We study the topological phase in a dipolar-coupled two-dimensional breathing square lattice of magnetic vortices. By evaluating the quantized Chern number and ${\mathbb{Z}}_4$ Berry phase, we obtain the phase diagram and identify that the second-order topological corner states appear only when the ratio of alternating bond lengths goes beyond a critical value. Interestingly, we uncover three corner states at different frequencies ranging from subgigahertz to tens of gigahertz by solving the generalized Thiele's equation, which has no counterpart in natural materials. We show that the emerging corner states are topologically protected by a generalized chiral symmetry of the quadripartite lattice, leading to particular robustness against disorder and defects. Full micromagnetic simulations confirm theoretical predictions with great agreement. A vortex-based display device is designed as a demonstration of the real-world application of the second-order magnetic topological insulator. Our findings provide a route for realizing symmetry-protected multiband corner states that are promising to achieve spintronic higher-order topological devices.

We study theoretically the Josephson effect between two two-band superconductors respecting time-reversal symmetry, where we assume a spin-singlet $s$-wave pair potential in each conduction band. The superconducting phase at the first band ${\phi }_1$ and that at the second band ${\phi }_2$ characterize a two-band superconducting state. We consider a Josephson junction where an insulating barrier separates two such two-band superconductors. By applying the tunnel Hamiltonian description, the Josephson current is calculated in terms of the anomalous Green's function on either side of the junction. We find that the Josephson current consists of three components which depend on three types of phase differences across the junction: the phase difference at the first band $\delta {\phi }_1$, the phase difference at the second band $\delta {\phi }_2$, and the difference at the center-of-mass phase $(\delta {\phi }_1+\delta {\phi }_2)/2$. A Cooper pair generated by the band hybridization carries the last current component. We discuss the relation between the Josephson current calculated in theories and that observed in experiments.

We present resistivity measurements of bilayer and trilayer films with layer-dependent Rashba spin-orbit interactions. A sharp upturn is observed in the temperature dependence of the parallel upper critical field. We show that it corresponds to a transition from a complex-stripe phase to a helical phase. Moreover, we propose the phase diagram of a multilayer system, which is obtained from experimental observations with the support of numerical calculations. These results pave the way for the clarification of non-trivial superconducting states in multilayer systems composed of two-dimensional Rashba superconductors.

In this paper, we study the statistics of permutation cycles of ground-state hardcore lattice bosons described by various two-dimensional Bose-Hubbard-type models on both square and kagome lattices. We find that it is possible to differentiate quantum phases by the statistics of permutations cycles. Indeed, features in the permutation cycles statistics can be used to uniquely identify certain insulating phases and are consistent with local resonances of occupation numbers in the ground-state expansion of the phase. We also confirm that suitable quantities derived from the probability distribution of the length of permutation cycles can be used to detect superfluid to insulator phase transitions.

Metamaterials exhibit optical properties not observed in traditional materials. Such behavior emerges from the interaction of light with precisely engineered subwavelength features built from different constituent materials. Recent research into the design and fabrication of metamaterial-based devices has established a foundation for the next generation of functional materials. Of particular interest is the all-dielectric metasurface, a two-dimensional metamaterial exploiting shape-dependent resonant features while avoiding losses through the use of dielectric building blocks. However, even this simple metamaterial class has a nearly infinite number of possible configurations; researchers now require new methods to efficiently explore these types of design spaces. In this work, we employ rigorous coupled wave analysis to calculate reflection and transmission spectra associated with a class of open-cylinder all-dielectric metasurface. By altering the geometric parameters of open-cylinder metasurfaces, we generate a sparse training data set and construct artificial neural networks capable of relating metasurface geometries to reflection and transmission spectra. Here, we successfully demonstrate that pseudo autodecoder neural networks can suggest device geometries based on a requested optical performance—inverting the design process for this metasurface class. As an example, we query for and discover a particular open-cylinder metasurface displaying a reflection band $R\ge 99\%$ centered at ${\lambda }_0=1550\mathrm{nm}$ that is much broader $\mathrm{\Delta }\lambda =450\mathrm{nm}$ than anything reported for optical metasurfaces. We then analyze the modal interplay in the open-cylinder metasurface to better understand the underlying physics driving the broadband behavior. Ultimately, we conclude that neural networks are ideally suited for generally approaching these types of complex inverse design problems.

