In the presence of a nonlocal potential in molecular device systems, generally the charge conservation cannot be satisfied, and in the literature the modifications of the conventional definition of current were given to solve this problem. We demonstrate that, however, the nonconservation is not due to the invalidation of the conventional definition of current, but originates respectively from the improper approximations to electron-electron interactions and the inappropriate definition of current using pseudo wave functions in pseudopotential implementations. In this work, we propose a nonlocal-potential formulation of the interactions to fulfill the charge conservation and also give a discussion about the calculation of current when the pseudopotential is involved. As an example of application of our formulation, we further present the calculated results of a double-barrier model.

A pair of tunnel-coupled quantum dots has advantages over single dots in tunability and spin coherence, but far less work has been done to measure and understand the quantum optics of this system. In particular, the two-electron singlet-triplet system with one electron in each dot generates an eight-level system in which two-level and four-level double-Λ systems are coupled only through the hyperfine interaction and other spin relaxation processes. We first measure the emission spectrum under resonant driving with a continuous-wave laser and then perform time-correlated Hanbury Brown-Twiss (HBT) and Hong-Ou-Mandel (HOM) interferometric measurements to examine nonclassical photon properties of spin-flip Raman emission and resonance fluorescence. The shapes of second-order correlation functions $\left[g^{\left(2\right)}\left(\tau \right)\right]$ from HBT are strikingly different between resonance fluorescence and spin-flip Raman emission, reflecting the spin dynamics of the singlet-triplet system. In addition, our two-photon HOM measurements demonstrate a high raw visibility of 0.96, with a coherence time exceeding the radiative lifetime.

We study the quantum phase transition from a Dirac spin liquid to an antiferromagnet driven by condensing monopoles with spin quantum numbers. We describe the transition in field theory by tuning a fermion interaction to condense a spin-Hall mass, which in turn allows the appropriate monopole operators to proliferate and confine the fermions. We compute various critical exponents at the quantum critical point (QCP), including the scaling dimensions of monopole operators by using the state-operator correspondence of conformal field theory. We find that the degeneracy of monopoles in ${\mathrm{QED}}_3$ is lifted and yields a nontrivial monopole hierarchy at the QCP. In particular, the lowest monopole dimension is found to be smaller than that of ${\mathrm{QED}}_3$ using a large-$N_f$ expansion, where $2N_f$ is the number of fermion flavors. For the minimal magnetic charge, this dimension is $0.39N_f$ at leading order. We also study the QCP between Dirac and chiral spin liquids, which allows us to test a conjectured duality to a bosonic ${\mathrm{CP}}^1$ theory. Finally, we discuss the implications of our results for quantum magnets on the kagome lattice.

The mechanism of a magnetoelectric coupling in a room-temperature multiferroic, $\mathrm{S}{\mathrm{r}}_3\mathrm{C}{\mathrm{o}}_2\mathrm{F}{\mathrm{e}}_{24}{\mathrm{O}}_{41}$, with the Z-type hexaferrite structure, is examined by three approaches: observations of domain structures and their field responses, measurements of magnetic-field effect on electric polarization, i.e., magnetoelectric effect, and phenomenological discussions on the interplay among coexisting order parameters. With use of a resonant soft x-ray microdiffraction technique, we visualized magnetic-field responses of two types of magnetic domains ascribed to ferrimagnetic and spiral components inherent in a transverse conical magnetic structure of the hexaferrite. A simultaneous inversion of these magnetic domains by a magnetic-field reversal was observed, meaning that the process of a magnetization reversal corresponds to a 180° rotation of the cone axis. The reversal process of the magnetic structure, together with experimental results of the magnetoelectric effect, leads us to the conclusion that the magnetoelectricity in the Z-type hexaferrite originates mainly from the spin-dependent metal-ligand orbital hybridization, with minor contribution from the asymmetric spin-exchange interaction. Furthermore, such a mechanism is discussed by the symmetry analysis based on the Landau theory and is well described in terms of couplings among the coexisting order parameters included in the free energy. Thus, observations on field responses of multiple domains in multiferroics provide insights into underlying microscopic magnetoelectric coupling mechanisms.

