PtBi2 an ideal platform to study low dimensional and unconventional superconductivity in topological semimetals.

Frozen Deconfined Quantum Criticality.

There is a number of contradictory findings with regard to whether the theory describing easy-plane quantum antiferromagnets undergoes a second-order phase transition. The traditional Landau-Ginzburg-Wilson approach suggests a first-order phase transition, as there are two different competing order parameters. On the other hand, it is known that the theory has the property of self-duality which has been connected to the existence of a deconfined quantum critical point (DQCP). The latter regime suggests that order parameters are not the elementary building blocks of the theory, but rather consist of fractionalized particles that are confined in both phases of the transition and only appear-deconfine-at the critical point. Nevertheless, many numerical Monte Carlo simulations disagree with the claim of a DQCP in the system, indicating instead a first-order phase transition. Here we establish from exact lattice duality transformations and renormalization group analysis that the easy-plane CP^{1} antiferromagnet does feature a DQCP. We uncover the criticality starting from a regime analogous to the zero temperature limit of a certain classical statistical mechanics system which we therefore dub frozen. At criticality our bosonic theory is dual to a fermionic one with two massless Dirac fermions, which thus undergoes a second-order phase transition as well.

Non-Hermitian Physics without Gain or Loss: The Skin Effect of Reflected Waves.

Physically, one tends to think of non-Hermitian systems in terms of gain and loss: the decay or amplification of a mode is given by the imaginary part of its energy. Here, we introduce an alternative avenue to the realm of non-Hermitian physics, which involves neither gain nor loss. Instead, complex eigenvalues emerge from the amplitudes and phase differences of waves backscattered from the boundary of insulators. We show that for any strong topological insulator in a Wigner-Dyson class, the reflected waves are characterized by a reflection matrix exhibiting the non-Hermitian skin effect. This leads to an unconventional Goos-Hänchen effect: due to non-Hermitian topology, waves undergo a lateral shift upon reflection, even at normal incidence. Going beyond systems with gain and loss vastly expands the set of experimental platforms that can access non-Hermitian physics and show signatures associated with non-Hermitian topology.

Dirac fermions and flat bands in the ideal kagome metal FeSn.

A kagome lattice of 3d transition metal ions is a versatile platform for correlated topological phases hosting symmetry-protected electronic excitations and magnetic ground states. However, the paradigmatic states of the idealized two-dimensional kagome lattice-Dirac fermions and flat bands-have not been simultaneously observed. Here, we use angle-resolved photoemission spectroscopy and de Haas-van Alphen quantum oscillations to reveal coexisting surface and bulk Dirac fermions as well as flat bands in the antiferromagnetic kagome metal FeSn, which has spatially decoupled kagome planes. Our band structure calculations and matrix element simulations demonstrate that the bulk Dirac bands arise from in-plane localized Fe-3d orbitals, and evidence that the coexisting Dirac surface state realizes a rare example of fully spin-polarized two-dimensional Dirac fermions due to spin-layer locking in FeSn. The prospect to harness these prototypical excitations in a kagome lattice is a frontier of great promise at the confluence of topology, magnetism and strongly correlated physics.

Deconfined Criticality and Bosonization Duality in Easy-Plane Chern-Simons Two-Dimensional Antiferromagnets.

Two-dimensional quantum systems with competing orders can feature a deconfined quantum critical point, yielding a continuous phase transition that is incompatible with the Landau-Ginzburg-Wilson scenario, predicting instead a first-order phase transition. This is caused by the LGW order parameter breaking up into new elementary excitations at the critical point. Canonical candidates for deconfined quantum criticality are quantum antiferromagnets with competing magnetic orders, captured by the easy-plane CP^{1} model. A delicate issue however is that numerics indicates the easy-plane CP^{1} antiferromagnet to exhibit a first-order transition. Here we show that an additional topological Chern-Simons term in the action changes this picture completely in several ways. We find that the topological easy-plane antiferromagnet undergoes a second-order transition with quantized critical exponents. Further, a particle-vortex duality naturally maps the partition function of the Chern-Simons easy-plane antiferromagnet into one of massless Dirac fermions.

