The crystal and magnetic structures of the spin $S=1$ hexamer cluster fedotovite-like $A_2{\mathrm{Cu}}_3\mathrm{O}{\left({\mathrm{SO}}_4\right)}_3$ ($A_2={\mathrm{K}}_2$, NaK, ${\mathrm{Na}}_2$) were studied by neutron powder diffraction at temperatures 1.6–290 K. The crystal structures in all compounds are well refined in the monoclinic space group C2/c. The basic magnetic units of the compounds are copper hexamers, which are coupled by weak superexchange interactions giving rise to three-dimensional long-range magnetic order below $3.0<T_N<4.7$ K. We have found that for $A_2={\mathrm{K}}_2$ and NaK the propagation vector of the magnetic structure is $\mathit{k}=[0,0,0]$, and the coupling of the Cu hexamers is ferromagnetic (FM) along the $ab$ diagonal and antiferromagnetic along the $bc$ diagonal. In contrast, for $A=\mathrm{Na}$ the propagation vector is $\mathit{k}=[0,1,0]$, and the Cu hexamers are coupled antiferromagnetically (AFM) along the $ab$ diagonal. The hexamers are formed by three Cu pairs arranged along the $b$ axis. The calculated spin expectation values $\langle s\rangle$ for the simplest symmetric spin Hamiltonian (obtained from inelastic neutron spectroscopy) of the isolated hexamers in the mean field amounted to $\langle s\rangle =3/8$ for the side spins Cu1 and Cu2 and $\langle s\rangle =1/4$ for Cu3 in the middle. The Cu spins are FM coupled in pairs and AFM between neighboring pairs. The experimental magnetic moments of the ${\mathrm{Cu}}^{2+}$ ions turn out to be not completely collinear due to spin frustrations within the weak interhexamer interactions. The sizes of magnetic moments of Cu in the hexamers determined from the diffraction data are in fair agreement with the calculated values.

Quantum spin ice (QSI) is an emblematic three-dimensional $U\left(1\right)$ quantum spin liquid (QSL) on the pyrochlore lattice that hosts gapless photon-like modes and spinon excitations. Despite its notable status and the current rise of strong material candidates ${\mathrm{Ce}}_2$(Zr, Sn, ${\mathrm{Hf})}_2{\mathrm{O}}_7$, there are still only a few analytical approaches to model the low-energy physics of QSI. These analytical methods are essential to gain insight into the physical interpretation of measurements. We here introduce the self-consistent exclusive boson representation (SCEBR) to model emergent spinon excitations in QSI. By treating the presence of other emergent charges in an average way, the SCEBR extends the range of validity of the exclusive boson representation previously introduced in [Hao, Day, and Gingras, Phys. Rev. B 90, 214430 (2014)] to numerous cases of physical relevance. We extensively benchmark the approach and provide detailed analytical expressions for the spinon dispersion, the Bogoliubov transformation that diagonalizes the system, and the dynamical spin structure factor for 0- and $\pi$-flux QSI. Finite-temperature properties are further investigated to highlight essential differences between the thermodynamic behavior of the 0- and $\pi$-flux phases. We notably show that the SCEBR predicts a reduction of the spinon bandwidth with increasing temperature, consistent with previous quantum Monte Carlo results, through suppression of spinon hopping by thermal occupation. The SCEBR thus provides a powerful analytical tool to interpret experiments on current and future candidate material that has several advantages over other widely used methods.

Motivated by a recent experiment on a square-lattice Rydberg atom array realizing a long-range dipolar XY model [C. Chen et al., Nature (London) 616, 691 (2023)], we numerically study the model's equilibrium properties. We obtain the phase diagram, critical properties, entropies, variance of the magnetization, and site-resolved correlation functions. We consider both ferromagnetic and antiferromagnetic interactions and apply quantum Monte Carlo and pseudo-Majorana functional renormalization group techniques, generalizing the latter to a $U\left(1\right)$ symmetric setting. Our simulations perform extensive thermometry in dipolar Rydberg atom arrays and establish conditions for adiabaticity and thermodynamic equilibrium. On the ferromagnetic side of the experiment, we determine the entropy per particle $S/N\approx 0.5$, close to the one at the critical temperature, $S_c/N=0.585\left(15\right)$. The simulations suggest the presence of an out-of-equilibrium plateau at large distances in the correlation function, thus motivating future studies on the nonequilibrium dynamics of the system.

