The spectrum of charged particles in translation-invariant systems in a magnetic field is characterized by the Landau levels, which play a fundamental role in the thermodynamic and transport properties of solids. The topological nature and the approximate degeneracy of the Landau levels are known to also survive on crystalline lattices with discrete translation symmetry when the magnetic flux through a primitive cell is small compared to the flux quantum. Here we show that the notion of Landau levels and the quantum Hall effect can be generalized to two-dimensional (2D) noncrystalline lattices without spatial long-range order. Remarkably, even when the spatial correlations decay over microscopic distances, 2D systems can exhibit a number of well-resolved Landau-like bands. The existence of these bands imply that noncrystalline systems in magnetic fields can support the hallmark quantum effects which have been typically associated with crystalline solids.

The ability to control levitated nanoparticles allows one to explore various fields of physics, including quantum optics, quantum metrology, and nonequilibrium physics. It has been recently demonstrated that the arrangement of two levitated nanoparticles naturally realizes the tunable nonreciprocal dipole-dipole interaction. Motivated by this development, we here propose and analyze an array of levitated nanoparticles as an ideal platform to study non-Hermitian physics in a highly controlled manner. We employ the non-Bloch band theory to determine the continuum bands of the proposed setup and investigate the non-Hermitian skin effect therein. In particular, we point out that the levitated nanoparticle array exhibits rich dynamical phases, including the dynamically unstable phase and the unconventional critical phase where the spectral singularity persists over a broad region of the controllable parameters. We also show that the long-range nature of the dipole-dipole interaction gives rise to the unique self-crossing point of the continuum band.

Recently, topologically nontrivial polarization textures have been predicted and observed in nanoscale systems. While these polarization textures are interesting and promising in terms of applications, their topology in general is yet to be fully understood. For example, the relation between topological polarization structures and band topology has not been explored, and polar domain structures are typically considered in topologically trivial systems. In particular, the local polarization in a crystal supercell is not well-defined, and typically calculated using approximations that do not satisfy gauge invariance. Furthermore, local polarization in supercells is typically approximated using calculations involving smaller unit cells, meaning the connection to the electronic structure of the supercell is lost. In this work, we propose a definition of local polarization which is gauge invariant and can be calculated directly from a supercell without approximations. We show using first-principles calculations for commensurate bilayer hexagonal boron nitride that our expressions for local polarization give the correct result at the unit cell level, which is a first approximation to the local polarization in a moiré superlattice. We also illustrate using an effective model that the local polarization can be directly calculated in real space. Finally, we discuss the relation between polarization and band topology, for which it is essential to have a correct definition of polarization textures.

The spin phenomena observed at a clean metal-insulator interface are typically reduced to the Rashba-Edelstein effect, which leads to spin accumulation over a few monolayers. We demonstrate that the presence of interface disorder significantly expands the range of potential phenomena. Specifically, the skew scattering at the metal-insulator boundary gives rise to the “kinetic Rashba-Edelstein effect,” where spin accumulation occurs on a much larger length scale comparable to the mean free path. Moreover, at higher orders of spin-orbit interaction, skew scattering is accompanied with spin relaxation resulting in the interface spin-Hall effect—a conversion of electrical current to spin current at the metal surface. Unlike the conventional spin-Hall effect, this phenomenon persists even within the Born approximation. These two predicted phenomena can dominate the spin density and spin current in devices of intermediate thickness.

Strong correlation and topology are two main pillars of modern physics, which can be bridged by fractional quantum Hall states and their lattice analogs known as fractional Chern insulators. A particularly pressing question for fractional Chern insulators is if there exists a lattice analog of the Laughlin state in the 1/3-filled Chern flat band dubbed the Chern-Laughlin state, and if so, how to detect it experimentally. The exact ground state in the 1/3-filled Chern flat band depends on the form of the electron-electron interaction, which can generate various competing ground states derived from, for example, the Laughlin, parafermion, parton, and stripe/nematic states in the 1/3-filled Landau level. In this context, it is of critical importance to precisely identify the exact ground state for a given electron-electron interaction. Here, we propose that the existence of an adiabatic path from the 1/3-filled fractional Chern insulator to the Tao-Thouless state, i.e., the root partition state of the Laughlin state in the thin torus limit, can serve as an effective order parameter for the precise identification of the Chern-Laughlin state. Specifically, by devising a hybrid adiabatic path of first deforming the electron-electron interaction and then taking the thin torus limit, we show that two-dimensional bulk Chern flat bands can host the Chern-Laughlin state at 1/3 filling. More importantly, our results suggest that, unless the electron-electron interaction is strictly of the nearest-neighbor form, the Tao-Thouless state can actually be detected in experiments, for example by using an incommensurate double-walled carbon nanotube made out of the magic-angle twisted bilayer graphene, which allows charge-sensitive surface measurements such as scanning tunneling microscopy. This method can be extended to various other fractional Chern insulators corresponding to both Abelian and non-Abelian fractional quantum Hall states.

