Guided by the multiparticle Mie theory, we address Dirac electron scattering from a cluster of electrostatically defined circular quantum dots in graphene. Even a dimer composed of two quantum dots exhibits rich physics: Not only the length of the dimer but also its inclination with respect to the incident electron wave vector affect the scattering efficiency, scattering pattern, suppression of Klein tunneling, Fano resonances, vortex pattern, and electron density. A finite cluster with no axis of mirror symmetry aligned with the direction of incident electron exhibits an asymmetric scattering pattern. As a result of deflection of charge carriers to one side of a finite sample, a transverse voltage may be generated. Our results suggest that not only ordered but also disordered clusters of quantum dots can be used to engineer the transport properties of the native graphene.

The adsorption of iron phthalocyanine (FePc) on the passivated H/Si(111) surface is explored from first principles. We find that the organic molecule is predominantly physisorbed with a distance to the surface of $2.6\pm 0.1\AA$ and an adsorption energy of $1.55\pm 0.1$ eV but also exhibits sizable resonance with the underlying substrate. This establishes the present system as interesting mixed covalent–van der Waals–bound test case, which we use to compare the impact of different approaches to van der Waals interactions. Spin-polarized scanning tunneling microscopy (SP STM) images are simulated, selectively accessing different molecular orbitals via the applied bias voltage in the spirit of scanning tunneling spectroscopy. Comparison with experimental STM images reveals very good agreement. We report a significant magnetic contrast exceeding $\pm 1\AA$ in the SP STM images for $-2$ and $+1.5$ V. Aiming for a magnetic functionalization of Si for possible spintronics applications, magnetic moments and binding energies of different (transition-metal) atoms in the center of the Pc ring are presented, which particularly show that Fe is strongly bound in the molecule (about 9.6 eV). Finally, we discuss different mechanisms for subsurface Fe doping by room-temperature FePc deposition and point out two feasible reactions. Concomitantly, we identify the crucial role of a preceding destabilization of FePc, for instance, by preadsorbed H atoms, which subsequently strongly stabilize the final state of the reaction.

The bulk electronic properties of compensated topological insulators are strongly affected by the self-organized formation of charge puddles at low temperature, but their response in the microwave frequency range is little studied. We employed broadband impedance spectroscopy up to 5 GHz to address the ac transport properties of well-compensated ${\mathrm{BiSbTeSe}}_2$, where charge puddles are known to form as metallic entities embedded in an insulating host. It turns out that the average puddle size sets the characteristic frequency ${\nu }_c$ in the gigahertz range, across which the insulating dc behavior is separated from a metal-like high-frequency response of delocalized carriers within the puddles. This ${\nu }_c$ is found to be controlled by a magnetic field, giving rise to a large positive magnetoconductivity observable only in the gigahertz range. This curious phenomenon is driven by the Zeeman energy which affects the local band filling in the disordered potential landscape to enhance the puddle size.

Exotic links and chains attract interest across various disciplines including mathematics, biology, chemistry, and physics. Here, we propose that topological Hopf-chain networks, consisting of one-, two-, and three-dimensional (3D) Hopf chains, can be found in the momentum space. These networks can be evolved from a 3D triple-points phase by varying symmetries. Moreover, we identify that the Hopf-chain networks exist in a family of crystals $\mathrm{S}{\mathrm{c}}_{3}X\mathrm{C}\left(X=\mathrm{Al},\mathrm{Ga},\mathrm{In},\mathrm{Tl}\right)$. The crystals are 3D triple-points metals, and transit to topological metals with Hopf-chain networks under strains. These Hopf networks will exhibit unique magnetotransport properties.

Exceptional points (EPs) associated with the coalescence of eigenstates in non-Hermitian systems have many exotic features. The EPs are generally sensitive to system parameters; here we report symmetry protected isolated EPs in the Brillouin zone (BZ) of a two-dimensional non-Hermitian bilayer square lattice. Protected by symmetry, the isolated EPs only move, merge, and split in the BZ. The average values of Pauli matrices under the eigenstate of the system's Bloch Hamiltonian define a real planar vector field, the topological defects of which are isolated EPs associated with vortices. The winding number characterizes the vortices and reveals the topological properties of the non-Hermitian system. Different topological phases correspond to different EP configurations, which are unchanged unless topological phase transition occurs accompanying the EPs merging or splitting.

We study the observable properties of quantum systems which involve a quantum continuum as a subpart. We show in a very general way that in any system, which consists of at least two isolated states coupled to a continuum, the spectral function of one of the states exhibits an isolated zero at the energy of the other state. Several examples of quantum systems exhibiting such isolated zeros are discussed. Although very general, this phenomenon can be particularly useful as an indirect detection tool for the continuum spectrum in the laboratory realizations of quantum critical behavior.