Two recent preprints [Lee et al., arXiv:2307.12008 and Lee et al., arXiv:2307.12037] have received attention because they claim experimental evidence that a Cu-substituted apatite material (dubbed LK-99) exhibits superconductivity at room temperature and pressure. If this proves to be true, LK-99 will be a holy grail of superconductors. In this work, we use density functional theory $+$ $U$ calculations to elucidate some key features of the electronic structure of LK-99. We find two different phases of this material: (i) a hexagonal lattice featuring metallic half-filled and spin-split bands, nesting of the Fermi surface, and a remarkably large electron-phonon coupling that is vibrationally unstable and (ii) a triclinic lattice, with the Cu and surrounding O distorted. This lattice is vibrationally stable, and its bands correspond to an insulator. In a crystal, the Cu atoms should oscillate between equivalent triclinic positions, with an average close to the hexagonal positions. We discuss the electronic structure expected from these fluctuations and whether it is compatible with superconductivity.

Bilayer quantum Hall states have been shown to be described by a BCS-paired state of composite fermions. However, finding a qualitatively accurate model state valid across all values of the bilayer separation is challenging. Here, we introduce two variational wave functions, each with a single variational parameter, which can be thought of as a proxy for the BCS order parameter. Studying systems of up to $9+9$ electrons in a spherical geometry using Monte Carlo methods, we show that the ground state can be accurately described by these single-parameter variational states. In addition, we provide a numerically exact wave function for the Halperin-111 state in terms of composite fermions.

We report on the investigation of periodic superstructures in twisted bilayer graphene (tBLG) van der Waals heterostructures, where one of the graphene layers is aligned to hexagonal boron nitride (hBN). Our theoretical simulations reveal that if the ratio of the resulting two moiré unit-cell areas is a simple fraction, the graphene/hBN moiré lattice acts as a staggered potential, breaking the degeneracy between tBLG AA sites. This leads to additional band gaps at energies where a subset of tBLG AA sites is fully occupied. These gaps manifest as Landau fans in magnetotransport, which we experimentally observe in an aligned tBLG/hBN heterostructure. Our study demonstrates the identification of commensurate tBLG/hBN van der Waals heterostructures by magnetotransport, highlights the persistence of moiré effects on length scales of tens of nanometers, and represents an interesting step forward in the ongoing effort to realize designed quantum materials with tailored properties.

Heat transfer is studied in the system of electron double layers of correlated composite fermion quantum liquids. In the near-field regime, the primary mechanism governing interlayer energy transfer is mediated by the Coulomb interaction of thermally-driven charge density fluctuations. The corresponding interlayer thermal conductance is computed across various limiting cases of the composite fermion Chern-Simons gauge theory, encompassing ballistic, diffusive, and hydrodynamic regimes. Plasmon enhancement of the heat transfer is discussed. The relationship between the heat transfer conductance and the drag resistance is presented for electron states formed in the fractional quantum Hall effect of even denominator filling fractions.

We develop a theory of tunneling between two systems of spinless chiral fermions. This setup can be realized at the edge of a quantum Hall bilayer structure. We find that the differential conductance of such a device in the absence of interactions has an infinitely sharp peak as a function of applied voltage. Interaction between fermions results in broadening of the conductance peak. We focus on the regime of strong interactions, in which the shape of the peak manifests well defined features associated with the elementary excitations of the system.

The concept of valleytronics has recently gained considerable research attention due to its intriguing physical phenomena and practical applications in optoelectronics and quantum information. In this study, by employing the Green function-Bethe-Salpeter equation (GW-BSE) calculations and symmetry analysis, we demonstrate that single-layer orthorhombic SnS and SnSe possess remarkable carrier mobility and exceptional excitonic effects. These materials display spontaneous linearly polarized optical selectivity, a behavior that differs from the valley-selective circular dichroism observed in the hexagonal lattices. Specifically, when the two-dimensional tin chalcogenide is subjected to a zigzag polarization of light, only the A exciton becomes optically active, while the B exciton remains dark. The armchair-polarized light triggers the opposite behavior. This selective optical excitation arises from the symmetry of the bands under mirror symmetry. Additionally, the study reveals a strong coupling between valley physics and ferroelectricity in layered tin chalcogenides, enabling the manipulation of exciton polarization. Layered tin chalcogenides thus emerge as promising candidates for valleytronic materials.