Recent years have seen a surge of interest in studies of hydrodynamic transport in electronic systems. We investigate the electron viscosity of metals and find a component that is closely related to Coulomb drag. By using linear-response theory, viscosity, which is a transport coefficient for momentum, can be extracted from the retarded correlation function of the momentum flux, i.e., the stress tensor. There exists a previously overlooked contribution to the shear viscosity from the interacting part of the stress tensor which accounts for the momentum flow induced by interactions. This contribution, which we dub drag viscosity, is caused by the frictional drag force due to long-range interactions. It is therefore linked to Coulomb drag which also originates from the interaction-induced drag force. Starting from the Kubo formula and using the Keldysh technique, we compute the drag viscosity of two- and three-dimensional metals along with the drag resistivity of double-layer two-dimensional electronic systems. Both the drag resistivity and drag viscosity exhibit a crossover from quadratic-in-$T$ behavior at low temperatures to a linear behavior at higher temperatures. Although the drag viscosity appears relatively small compared with the normal Drude component for the clean metals, it may dominate hydrodynamic transport in some systems, which are discussed in the conclusion.

Performing an exact diagonalization of the effective spin problem, a ferromagnetic ground state of kinetic origin is shown to emerge in a system of $N$ strongly correlated electrons on a $L$-site ring ($L>N$). A problem of $N$ constrained spinful electrons on a $L$-site ring is argued to reduce to that of the spinless fermions with an effective flux threading through the ring. This phenomenon is brought about by the quantum necklace statistics originated by the no-double-occupancy constraint, leading to a fractional shifted electron momentum quantization. As a consequence of such special energy-level distribution, the kinetic ferromagnetism is stable only for $N=3$. For odd $N>3$ the fully polarized FM-state energy is only a local minimum but it is protected by a finite energy barrier that inhibits one spin-flip processes. The metastable ferromagnetic state survives perturbations of small magnitude, opening up a possibility of being experimentally observed by an appropriate tuning of interdot tunneling amplitudes in currently available quantum dot arrays.

Hidden magnetic order in the correlated iridate ${\mathrm{Sr}}_2{\mathrm{Ir}}_{1-x}{\mathrm{Rh}}_x{\mathrm{O}}_4, x=0.05$ and 0.1, has been studied using muon spin relaxation spectroscopy. In zero field (ZF) and weak longitudinal fields (LFs) ($\lesssim 2\mathrm{mT}$), the muon spin relaxation data indicate that static and dynamic local fields coexist at each muon site, and can be well described by exponentially damped static Lorentzian Kubo-Toyabe functions. The ZF relaxation rate is dominated by the static-field distribution, and a broad relaxation rate maximum at 175 K for $x=0.1$ in ZF is attributed to muon diffusion and trapping. For $\text{LF}\gtrsim 2\mathrm{mT}$ the static rate is completely decoupled, and the exponential decay is due to dynamic spin fluctuations. The temperature dependencies of the relaxation rates exhibit maxima at 215 K ($x=0.05$) and 175 K ($x=0.1$), in agreement with previous second harmonic generation and polarized neutron diffraction determinations of transition temperatures to a hidden-order state. The maxima are most likely due to critical slowing down of electronic spin fluctuations. The field dependencies of the dynamic spin fluctuation rates can be well described by the Redfield relation, from which the rms width $B_{\mathrm{loc}}^{\mathrm{rms}}$ and correlation time ${\tau }_{\mathrm{c}}$ of the fluctuating field are obtained. Values of ${\tau }_c$ are in the range of 1.5–4 ns for $x=0.1$ and shorter than 2 ns for $x=0.05$, suggesting an increase with increasing Rh concentration. Values of $B_{\mathrm{loc}}^{\mathrm{rms}}$ are on the order of 1 mT, consistent with the polarized neutron diffraction cross section.

We consider a scheme for on-demand teleportation of a dual-rail electron qubit state, based on single-electron sources and detectors. The scheme has a maximal efficiency of 25%, which is limited both by the shared entangled state as well as the Bell-state measurement. We consider two experimental implementations, realizable with current technology. The first relies on surface acoustic waves, where all the ingredients are readily available. The second is based on Lorentzian voltage pulses in quantum Hall edge channels. As single-electron detection is not yet experimentally established in these systems, we consider a tomographic detection of teleportation using current correlators up to (and including) third order. For both implementations, we take into account environmental effects.

The renormalization of conductances in a $Y$ junction of spinless Luttinger-liquid wires additionally coupled to acoustic longitudinal phonons is investigated in fermionic representation. This system corresponds to geometry of a tunneling experiment and exhibits the interplay between the Coulomb repulsion and the attractive retarded interaction mediated by phonons. The retardation effects related to the propagation of phonons through the junction with arbitrary transmission and reflection amplitudes are taken into account. The appearing logarithmic corrections to conductances of the junction are treated in a renormalization group approach, and scaling exponents are calculated up to infinite order in the interaction after RPA-type summation. The fixed points and corresponding scaling exponents are considered in various nonequilibrium regimes. We show that the boundary exponent and the bulk anomalous dimension of fermion operator are characterized by two different Luttinger parameters, referring to the main wire, thanks to nonlocal character of phonon-mediated interaction. In the limiting case of the junction of only two wires, the scaling exponents found by our method are in exact correspondence with previous bosonization analysis.