Infinite Berry Curvature of Weyl Fermi Arcs.

We show that Weyl Fermi arcs are generically accompanied by a divergence of the surface Berry curvature scaling as 1/k^{2}, where k is the distance to a hot line in the surface Brillouin zone that connects the projection of Weyl nodes with opposite chirality, but which is distinct from the Fermi arc itself. Such surface Berry curvature appears whenever the bulk Weyl dispersion has a velocity tilt toward the surface of interest. This divergence is reflected in a variety of Berry curvature mediated effects that are readily accessible experimentally and, in particular, leads to a surface Berry curvature dipole that grows linearly with the thickness of a slab of a Weyl semimetal material in the limit of the long lifetime of surface states. This implies the emergence of a gigantic contribution to the nonlinear Hall effect in such devices.

Unraveling the Orbital Physics in a Canonical Orbital System KCuF_{3}.

We explore the existence of the collective orbital excitations, orbitons, in the canonical orbital system KCuF_{3} using the Cu L_{3}-edge resonant inelastic x-ray scattering. We show that the nondispersive high-energy peaks result from the Cu^{2+} dd orbital excitations. These high-energy modes display good agreement with the ab initio quantum chemistry calculation, indicating that the dd excitations are highly localized. At the same time, the low-energy excitations present clear dispersion. They match extremely well with the two-spinon continuum following the comparison with Müller ansatz calculations. The localized dd excitations and the observation of the strongly dispersive magnetic excitations suggest that the orbiton dispersion is below the resolution detection limit. Our results can reconcile with the strong local Jahn-Teller effect in KCuF_{3}, which predominantly drives orbital ordering.

Curvilinear One-Dimensional Antiferromagnets.

Antiferromagnets host exotic quasiparticles, support high frequency excitations and are key enablers of the prospective spintronic and spin-orbitronic technologies. Here, we propose a concept of a curvilinear antiferromagnetism where material responses can be tailored by a geometrical curvature without the need to adjust material parameters. We show that an intrinsically achiral one-dimensional (1D) curvilinear antiferromagnet behaves as a chiral helimagnet with geometrically tunable Dzyaloshinskii-Moriya interaction (DMI) and orientation of the Néel vector. The curvature-induced DMI results in the hybridization of spin wave modes and enables a geometrically driven local minimum of the low-frequency branch. This positions curvilinear 1D antiferromagnets as a novel platform for the realization of geometrically tunable chiral antiferromagnets for antiferromagnetic spin-orbitronics and fundamental discoveries in the formation of coherent magnon condensates in the momentum space.

Signatures of the Magnetic Entropy in the Thermopower Signals in Nanoribbons of the Magnetic Weyl Semimetal Co3Sn2S2.

Weyl semimetals exhibit interesting electronic properties due to their topological band structure. In particular, large anomalous Hall and anomalous Nernst signals are often reported, which allow for a detailed and quantitative study of subtle features. We pattern single crystals of the magnetic Weyl semimetal Co3Sn2S2 into nanoribbon devices using focused ion beam cutting and optical lithography. This approach enables a very precise study of the galvano- and thermomagnetic transport properties. Indeed, we found interesting features in the temperature dependency of the anomalous Hall and Nernst effects. We present an analysis of the data based on the Mott relation and identify in the Nernst response signatures of magnetic fluctuations enhancing the anomalous Nernst conductivity at the magnetic phase transition.

Experimental Determination of Momentum-Resolved Electron-Phonon Coupling.

We provide a novel experimental method to quantitatively estimate the electron-phonon coupling and its momentum dependence from resonant inelastic x-ray scattering (RIXS) spectra based on the detuning of the incident photon energy away from an absorption resonance. We apply it to the cuprate parent compound NdBa_{2}Cu_{3}O_{6} and find that the electronic coupling to the oxygen half-breathing phonon branch is strongest at the Brillouin zone boundary, where it amounts to ∼0.17 eV, in agreement with previous studies. In principle, this method is applicable to any absorption resonance suitable for RIXS measurements and will help to define the contribution of lattice vibrations to the peculiar properties of quantum materials.