Twisted bilayer graphene is one of the simplest van der Waals structures, and its inhomogeneous interlayer coupling can induce rich electronic properties. In twisted bilayer graphene nanoribbons (tBLGNRs), the interlayer coupling strengths are different for two ribbon edges due to the inhomogeneous bonding, which splits the edge states into two individuals in energy. The lower-energy state, localizing at the ribbon edge with the stronger interlayer coupling, is a good candidate to generate one-dimensional (1D) topological superconductivity in the presence of Rashba spin-orbit coupling, Zeeman field, and $s$-wave superconductivity. Majorana zero modes (MZMs) are found to be localized at both ends of this edge. The topological invariants of the system are explored by evaluating the Berry phase for infinite-length ribbons and Majorana polarization for quasi-1D ribbons, giving the same topological phase diagram. More importantly, by adjusting interlayer dislocation and uniaxial strain of tBLGNRs across the critical values, the lower-energy edge changes and 1D topological superconductivity can “jump” from one ribbon edge to the other one. Finally, by applying a gate voltage bias between bilayers or changing the interlayer distance, a MZM can transfer along the ribbon edge. The tBLGNRs provide an alternative platform to study 1D topological superconductivity and MZMs.

The electronic structure of non-Kramers ${\mathrm{Tb}}^{3+}$ centers in single crystals of yttrium aluminum garnet (YAG) was studied using a new-generation high-frequency magnetic resonance spectrometer that allows measurements of electron paramagnetic resonance (EPR), electron spin echo (ESE), the photon echo on hyperfine components of Stark levels in zero magnetic field, and optically detected magnetic resonance (ODMR). It was created on the basis of a highly stable microwave bridge operating in the near-terahertz region (0.094 or 0.130 THz), both in continuous-wave (cw) and pulse modes, a nonresonant system for supplying microwave power to a sample, and a cryogen-free magneto-optical cryostat. EPR, ESE, and cw measurements at two frequencies allowed us to reliably and with high accuracy determine the parameters of ${\mathrm{Tb}}^{3+}$ centers that occupy yttrium dodecahedral positions in YAG: $g_{\left|\right|}=15.8\pm 0.2$, $g_{\perp }\approx 0$ (|| corresponds to one of the $\langle 100\rangle$ crystal axes), the zero-field splitting $\mathrm{\Delta }=2.705\pm 0.005\mathrm{c}{\mathrm{m}}^{-1}$, and the hyperfine interaction constant $A=0.197\pm 0.005\mathrm{c}{\mathrm{m}}^{-1}$. In addition to the ${\mathrm{Tb}}^{3+}$ centers in a regular environment, EPR spectra with lower intensity and a resolved hyperfine structure were found for at least three types of additional ${\mathrm{Tb}}^{3+}$ centers. They have symmetry, $g$ factors, and hyperfine interaction constants which are close to those of the main ${\mathrm{Tb}}^{3+}$ centers but differ in the zero-field splitting parameters Δ that strongly depend on the crystal field. They were ascribed to ${\mathrm{Tb}}^{3+}$ centers with nearby antisite ${\mathrm{Y}}_{\mathrm{Al}}$ defects. Similarity with several types of ${\mathrm{Ce}}^{3+}$ centers in YAG crystals, the types, and relative concentrations of antisite defects are discussed. For one of the additional ${\mathrm{Tb}}^{3+}$ centers, splitting of the energy levels in the zero field turned out to be close to an energy of 94 GHz microwave quanta, and intense echo signals were observed in weak magnetic fields and in the zero field corresponding to the EPR transitions between the hyperfine components of the ${\mathrm{Tb}}^{3+}$ spin levels. ODMR spectra of ${\mathrm{Tb}}^{3+}$ centers in YAG crystals, containing Ce and Tb, were obtained by monitoring the intensity of the ${\mathrm{Ce}}^{3+}$ luminescence, which implies the transfer of energy from ${\mathrm{Tb}}^{3+}$ ions to ${\mathrm{Ce}}^{3+}$ ions with conservation of spin. This result seems to be important, since these systems are of interest for quantum communication and computations. Taking into account that cerium does not have isotopes with a nuclear spin and that terbium has 100% ${}^{159}\mathrm{Tb}$ having nuclear spin $I=3/2$ and a sufficiently large nuclear magnetic moment, the ${\mathrm{Tb}}^{3+}-{\mathrm{Ce}}^{3+}$ system in garnet crystals can be promising for coherent information processing. ${\mathrm{Tb}}^{3+}$ ions can play a role of qubits and ${\mathrm{Ce}}^{3+}$ ion with a lifetime of about 50 ns, and almost unity quantum efficiency of optical transitions can be used as a single-ion readout arrangement. The prospects for using this system as hardware for quantum communication and computations are discussed.