We report on a certain class of three-dimensional topological insulators and semimetals protected by spinless $\mathcal{P}\mathcal{T}$ symmetry, hosting an integer-valued bulk invariant. We show using homotopy arguments that these phases host multigap topology, providing a realization of a single $\mathbb{Z}$ invariant in three spatial dimensions that is distinct from the Hopf index. We identify this invariant with the Pontryagin index, which describes Belavin-Polyakov-Schwartz-Tyupkin (BPST) instantons in particle physics contexts and corresponds to a three-sphere winding number. We study naturally arising multigap linked nodal rings, topologically characterized by split-biquaternion charges, which can be removed by non-Abelian braiding of nodal rings, even without closing a gap. We additionally recast the describing winding number in terms of gauge-invariant combinations of non-Abelian Berry connection elements, indicating relations to Pontryagin characteristic class in four dimensions. These topological configurations are furthermore related to fully nondegenerate multigap phases that are characterized by a pair of winding numbers relating to two isoclinic rotations in the case of four bands and can be generalized to an arbitrary number of bands. From a physical perspective, we also analyze the edge states corresponding to this Pontryagin index as well as their dissolution subject to the gap-closing disorder. Finally, we elaborate on the realization of these novel non-Abelian phases, their edge states, and linked nodal structures in acoustic metamaterials and trapped-ion experiments.

Excitons, as bound states of electrons and holes, embody the solid state analog of the hydrogen atom, whose quantum spectrum is explained within a classical framework by the Bohr-Sommerfeld atomic model. In a first hydrogenlike approximation the spectra of excitons are also well described by a Rydberg series, however, due to the surrounding crystal environment deviations from this series can be observed. A theoretical treatment of excitons in cuprous oxide needs to include the band structure of the crystal, leading to a prominent fine-structure splitting in the quantum spectra. This is achieved by introducing additional spin degrees of freedom into the system, making the existence and meaningfulness of classical exciton orbits in the physical system a nontrivial question. Recently, we have uncovered the contributions of periodic exciton orbits directly in the quantum mechanical recurrence spectra of cuprous oxide [J. Ertl et al., Phys. Rev. Lett. 129, 067401 (2022)] by application of a scaling technique and fixing the energy of the classical dynamics to a value corresponding to a principle quantum number $n=5$ in the hydrogenlike case. Here, we present a comprehensive derivation of the classical and semiclassical theory of excitons in cuprous oxide. In particular, we investigate the energy dependence of the exciton dynamics. Both the semiclassical and quantum mechanical recurrence spectra exhibit stronger deviations from the hydrogenlike behavior with decreasing energy, which is related to a growing influence of the spin-orbit coupling and thus a higher velocity of the secular motion of the exciton orbits. The excellent agreement between semiclassical and quantum mechanical exciton recurrence spectra demonstrates the validity of the classical and semiclassical approach to excitons in cuprous oxide.

We theoretically investigate the coupling between the exciton internal and center-of-mass motions in monolayer transition-metal dichalcogenides subjected to a periodic electrostatic potential. The coupling leads to the emergence of multiple absorption peaks in the exciton spectrum, which are the hybridizations of $1s, 2s$, and $2p_{\pm }$ Rydberg states with different center-of-mass momentums. The energies and wave functions of hybrid states can be strongly modulated by varying the profile of the periodic electrostatic potential, which well reproduces the recent experimental observations. Combined with the electron-hole exchange interaction, nondegenerate valley-coherent bright excitons can be realized by applying an in-plane electric field, with the valley coherence determined by the field direction.