Fractional Angular Momentum at Topological Insulator Interfaces.

Recently, two fundamental topological properties of a magnetic vortex at the interface of a superconductor (SC) and a strong topological insulator (TI) have been established: The vortex carries both a Majorana zero mode relevant for topological quantum computation and, for a time-reversal invariant TI, a charge of e/4. This fractional charge is caused by the axion term in the electromagnetic Lagrangian of the TI. Here we determine the angular momentum J of the vortices, which in turn determines their mutual statistics. Solving the axion-London electrodynamic equations including screening in both a SC and a TI, we find that the elementary quantum of angular momentum of the vortex is -n^{2}ℏ/8, where n is the flux quantum of the vortex line. Exchanging two elementary fluxes thus changes the phase of the wave function by -π/4.

Strong Effect of Hydrogen Order on Magnetic Kitaev Interactions in H_{3}LiIr_{2}O_{6}.

Very recently a quantum liquid was reported to form in H_{3}LiIr_{2}O_{6}, an iridate proposed to be a close realization of the Kitaev honeycomb model. To test this assertion we perform detailed quantum chemistry calculations to determine the magnetic interactions between Ir moments. We find that weakly bond dependent ferromagnetic Kitaev exchange dominates over other couplings, but still is substantially lower than in Na_{2}IrO_{3}. This reduction is caused by the peculiar position of the interlayer species: removing hydrogen cations next to a Ir_{2}O_{2} plaquette increases the Kitaev exchange by more than a factor of 3 on the corresponding Ir─Ir link. Consequently, any lack of hydrogen order will have a drastic effect on the magnetic interactions and strongly promote spin disordering.

Strongly Enhanced Berry Dipole at Topological Phase Transitions in BiTeI.

Transitions between topologically distinct electronic states have been predicted in different classes of materials and observed in some. A major goal is the identification of measurable properties that directly expose the topological nature of such transitions. Here, we focus on the giant Rashba material bismuth tellurium iodine which exhibits a pressure-driven phase transition between topological and trivial insulators in three dimensions. We demonstrate that this transition, which proceeds through an intermediate Weyl semimetallic state, is accompanied by a giant enhancement of the Berry curvature dipole which can be probed in transport and optoelectronic experiments. From first-principles calculations, we show that the Berry dipole-a vector along the polar axis of this material-has opposite orientations in the trivial and topological insulating phases and peaks at the insulator-to-Weyl critical points, at which the nonlinear Hall conductivity can increase by over 2 orders of magnitude.

Multiplet of Skyrmion States on a Curvilinear Defect: Reconfigurable Skyrmion Lattices.

Typically, the chiral magnetic Skyrmion is a single-state excitation. Here we propose a system, where multiplet of Skyrmion states appears and one of these states can be the ground one. We show that the presence of a localized curvilinear defect drastically changes the magnetic properties of a thin perpendicularly magnetized ferromagnetic film. For a large enough defect amplitude a discrete set of equilibrium magnetization states appears forming a ladder of energy levels. Each equilibrium state has either a zero or a unit topological charge; i.e., topologically trivial and Skyrmion multiplets generally appear. Transitions between the levels with the same topological charge are allowed and can be utilized to encode and switch a bit of information. There is a wide range of geometrical and material parameters, where the Skyrmion level has the lowest energy. Thus, periodically arranged curvilinear defects can result in a Skyrmion lattice as the ground state.

Generic Coexistence of Fermi Arcs and Dirac Cones on the Surface of Time-Reversal Invariant Weyl Semimetals.