We utilize microwave spectroscopy to study the auto-oscillation modes in the nanogap spin Hall nano-oscillators based on Permalloy/Pt bilayers. We show that two distinct spin-wave modes appear in such oscillators, regardless of the magnetic film thicknesses or the size of the electrode gap. We identify the primary mode as a nonlinear self-localized bullet soliton localized at the center of the gap between the electrodes, which is excited over a broad range of currents, field magnitudes, and orientations. The secondary high-frequency mode appears at higher currents and coexists with the primary bullet mode. Micromagnetic modeling shows that this mode is stabilized by the dipolar field of the bullet, and its spatial profile exhibits two maxima offset from the center of the gap in two opposite directions collinear with the field. Simulations also suggest chaotic dynamics that emerges at large currents due to the incoherent coupling between the two modes. Our results demonstrate the possibility to induce and control complex nonlinear dynamical phenomena in spin Hall oscillators, which can be utilized in the emergent neuromorphic and reservoir computing applications.

We demonstrate a real-space imaging of a heterodyne signal of light that is produced as a result of the Brillouin light scattering by coherently driven magnons in magnetostatic modes. With this imaging technique, we characterize surface magnetostatic modes (Damon-Eshbach modes) in a one-dimensional magnonic crystal, which is formed by patterned aluminum strips deposited on the ferromagnetic film. The modified band structures of the magnonic crystal are deduced from the Fourier transforms of the real-space images. The heterodyne imaging provides a simple and powerful method to probe magnons in structured ferromagnetic films, paving a way to investigate more complex phenomena, such as Anderson localization and topological transport with magnons.

We investigate the damping experienced by quartz tuning fork resonators in normal and superfluid ${}^3\mathrm{He}$ as a function of their resonance frequency from 22 to 250 kHz and contrast it with the behavior of the forks in ${}^4\mathrm{He}$. For our set of tuning forks the low frequency damping in both fluids is well described by the existing hydrodynamic models. We find that the acoustic emission becomes the dominating dissipation mechanism at resonator frequencies exceeding approximately 100 kHz. Our results show that the acoustic emission model used in ${}^4\mathrm{He}$ fluid also describes acoustic damping in superfluid ${}^3\mathrm{He}$ and normal ${}^3\mathrm{He}$ at low temperatures using the same geometrical prefactor. The high temperature acoustic damping in normal ${}^3\mathrm{He}$ does not exceed prediction of this model and thus the acoustic damping of moderate frequency devices measured in ${}^4\mathrm{He}$ should be similar or smaller in ${}^3\mathrm{He}$ liquid.

Based on local density approximation plus dynamical mean-field theory ($\text{LDA}+\text{DMFT}$) calculations, we revisit the long-standing quasiparticle band narrowing problem of sodium metal. Using an on-site Coulomb interaction $U$ derived from angle-resolved photoemission spectroscopy mass enhancement, we can describe various properties of this weakly correlated electron system. Intrinsic self-energy corrections lead to a Landau-Fermi liquid state with many-particle coherence and dynamical spectral weight transfer relevant to electronic structure and scattering rates of alkali metals.