We use a Langevin approach to treat the finite temperature dynamics of displacement variables in the half-filled spinless Holstein model. Working in the adiabatic regime we exploit the smallness of the adiabatic parameter to simplify the memory effects and estimate displacement costs from an “instantaneous” electronic Hamiltonian. We use a phenomenological damping rate and uncorrelated thermal noise. The low temperature state has checkerboard charge order (CO) and the Langevin scheme generates equilibrium thermodynamic properties that accurately match Monte Carlo results. It additionally yields the dynamical structure factor, $D(\mathbf{q},\omega )$, from the displacement field $x(\mathbf{r},t)$. We observe four regimes with increasing temperature $T$ classified in relation to the charge ordering temperature $T_c$ and the ‘polaron formation’ temperature $T_P$, with $T_c\ll T_P$. For $T\ll T_c$ the oscillations are harmonic, leading to dispersive phonons, with increasing $T$ bringing in anharmonic, momentum dependent, corrections. For $T\sim T_c$, thermal tunneling events of the $x\left(\mathbf{r}\right)$ field occur, with a propagating ‘domain’ pattern at wave vector $\mathbf{q}\sim (\pi ,\pi )$ and low energy weight in $D(\mathbf{q},\omega )$. When $T_c<T<T_P$, the disordered polaron regime, domain structures vanish, the dispersion narrows, and low energy weight is lost. For $T\gtrsim T_P$ we essentially have uncorrelated local oscillations. We propose simple models to analyze the rich dynamics.

An optical second-harmonic generation (SHG) allows to probe various structural and symmetry-related properties of materials, since it is sensitive to the inversion symmetry breaking in the system. Here, we investigate the SHG response from a single layer of graphene disposed on an insulating hexagonal boron nitride (hBN) and silicon carbide (SiC) substrates. The considered systems are described by a noninteracting tight-binding model with a mass term, which describes a nonequivalence of two sublattices of graphene when the latter is placed on a substrate. The resulting SHG signal linearly depends on the degree of the inversion symmetry breaking (value of the mass term) and reveals several resonances associated with the band gap, van Hove singularity, and bandwidth. The difficulty in distinguishing between SHG signals coming from the considered heterostructure and environment (insulating substrate) can be avoided by applying a homogeneous magnetic field. The latter creates Landau levels in the energy spectrum and leads to multiple resonances in the SHG spectrum. Position of these resonances explicitly depends on the value of the mass term. We show that at energies below the band gap of the substrate the SHG signal from the massive graphene becomes resonant at physically relevant values of the applied magnetic field, while the SHG response from the environment stays off resonant.

Quantum effect is expected to dictate the behavior of physical systems at low temperature. For quantum magnets with geometrical frustration, quantum fluctuation usually lifts the macroscopic classical degeneracy, and exotic quantum states emerge. However, how different types of quantum processes entangle wave functions in a constrained Hilbert space is not well understood. Here, we study the topological entanglement entropy and the thermal entropy of a quantum ice model on a geometrically frustrated kagome lattice. We find that the system does not show a $Z_2$ topological order down to extremely low temperature, yet continues to behave like a classical kagome ice with finite residual entropy. Our theoretical analysis indicates an intricate competition of off-diagonal and diagonal quantum processes leading to the quasidegeneracy of states and effectively, the classical degeneracy is restored.

We study the spin-$\frac{1}{2}$ antiferromagnetic Heisenberg model on an $\infty \times N$ square lattice for even $N$'s up to 14. Previously, the nonlinear sigma model perturbatively predicted that its spin-rotational symmetry breaks asymptotically with $N\to \infty$, i.e., when it becomes two dimensional (2D). However, we identify a critical width $N_c=10$ for which this symmetry breaks spontaneously. It shows the signature of a dimensional transition from one dimensional (1D) including quasi-1D to 2D. The finite-size effect differs from that of the $N\times N$ lattice. The ground-state (GS) energy per site approaches the thermodynamic limit value, in agreement with the previously accepted value, by one order of $1/N$ faster than when using $N\times N$ lattices in the literature. Methodwise, we build and variationally solve a matrix product state (MPS) on a chain, converting the $N$ sites in each rung into an effective site. We show that the area law of entanglement entropy does not apply when $N$ increases in our method and the reduced density matrix of each effective site has a saturating number of dominant diagonal elements with increasing $N$. These two characteristics make the MPS rank needed to obtain a desired energy accuracy quickly saturate when $N$ is large, making our algorithm efficient for large $N$'s. Furthermore, the latter enables space reduction in MPS. Within the framework of MPS, we prove a theorem that the spin-spin correlation at infinite separation is the square of staggered magnetization and demonstrate that the eigenvalue structure of a building MPS unit of $\langle g|g\rangle ,|g\rangle$ being the GS is responsible for order, disorder, and quasi-long-range order.