Quantum information engines can advantageously convert information into work, usually through a feedback mechanism operated by a Maxwell demon. In principle, this opens prospects of autonomous machines that challenge the classical second law of thermodynamics. Yet prior research, which typically tests a given concept in isolation, usually makes strong assumptions on turning on/off internal interactions or the connection to the baths, which has fueled skepticism. Meanwhile, several recent experiments describe an autonomous spintronic engine that purportedly combines several concepts using inherent electronic interactions to harvest spin fluctuations and quantum correlations. So far, no full-fledged theory has described it. In this article, we address these several interdisciplinary shortcomings by presenting a theory for a solid-state, fully electronic spintronic quantum information engine that converts the energy of quantum coherence into useful electrical work thanks to quantum measurements. Our simple two-stroke engine operates on two correlated atomic, single-spin quantum dots (QDs) that are connected in series with two ferromagnetic electrodes. The ultrafast measurement stroke destroys the quantum coherence stored within the QDs and projects the system into a local high-energy separated state. The resulting energy is then released into the leads as electrical current when the partial thermalizing stroke restores quantum coherence. Using a master equation approach, we show that a robust steady-state current can flow between the electrodes despite the absence of a tunneling path and at thermal equilibrium. Our model proves the feasibility of harvesting quantum fluctuations by the measurement back-action through the on-site Coulomb interaction, and can reproduce experimental output power levels if bosons mediate this transport in the presence of an additional nonequilibrium resource. This can for instance be accomplished by the spin bias that is inherently generated by the ferromagnetic electrodes. Our work raises the prospect of measuring the “spintronic temperature” of the leads using magnetization dynamics experiments, while the model's underpinnings of built-in, materials-inherent measurements of quantum information can in principle be adapted to describe fundamental quantum processes in chemistry and biology.

We address dissipative dynamics of the one-dimensional nearest-neighbour XX spin-$1/2$ chain governed by the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation. In the absence of dissipation, the model is integrable. We identify a broad class of dissipative terms that generically destroy integrability but leave the operator space of the model fragmented into an extensive number of dynamically disjoint subspaces of varying dimensions. In sufficiently small subspaces, the GKSL equation in the Heisenberg representation can be easily solved, sometimes in a closed analytical form. We provide an example of such an exact solution for a specific choice of dissipative terms. It is found that observables experience the Wannier-Stark localization in the corresponding operator subspace. As a result, the expectation values of the observables are linear combinations of essentially a few discrete decay modes, the long time dynamics being governed by the slowest mode. We examine the complex Liouvillian eigenvalue corresponding to this latter mode as a function of the dissipation strength. We find an exceptional point at a critical dissipation strength that separates oscillating and nonoscillating decay. We also describe a different type of dissipation that leads to a single decay mode in the whole operator subspace. Finally, we point out that our exact solutions of the GKSL equation entail exact solutions of the Schrödinger equation describing the quench dynamics in closed spin ladders dual to the dissipative spin chains.

Topological interfaces of two-dimensional conformal field theories contain information about symmetries of the theory and exhibit striking spectral and entanglement characteristics. While lattice realizations of these interfaces have been proposed for unitary minimal models, the same has remained elusive for the paradigmatic Luttinger liquid, i.e., the free, compact boson model. Here, we show that a topological interface of two Luttinger liquids can be realized by coupling special one-dimensional superconductors. The gapless excitations in the latter carry charges that are specific integer multiples of the charge of Cooper pairs. The aforementioned integers are determined by the windings in the target space of the bosonic fields — a crucial element required to give rise to nontrivial topological interfaces. The latter occur due to the perfect transmission of certain number of Cooper pairs across the interface. The topological interfaces arise naturally in Josephson junction arrays with the simplest case being realized by an array of experimentally demonstrated $0-\pi$ qubits, capacitors and ordinary Josephson junctions. Signatures of the topological interface are obtained through entanglement entropy computations. In particular, the subleading contribution to the so-called interface entropy is shown to differ from existing field theory predictions. The proposed lattice model provides an experimentally realizable alternative to spin and anyon chains for the analysis of several conjectured conformal fixed points which have so far eluded ab initio investigation.

Transition metal dichalcogenides (TMDCs) monolayers, as two-dimensional (2D) direct bandgap semiconductors, hold promise for advanced optoelectronic and photocatalytic devices. Interaction with three-dimensional (3D) metals, like Au, profoundly affects their optical properties, posing challenges in characterizing the monolayer's optical responses within the semiconductor-metal junction. In this study, using precise polarization-controlled final-state sum frequency generation (FS-SFG), we successfully isolated the optical responses of a ${\mathrm{MoS}}_2$ monolayer from a ${\mathrm{MoS}}_2/\mathrm{Au}$ junction. The resulting SFG spectra exhibit a linear lineshape, devoid of A or B exciton features, attributed to the strong dielectric screening and substrate induced doping. The linear lineshape illustrates the expected constant density of states (DOS) at the band edge of the 2D semiconductor, a feature often obscured by excitonic interactions in weak-screening conditions such as in a free-standing monolayer. Extrapolation yields the onset of a direct quasiparticle bandgap of about $1.65\pm 0.20\mathrm{eV}$, indicating a strong bandgap renormalization. This study not only enriches our understanding of the optical responses of a 2D semiconductor in extreme screening conditions but also provides a critical reference for advancing 2D semiconductor-based photocatalytic applications.