Coulomb interaction might have important effects on the physical observables in topological semimetals with vanishing density of states at the band touching due to the weak screening. In this work, we show that Kohn's theorem is not fulfilled in nodal-line semimetals (NLSMs), which implies nonvanishing interaction corrections to the conductivity. Using renormalized perturbation theory, we determine the first-order optical conductivity in a clean NLSM to be ${\sigma }_{\perp \perp }\left(\mathrm{\Omega }\right)=2{\sigma }_{\parallel \parallel }\left(\mathrm{\Omega }\right)={\sigma }_0[1+C_2{\alpha }_R\left(\mathrm{\Omega }\right)]$, where $\perp$ and $\parallel$ denote the perpendicular and parallel components with respect to the nodal loop, ${\sigma }_0=\left(2\pi k_0\right)e^2/\left(16h\right)$ is the conductivity in the noninteracting limit, $2\pi k_0$ is the nodal-loop perimeter, $C_2=(19-6\pi )/12\simeq 0.013$ is a numerical constant, and ${\alpha }_R\left(\mathrm{\Omega }\right)$ is the renormalized fine-structure constant in the NLSM. The analogies between three-dimensional NLSMs and two-dimensional Dirac fermions are reflected in the parallelism between their respective optical conductivities, both in the noninteracting limit and in the correction, as pointed out by the equality of the universal coefficient $C_2$ in both systems. Finally, we analyze some experiments that have determined the optical conductivity in NLSMs, discussing the possibility of experimentally measuring our result.

Tight binding models like the Hubbard Hamiltonian are most often explored in the context of uniform intersite hopping $t$. The electron-electron interactions, if sufficiently large compared to this translationally invariant $t$, can give rise to ordered magnetic phases and Mott insulator transitions, especially at commensurate filling. The more complex situation of nonuniform $t$ has been studied within a number of situations, perhaps most prominently in multiband geometries where there is a natural distinction of hopping between orbitals of different degree of overlap. In this paper we explore related questions arising from the interplay of multiple kinetic energy scales and electron-phonon interactions. Specifically, we use determinant quantum Monte Carlo (DQMC) to solve the half-filled Holstein Hamiltonian on a “decorated honeycomb lattice,” consisting of hexagons with internal hopping $t$ coupled together by $t^{\prime }$. This modulation of the hopping introduces a gap in the Dirac spectrum and affects the nature of the topological phases. We determine the range of $t/t^{\prime }$ values which support a charge density wave phase about the Dirac point of uniform hopping $t=t^{\prime }$, as well as the critical transition temperature $T_c$. The QMC simulations are compared with the results of mean field theory.

There have been several proposals that three-dimensional allotropes of carbon formed by graphene networks can support two types of topological nodal line semimetals: type A has closed nodal rings inside the first Brillouin zone (BZ), and type B has nodal lines traversing the whole BZ to be periodically connected. Among these proposals, it has been found that nearly all-$s{p}^2$ hybridized allotropes tend to hold A-type closed nodal rings, while the $s{p}^2\text{−}s{p}^3$ hybridized allotropes tend to hold B-type periodic nodal lines. Here we identify by ab initio calculations an $s{p}^2\text{−}s{p}^3$ hybridized carbon allotrope in $Pcca$ ($D_{2h}^8$) symmetry as a topological nodal line semimetal with two A-type closed nodal rings on the $k_y=0$ and $k_y=\pi$ mirror planes, respectively. The projections of these two nodal rings onto (010) surfaces form concentric ellipses with different size. The drumhead surface states appear in the region enclosed by the bigger ring but disappear inside of the smaller ring. This is consistent with the distribution of the Berry phase calculated along the [010] periodic reciprocal lattice. An effective $k·p$ model has been proposed, and the parameters have been obtained through fitting the ab initio results. The model can reproduce the nodal rings in the shape of an ellipse, satisfying the twofold rotational symmetry. Meanwhile, the simulated x-ray diffraction spectrum matches well with the recently reported distinct diffraction peaks found in the diamond-rich coatings on stainless steel substrate. These results establish a carbon phase with intriguing structural and electronic properties and expand our understandings about topological nodal lines in carbon networks.