A chain of magnetic impurities deposited on the surface of a superconductor can form a topological Shiba band that supports Majorana zero modes and holds a promise for topological quantum computing. Yet, most experiments scrutinizing these zero modes rely on transport measurements, which only capture local properties. Here we propose to leverage the intrinsic dynamics of the magnetic impurities to access their nonlocal character. We use linear response theory to determine the dynamics of the uniform magnonic mode in the presence of external ac magnetic fields and coupling to Shiba electrons. We demonstrate that this mode, which spreads over the entire chain of atoms, becomes imprinted with the parity of the ground state and, moreover, can discriminate between Majorana and trivial zero modes located at the ends of the chain. Our approach offers a noninvasive alternative to the scanning tunneling microscopy techniques used to probe Majorana zero modes. Conversely, the magnons could facilitate the manipulation of Majorana zero modes in topological Shiba chains.

Spin-orbit coupling driven by broken inversion symmetry ($I$) is known to lead to unusual magnetic response of superconductors, including extremely large critical fields for spin-singlet superconductors. This unusual response is also known to appear in materials that have $I$, provided there is local $I$-breaking: fermions participating in superconductivity reside on crystal sites that lack $I$. Here we show that this unusual response exists even when the crystal sites preserve $I$. Indeed, we argue that the symmetry of Kramers degenerate fermionic pseudospin is more relevant than the local crystal site symmetry. We examine and classify nonsymmorphic materials with momentum space spin-textures that exhibit an anomalous pseudospin with different symmetry properties from usual spin-1/2. Since this anomalous pseudospin does not depend on the existence of local $I$-breaking crystal sites, and since it optimizes the unusual magnetic response traditionally associated with locally noncentrosymmetric superconductors, it dramatically extends the range of relevant materials. We further show that this anomalous pseudospin leads to fully gapped “nodal” superconductors and provides additional insight into the breakdown of Blount's theorem for pseudospin triplet superconductors. We apply our results to ${\mathrm{UPt}}_3, {\mathrm{BiS}}_2$-based superconductors, Fe-based superconductors, and paramagnetic UCoGe.

Multiply quantized vortices (MQVs) within single-component Bose-Einstein condensates are unstable and decay rapidly. We show that MQVs can be stabilized by adding a small number of atoms of a second species to the vortex cores, and that these atoms remain in the vortex core as the system evolves. A consequence of the stabilization is that nearby corotating vortices can orbit in the opposite sense to their individual rotations when enough of the second species is present. This has implications concerning the imaging of vortices, as well as quantum turbulence and vortex nucleation in two-component condensates, such as those involving mixtures of ${}^{87}\mathrm{Rb}$ and ${}^{133}\mathrm{Cs}$.

Artificial nanostructures, fabricated by placing atoms or molecules as building blocks in well-defined positions, are a powerful platform in which quantum effects can be studied and exploited. In particular, they offer the opportunity to reduce the electronic interaction between large aromatic molecules and the underlying metallic substrate, if the manipulation capabilities of scanning tunneling microscopy to lift the molecule into an upright geometry on a pedestal of two metal atoms are used. Here, we report a strategy to study this interaction by investigating the Kondo effect. Measurements at millikelvin temperatures and in magnetic fields reveal that this bottom-up assembled standing metal-molecule nanostructure has an $S=1/2$ spin which is screened by substrate electrons, resulting in a Kondo temperature of only $291\pm 13$ mK. We extract its Landé $g$ factor and its exchange coupling $J\rho$ to the substrate, using a third-order perturbation theory in the weak-coupling and high-field regimes. We also show that the interaction between the scanning tunneling microscope tip and the molecule can tune the exchange coupling.

We propose a platform for observing the Josephson diode effect: the Andreev molecule. This nonlocal electronic state is hosted in circuits made of two closely spaced Josephson junctions, through the hybridization of the Andreev states. The Josephson diode effect occurs at the level of one individual junction while the other one generates the required time-reversal and spatial-inversion symmetry breaking. We present a microscopic description of this phenomenon based on fermionic Andreev states, focusing on single channels in the short limit, and we compute both supercurrent and energy spectra. We demonstrate that the diode efficiency can be tuned by magnetic flux and the junctions' transmissions and can reach $45\%$. Going further, by analyzing the Andreev spectra, we demonstrate the key role played by the continuum, which consists of leaky Andreev states and is largely responsible for the critical current asymmetry. On top of proposing an experimentally accessible platform, this work elucidates the microscopic origin of the Josephson diode effect at the level of the fermionic Andreev states.

With an increasing number of experiments observing phonon thermal Hall effect in magnets, it is theoretically desired to have a minimal model for the phonon thermal Hall effect. In this work, we study a simple model of acoustic phonons and uncorrelated paramagnetic doublets. When the doublets are non-Kramers, a linear pseudospin-phonon coupling is allowed by time-reversal symmetry and yields resonant phonon-pseudospin scattering. We compute the thermal longitudinal and Hall conductivities of the model and find qualitative agreement with recent experiments in ${\mathrm{Pr}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ [Uehara et al., Nat. Commun. 13, 4604 (2022)].