Alkali-metal $\beta /{\beta }^{\prime \prime }$ aluminas are among the fastest ionic conductors, yet little is understood about the role of defects in the ion transport mechanism. Here, we use density functional theory (DFT) to investigate the crystal structures of the $\beta$ and ${\beta }^{\prime \prime }$ phases and their vacancy and interstitial defects. We find that charge transport is likely to be dominated by alkali-metal interstitials in $\beta$ aluminas and by vacancies in ${\beta }^{\prime \prime }$ aluminas. Lower bounds for the activation energy for diffusion are found by determining the minimum-energy paths for defect migration. The resulting migration barriers are lower than the experimental activation energies for conduction in Na $\beta$ and ${\beta }^{\prime \prime }$ aluminas, suggesting a latent potential for optimization. The lowest activation energy of about 20 meV is predicted for correlated vacancy migration in K ${\beta }^{\prime \prime }$ alumina.

Optically active spin qubits in wide-band-gap semiconductors exist in several charge states, though typically only specific charge states exhibit desirable spin or photonic properties. An understanding of how interconversion between different charge states occurs is important for most applications seeking to employ such defects in quantum sensing and information processing, and additionally serves as a means of testing and verifying models of the defect electronic structure. Here, we use charge-sensitive confocal imaging to study the wavelength dependence of optical carrier generation in diamonds hosting nitrogen vacancy (NV) centers, silicon vacancy (SiV) centers, and substitutional nitrogen (N). We study the generation of distinctive charge-capture patterns formed when photogenerated charge carriers are captured by photoluminescent defects, using light spanning 405–633 nm (1.96–3.06 eV). We observe distinct regimes where one- or two-photon ionization or recombination processes dominate, and a third regime where anti-Stokes mediated recombination drives weak NV charge cycling with red light. We then compare red-induced charge cycling to fast charge carrier transport between isolated single NV centers driven with green and blue light. This work reports optically mediated charge cycling processes of the NV centers, and has consequences for schemes using charge transfer to identify nonluminescent defects and photoelectric detection, where ambiguity exists as to the source of photocurrent.

We establish a comprehensive theoretical framework for systems subjected to a static uniform temperature gradient, employing the nonequilibrium Keldysh-Dyson formalism. This framework interprets the statistical force due to the temperature gradient as a mechanical force, utilizing both Luttinger's scalar and Moreno-Coleman-Tatara's vector potentials, which collectively emulate the gauge invariance stemming from the conservation of energy. Our approach has the ability to treat heat current and heat magnetization on an equal footing, thereby extending and generalizing previous formalisms. The derived result for the thermal conductivity is applied to investigate the thermal characteristics of Weyl magnons in a stacked honeycomb ferromagnet featuring a trivial insulator phase, a magnon Chern insulator phase, and three Weyl magnon phases. Against the expectation from the Berry curvature, the magnon Chern insulator phase exhibits the highest transverse thermal conductivity.

The manipulation of magnons in artificial magnonic crystals (MCs) leads to fascinating nonlinear wave phenomena such as the generation of gap solitons, which has been mostly limited to one-dimensional systems. Here, we propose a model system for the magnetization in two-dimensional MCs subjected to a periodic external magnetic field, describing the dynamics of magnetic gap solitons (MGSs) formed by nonlinear self-trapping. We show the formation, stability, and dynamics for various two-dimensional gap modes, including gap solitons and vortical ones. Their existence regions depend on the anisotropic axis orientation of the ferromagnetic film. The Bloch oscillation and depinning propagation of MGSs under constant spin-current injections are discovered and characterized. We design a scheme of pulse-current injection to achieve the distortionless propagation of MGSs. These findings show that the two-dimensional magnonic crystals can be viewed as a building block for MGS-based storage and transmission, where the propagation and localization are variously controlled and reconfigurable.