We report polarization-resolved Raman scattering measurements on single crystals of the pyrochlore compound ${\mathrm{Eu}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ which exhibits a ground state with noncollinear magnetic order, as well as its paramagnetic counterpart ${\mathrm{Pr}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$. The spectra reveal the six Raman-active optical phonons expected for the pyrochlore lattice symmetry. Combined with density functional calculations, polarization analysis of the Raman intensity allows us to assign all observed peaks to specific vibration patterns. Whereas most phonon profiles are weakly temperature dependent, an Ir-O-Ir bond-bending vibration in ${\mathrm{Eu}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ exhibits a pronounced Fano asymmetry in the paramagnetic state, and marked softening and line-shape anomalies at the magnetic phase transition. These observations indicate strong electron-phonon interactions, which must be considered in models of the electronic properties and phase behavior of the pyrochlore iridates. In addition, a prominent feature appears at 210 ${\mathrm{cm}}^{-1}$ in the Raman spectrum of ${\mathrm{Eu}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ below the magnetic transition temperature, possibly due to a magnetic excitation.

Recent investigations of the magnetic properties and the discovery of superconductivity in quasi-one-dimensional triangular lattice organic charge-transfer solids have indicated the severe limitations of the effective $\frac{1}{2}$-filled band Hubbard model for these and related systems. We present computational studies within the $\frac{1}{4}$-filled band Hubbard model for these highly anisotropic systems. Individual organic monomer molecules, and not their dimers, constitute the sites of the Hamiltonian within our theory. We find enhancement of the long-range component of superconducting pairing correlations by the Hubbard repulsive interaction $U$ for band parameters corresponding to $\kappa \text{−}{\left(\text{BEDT-}\mathrm{TTF}\right)}_2{\mathrm{CF}}_3{\mathrm{SO}}_3$, which is superconducting under moderate pressure. We find significantly weaker superconducting pairing at realistic values of $U$ in $\kappa \text{−}{\left(\text{BEDT-}\mathrm{TTF}\right)}_2\mathrm{B}{\left(\mathrm{CN}\right)}_4$, and we ascribe the experimentally observed transition to a spin-gapped insulator to the formation of a paired-electron crystal. We make the testable prediction that the spin gap will be accompanied by charge ordering and period doubling in two lattice directions. The weaker tendency to superconductivity in $\kappa \text{−}{\left(\text{BEDT-}\mathrm{TTF}\right)}_2\mathrm{B}{\left(\mathrm{CN}\right)}_4$ compared to $\kappa \text{−}{\left(\text{BEDT-}\mathrm{TTF}\right)}_2{\mathrm{CF}}_3{\mathrm{SO}}_3$ is consistent with the more one-dimensional character of the former. Pressure-induced superconductivity is, however, conceivable. The overall results support a valence bond theory of superconductivity we have proposed recently.

Orbital differentiation is a common theme in multiorbital systems, yet a complete understanding of it is still missing. Here, we consider a minimal model for orbital differentiation in Hund metals with a highly accurate method: We use the numerical renormalization group as a real-frequency impurity solver for a dynamical mean-field study of three-orbital Hubbard models, where a crystal field shifts one orbital in energy. The individual phases are characterized with dynamic correlation functions and their relation to diverse Kondo temperatures. Upon approaching the orbital-selective Mott transition, we find a strongly suppressed spin coherence scale and uncover the emergence of a singular Fermi liquid and interband doublon-holon excitations. Our theory describes the diverse polarization-driven phenomena in the $t_{2g}$ bands of materials such as ruthenates and iron-based superconductors, and our methodological advances pave the way toward real-frequency analyses of strongly correlated materials.

Topological crystalline phases in electronic structures can be generally classified using the spatial symmetry characters of the valence bands and mapping them onto appropriate symmetry indicators. These mappings have been recently applied to identify thousands of topological electronic materials. There can exist, however, topological crystalline nontrivial phases that go beyond this paradigm: They cannot be identified using spatial symmetry labels and consequently lack any classification. In this work, we achieve the first of such classifications showcasing the paradigmatic example of two-dimensional crystals with twofold rotation symmetry. We classify the gapped phases in time-reversal invariant systems with strong spin-orbit coupling identifying a set of three ${\mathbb{Z}}_2$ topological invariants, which correspond to nested quantized partial Berry phases. By further isolating the set of atomic insulators representable in terms of exponentially localized symmetric Wannier functions, we infer the existence of topological crystalline phases of the fragile type that would be diagnosed as topologically trivial using symmetry indicators and construct a number of microscopic models exhibiting this phase. Our work is expected to have important consequences given the central role fragile topological phases are expected to play in novel two-dimensional materials such as twisted bilayer graphene.