The hallmark of Weyl semimetals is the existence of open constant-energy contours on their surface-the so-called Fermi arcs-connecting Weyl points. Here, we show that, for time-reversal symmetric realizations of Weyl semimetals, these Fermi arcs, in many cases, coexist with closed Fermi pockets originating from surface Dirac cones pinned to time-reversal invariant momenta. The existence of Fermi pockets is required for certain Fermi-arc connectivities due to additional restrictions imposed by the six Z_{2} topological invariants characterizing a generic time-reversal invariant Weyl semimetal. We show that a change of the Fermi-arc connectivity generally leads to a different topology of the surface Fermi surface and identify the half-Heusler compound LaPtBi under in-plane compressive strain as a material that realizes this surface Lifshitz transition. We also discuss universal features of this coexistence in quasiparticle interference spectra.

Evidence for a Field-Induced Quantum Spin Liquid in α-RuCl_{3}.

We report a ^{35}Cl nuclear magnetic resonance study in the honeycomb lattice α-RuCl_{3}, a material that has been suggested to potentially realize a Kitaev quantum spin liquid (QSL) ground state. Our results provide direct evidence that α-RuCl_{3} exhibits a magnetic-field-induced QSL. For fields larger than ∼10 T, a spin gap opens up while resonance lines remain sharp, evidencing that spins are quantum disordered and locally fluctuating. The spin gap increases linearly with an increasing magnetic field, reaching ∼50 K at 15 T, and is nearly isotropic with respect to the field direction. The unusual rapid increase of the spin gap with increasing field and its isotropic nature are incompatible with conventional magnetic ordering and, in particular, exclude that the ground state is a fully polarized ferromagnet. The presence of such a field-induced gapped QSL phase has indeed been predicted in the Kitaev model.

Orbital-driven nematicity in FeSe.

A fundamental and unconventional characteristic of superconductivity in iron-based materials is that it occurs in the vicinity of two other instabilities. In addition to a tendency towards magnetic order, these Fe-based systems have a propensity for nematic ordering: a lowering of the rotational symmetry while time-reversal invariance is preserved. Setting the stage for superconductivity, it is heavily debated whether the nematic symmetry breaking is driven by lattice, orbital or spin degrees of freedom. Here, we report a very clear splitting of NMR resonance lines in FeSe at Tnem = 91 K, far above the superconducting Tc of 9.3 K. The splitting occurs for magnetic fields perpendicular to the Fe planes and has the temperature dependence of a Landau-type order parameter. Spin-lattice relaxation rates are not affected at Tnem, which unequivocally establishes orbital degrees of freedom as driving the nematic order. We demonstrate that superconductivity competes with the emerging nematicity.

Resonant Inelastic X-Ray Scattering Response of the Kitaev Honeycomb Model.

We calculate the resonant inelastic x-ray scattering (RIXS) response of the Kitaev honeycomb model, an exactly solvable quantum-spin-liquid model with fractionalized Majorana and flux excitations. We find that the fundamental RIXS channels, the spin-conserving (SC) and the non-spin-conserving (NSC) ones, do not interfere and give completely different responses. SC RIXS picks up exclusively the Majorana sector with a pronounced momentum dispersion, whereas NSC RIXS also creates immobile fluxes, thereby rendering the response only weakly momentum dependent, as in the spin structure factor measured by inelastic neutron scattering. RIXS can, therefore, pick up the fractionalized excitations of the Kitaev spin liquid separately, making it a sensitive probe to detect spin-liquid character in potential material incarnations of the Kitaev honeycomb model.

Strongly Enhanced Superconductivity in Coupled t-J Segments.

The t-J Hamiltonian is one of the cornerstones in the theoretical study of strongly correlated copper-oxide based materials. Using the density-matrix renormalization group method we obtain the phase diagram of the one-dimensional t-J chain in the presence of a periodic hopping modulation, as a prototype of coupled-segment models. While in the uniform 1D t-J model the near half-filling superconducting state dominates only at unphysically large values of the exchange coupling constant J/t>3; we show that a small hopping and exchange modulation very strongly reduces the critical coupling to be as low as J/t∼1/3--well within the physical regime. The phase diagram as a function of the electron filling also exhibits metallic, insulating line phases and regions of phase separation. We suggest that a superconducting state is easily stabilized if t-J segments creating local spin-singlet pairing are coupled to each other--another example is the ladder system.