Charge density waves in transition metal dichalcogenides have been intensively studied for their close correlation with Mott insulator, charge-transfer insulator, and superconductor. $\mathrm{VT}{\mathrm{e}}_2$ monolayer recently comes into sight because of its prominent electron correlations and the mysterious origin of charge density wave (CDW) orders. As a metal of more than one type of charge density waves, it involves complicated electron-electron and electron-phonon interactions. Through a scanning tunneling microscopy study, we observed triple-Q $4\times 4$ and single-Q $4\times 1$ modulations with significant charge and orbital separation. The triple-Q $4\times 4$ order arises strongly from the $p-d$ hybridized states, resulting in charge distribution in agreement with the V-atom clustering model. Associated with a lower Fermi level, the local single-Q $4\times 1$ electronic pattern is generated with the $p-d$ hybridized states remaining $4\times 4$ ordered. In the spectroscopic study, orbital- and atomic-selective charge density wave gaps with the size up to $\sim 400\mathrm{meV}$ were resolved on the atomic scale.

We propose schemes for calculation of optical functions of a semiconductor with Rydberg excitons for a wide interval of dimensions. We have started with a zero-dimensional structure (quantum dot), then going to one-dimensional (quantum wire), two-dimensional (quantum wells and wide quantum wells), and finally three-dimensional bulk crystals; our analytical findings are illustrated numerically, showing an agreement with available experimental data. Calculations including exciton-polaritons are performed; the case of a large number of polariton branches is discussed, and obtained theoretical absorption spectra show good agreement with experimental data.

Optical pump-probe time- and magnetic-field-resolved Kerr rotation measurements provide a window into the mechanisms that generate dynamic nuclear polarization in bulk gallium arsenide. Previously, we reported an unexpected dependence of the direction of the nuclear polarization on the sweep direction of the applied external magnetic field. In this paper, we present numerical calculations based on a model for this nuclear polarization due to the optical orientation and optical Stark effect produced by a train of ultrafast optical pulses. We demonstrate the correspondence of the model to our experimental measurements for different laser wavelengths and magnetic field sweep rates. Finally, we show that the model reproduces the sweep direction dependence and provides an explanation for this behavior.

Cu is usually considered as an effective dopant to introduce shallow acceptors in Zn chalcogenides because it is on the left-hand side of Zn in the Periodic Table. Here, using first-principles calculations based on the hybrid functional with spin polarization, we show that contrary to the common expectation, Cu substituting Zn ($\mathrm{C}{\mathrm{u}}_{\mathrm{Zn}}$) in bulk Zn chalcogenides actually generates rather deep acceptor levels in ZnO, ZnS, and ZnSe, i.e., 2.91, 1.03, and 0.53 eV above the valence-band maximum (VBM), respectively, except in ZnTe (0.13 eV). More interestingly, the absolute Cu impurity energy level does not follow the variation of the VBM, decreasing from ZnTe to ZnSe to ZnS to ZnO, instead, it is the highest in ZnO. The abnormal behavior of $\mathrm{C}{\mathrm{u}}_{\mathrm{Zn}}$ in ZnO is attributed to the fact that, due to the very low O $2p$-orbital energy, the $\mathrm{C}{\mathrm{u}}_{\mathrm{Zn}}$ defect wave function has dominantly localized the Cu $3d$-orbital component, whereas in other Zn chalcogenides, anion $p$ states are dominant. The localized Cu $3d$ state leads to the enhanced exchange energy that elevates the acceptor level, which explains why the Cu impurity level is abnormally deep in ZnO. This finding provides insight in designing shallow acceptor levels in II–VI semiconductors.

An extension of the Heisenberg Hamiltonian is discussed that allows us to go beyond the standard bilinear spin Hamiltonian taking into account various contributions due to multispin interactions having both chiral and nonchiral character. The parameters of the extended Hamiltonian are calculated from first principles within the framework of the multiple-scattering Green's function formalism giving access to an explicit representation of these parameters in real space. The discussions are focused on the chiral interactions, i.e., biquadratic and three-spin Dzyaloshinskii-Moriya-like vector interactions ${\vec{\mathcal{D}}}_{ijij}$ (BDMI) and ${\vec{\mathcal{D}}}_{ijkj}$ (TDMI), respectively, as well as the three-spin chiral interaction $J_{ijk}$. Although all parameters are driven by spin-orbit coupling (SOC), some differences in their properties are demonstrated by calculations for real materials. In particular it is shown that the three-spin chiral interactions $J_{ijk}$ may be topology as well as SOC induced, while the TDMI is associated only with the SOC. As the magnitude of the chiral interactions can be quite sizable, they can lead to a stabilization of a noncollinear magnetic texture in some materials that is absent when these interactions are neglected.