We performed ab initio molecular dynamics simulations for pressures and temperatures from 300–5000 GPa and 3000–30 000 K in order to determine the equation of state of solid and liquid iron. By employing a thermodynamic integration technique, we derive the ab initio entropy and Gibbs free energy of both phases, which allows us to construct solid and liquid adiabats and discuss implications for shock experiments. We derive the melting line by equating solid and liquid Gibbs free energies and represent it by a Simon fit $6469\mathrm{K}(1+(P/\mathrm{GPa}-300)/434.82{)}^{0.54369}$. Near 300 GPa, our melting line is higher than extrapolations of previous melting laws that were obtained with simulations at lower pressures but is in very good agreement with the most recent experiments by Kraus et al. Science 375, 202 (2022), that reached TPa pressures. The slope of our melting line is consistently steeper than that of our adiabats, which implies that the crystallization of iron in the cores of terrestrial planets always starts from their centers, like on Earth. We also construct models for Super-Earth interiors and compare with temperature profiles from published evolution models. These temperatures in many earlier publications are rather low, so that our melting line would imply completely frozen cores. Only later models by Stamenković et al. [Astrophys. J. 748, 41 (2012)] and Boujibar et al. [J. Geophys. Res. Planets 125, e2019JE006124 (2020)] consider a much wider range of interior temperatures, which imply that the core of Super-Earths may remain in a state with a partially molten core for a long time and the resulting buoyancy force will contribute to convection and the magnetic field generation.

Poincaré inertio-gravity modes described by the shallow water equations in a rotating frame have nontrivial topology, providing a perspective on the origin of equatorially trapped Kelvin and Yanai waves. We investigate the topology of rotating shallow water equations and continuously stratified primitive equations with and without background shear flow. Continuously stratified fluids support waves that are analogous to the edge modes of weak three-dimensional topological insulators. Background shear flow not only breaks the Hermiticity and homogeneity of the system but also leads to instabilities. By introducing a gauge-invariant winding number, we show that singularities in the phase of the Poincaré waves of the unforced shallow-water equations and primitive equations persist in the presence of both horizontal and vertical shear flows. Thus, the bulk Poincaré bands have nontrivial topology and we expect and confirm the persistence of the equatorial waves in the presence of shear along the equator where the Coriolis parameter $f$ changes signs.

Complex spin textures in itinerant electron magnets hold promises for next-generation memory and information technology. The long-ranged and often frustrated electron-mediated spin interactions in these materials give rise to intriguing localized spin structures such as skyrmions. Yet, simulations of magnetization dynamics for such itinerant magnets are computationally difficult due to the need for repeated solutions to the electronic structure problems. We present a convolutional neural network (CNN) model to accurately and efficiently predict the electron-induced magnetic torques acting on local spins. Importantly, as the convolutional operations with a fixed kernel (receptive field) size naturally take advantage of the locality principle for many-electron systems, CNNs offer a scalable machine learning approach to spin dynamics. We apply our approach to enable large-scale dynamical simulations of skyrmion phases in itinerant spin systems. By incorporating the CNN model into Landau-Lifshitz-Gilbert dynamics, our simulations successfully reproduce the relaxation process of the skyrmion phase and stabilize a skyrmion lattice in larger systems. The CNN model also allows us to compute the effective receptive fields, thus providing a systematic and unbiased method for determining the locality of the original electron models.

Metallic states near the Mott insulator show a variety of quantum phases, including various magnetic, charge-ordered states and high-temperature superconductivity in various transition metal oxides and organic solids. The emergence of a variety of phases and their competitions are likely intimately associated with quantum transitions between the electron-correlation-driven Mott insulator and metals characterized by its criticality, and is related to many central questions of condensed matter. The quantum criticality is, however, not well understood when the transition is controlled by the bandwidth through physical parameters such as pressure. Here, we quantitatively estimate the universality class of the transition characterized by a comprehensive set of critical exponents by using a variational Monte Carlo method implemented as an open-source innovated quantum many-body solver, with the help of established scaling laws at a typical bandwidth-controlled Mott transition. The criticality indicates a weaker charge and density instability in contrast to the filling-controlled transition realized by carrier doping, implying a weaker instability to superconductivity as well. The present comprehensive clarification opens up a number of routes for quantitative experimental studies for complete understanding of elusive quantum Mott transition and nearby strange metal that cultivate future design of functionality.

Non-Hermitian systems have attracted considerable interest in recent years owing to their unique topological properties that are absent in Hermitian systems. While such properties have been thoroughly characterized in free fermion models, they remain an open question for interacting bosonic systems. In this work, we present a precise definition of quantum phases for non-Hermitian systems and propose a family of phases referred to as composite quantum phases. We demonstrate the existence of these phases in a one-dimensional spin-1 system and show their robustness against perturbations through numerical simulations. Furthermore, we investigate the phase diagram of our model, indicating the extensive presence of these phases in non-Hermitian systems. Our work establishes an alternate framework for studying and constructing quantum phases in non-Hermitian interacting systems, revealing exciting possibilities beyond the single-particle picture.