Motivated by the recent experimental realization of the topological Anderson insulator and research interest on the topological quasicrystal lattices, we investigate the effects of disorder on topological properties of a two-dimensional Penrose-type quasicrystal lattice that supports the quantum spin Hall insulator (QSHI) and normal insulator (NI) phases in the clean limit. It is shown that the helical edge state of the QSHI phase is robust against weak disorder. Most saliently, it is found that disorder can induce a phase transition from NI to QSHI phase in the quasicrystal system. The numerical results based on a two-terminal device show that a quantized conductance plateau can arise inside the energy gap of the NI phase for moderate Anderson disorder strength. Further, it is confirmed that the local current distributions of the disorder-induced quantized conductance plateau are located on the two edges of the sample. Finally, we identify this disorder-induced phase as topological Anderson insulator phase by computing the disorder-averaged spin Bott index.

The nuclear spin of a phosphorus atom in silicon has been used as a quantum bit in various quantum-information experiments. It has been proposed that this nuclear-spin qubit can be efficiently controlled by an ac electric field, when embedded in a two-electron dot-donor setup subject to intrinsic or artificial spin-orbit interaction. Exposing the qubit to control electric fields in that setup exposes it to electric noise as well. In this work, we describe the effect of electric noise mechanisms, such as phonons and $1/f$ charge noise, and estimate the corresponding decoherence timescales of the nuclear-spin qubit. We identify a promising parameter range where the electrical single-qubit operations are at least an order of magnitude faster then the decoherence. In this regime, decoherence is dominated by dephasing due to $1/f$ charge noise. Our results facilitate the optimized design of nanostructures to demonstrate electrically driven nuclear-spin resonance.

We propose and evaluate the heterostructure based on the graphene layer (GL) with the lateral electron injection from the side contacts and the hole vertical injection via the black phosphorus layer (BL) $({\mathrm{P}}^{+}\text{−}\mathrm{PL}$-PL-GL heterostructure). Due to a relatively small energy of the holes injected from the PL into the GL (about 100 meV, smaller than the energy of optical phonons in the GL which is about 200 meV), the hole injection can effectively cool down the two-dimensional electron-hole plasma in the GL. This simplifies the realization of the interband population inversion and the achievement of the negative dynamic conductivity in the terahertz (THz) frequency range enabling the amplification of the surface plasmon modes. The latter can lead to the plasmon lasing. The conversion of the plasmons into the output radiation can be used for new types of the THz sources.

Atomically thin crystals of transition-metal dichalcogenides are ideally suited to study the interplay of light-matter coupling, polarization, and magnetic field effects. In this Rapid Communication, we investigate the formation of exciton polaritons in a ${\mathrm{MoSe}}_2$ monolayer, which is integrated in a fully grown, monolithic microcavity. Due to the narrow linewidth of the polaritonic resonances, we are able to directly investigate the emerging valley Zeeman splitting of the hybrid light-matter resonances in the presence of a magnetic field. At a detuning of $-54.5$ meV (13.5% matter constituent of the lower polariton branch), we find a Zeeman splitting of the lower polariton branch of 0.36 meV, which can be directly associated with an excitonic $g$-factor of $3.94\pm 0.13$. Remarkably, we find that a magnetic field of 6 T is sufficient to induce a notable valley polarization of 15% in our polariton system, which approaches 30% at 9 T. This circular polarization degree of the polariton (ground) state exceeds the polarization of the exciton reservoir for equal magnetic field magnitudes by approximately 50%, which is a clear hint of valley-dependent bosonic stimulation in our strongly coupled system in the subthreshold, fluctuation-dominated regime.

In this Rapid Communication, we develop the concept of charge qubits in van der Waals heterostructures. A theoretical proof of concept is provided for the ${\mathrm{ZrSe}}_2/{\mathrm{SnSe}}_2$ system, in which a framework connecting the electronic structure with quantum information is described. The quantum state is prepared by applying a vertical electric field, manipulated by short field pulses, and measured via electric currents. The proposed qubit is robust, operational at high temperature, and compatible with two-dimensional material technology, opening different avenues for the field.