We theoretically study magnetoelectric effects in a heterostructure of a generic band insulator and a ferromagnet. In contrast to the kinetic magnetoelectric effect in metals, referred to as the Edelstein effect or the inverse spin galvanic effect, our mechanism relies on virtual interband transitions between the valence and conduction bands and is therefore immune to disorder or impurity scattering. By calculating electric field-induced magnetization by the linear response theory, we reveal that the magnetoelectric effect shows up without specific parameter choices. The magnetoelectric effect qualitatively varies by changing the direction of the magnetic moment in the ferromagnet: the response is diagonal for the out-of-plane moment, whereas it is off-diagonal for the in-plane moment. We also find out that in optical frequencies, the magnetoelectric signal can be drastically enhanced via interband resonant excitations. Finally, we estimate the magnitude of the magnetoelectric effect for a hybrid halide perovskite semiconductor as an example of the band insulator and compare it with other magnetoelectric materials. We underscore that our mechanism is quite general and widely expectable, only requiring the Rashba spin-orbit coupling and exchange coupling. Our result could potentially offer a promising method of Joule heating-free electric manipulation of magnetic moments in spintronic devices.

The pressure dependence of the magnetism of the double perovskite ${\mathrm{Sr}}_2{\mathrm{FeOsO}}_6$ was investigated by temperature- and magnetic-field-dependent synchrotron ${}^{57}\mathrm{Fe}$ Mössbauer spectroscopy in the energy domain up to $\sim 50$ GPa. ${\mathrm{Sr}}_2{\mathrm{FeOsO}}_6$ is known to feature antiferromagnetic ordering below $T_{\mathrm{N}}\sim 140$ K and a change in spin structure from AF1 to AF2 near 70 K at ambient pressure. Previous Os $L_{2,3}$ x-ray magnetic circular dichroism (XMCD) spectra [Veiga et al., Phys. Rev. B 91, 235135 (2015)] indicated a pressure-driven change from the antiferromagnetic to the ferrimagnetic state. Raman spectra of ${\mathrm{Sr}}_2{\mathrm{FeOsO}}_6$ collected at room temperature and up to 34 GPa are in agreement with previous x-ray-diffraction studies which verified that the tetragonal ambient pressure crystal structure is retained at high pressure. The Mössbauer investigations show that the Fe ions remain in the +3 high-spin $\left({t_{2g}}^3{e}_g^2\right)$ state over the whole pressure range. The magnetic ordering is strongly stabilized by high pressure and for $p>30$ GPa the ordering temperature is increased to above room temperature. Broad magnetic hyperfine patterns as well as coexistence of magnetic and paramagnetic signals at high pressures indicate the formation of inhomogeneous magnetic states. The shapes of applied-field Mössbauer spectra at low temperature are similar at 2 and 33 GPa and do not allow resolution of distinct antiferromagnetic and ferrimagnetic components. Pressure-induced spin canting in a basically antiferromagnetic spin structure or magnetic phase separation involving a pressure-induced minority ferrimagnetic phase may be the origin for the ferromagnetic XMCD signal.

Compulsory Dirac multipoles in the bilayer perovskite $\mathrm{C}{\mathrm{a}}_3\mathrm{R}{\mathrm{u}}_2{\mathrm{O}}_7$ are absent in published analyses of experimental data. In a first step at correcting knowledge of the magnetic structure, we have analyzed existing Bragg diffraction patterns gathered on samples held well below the Néel temperature at which $A$-type antiferromagnetic order of axial dipoles spontaneously develops. Patterns were gathered with neutrons, and linearly polarized x rays tuned in energy to a ruthenium atomic resonance. Neutron diffraction data contain solid evidence of Dirac dipoles (anapoles or toroidal moments). No such conclusion is reached with existing x-ray diffraction data, which instead is ambiguous on the question. To address this shortcoming by future experiments, we calculated additional diffraction patterns. Chiral order of Dirac multipoles is allowed by magnetic space-group $P_{C}na{2}_1$, and it can be exposed in Bragg diffraction using circularly polarized x rays. Likewise, a similar experiment can expose a chiral order of axial dipoles. A magnetic field applied parallel to the $b$ axis creates a ferrimagnetic structure in which bulk magnetization arises from field-induced nonequivalent Ru sites (magnetic space-group $P{m}^{\prime }{c}^{\prime }{2}_1)$.

Microscopic spin interactions on a deformed kagome lattice of volborthite are investigated through magnetoelastic couplings. A negative longitudinal magnetostriction $\mathrm{\Delta }L/L<0$ in the $b$ axis is observed, which depends on the magnetization $M$ with a peculiar relation of $\mathrm{\Delta }L/L\propto M^{1.3}$. Based on the exchange striction model, it is argued that the negative magnetostriction originates from a pantographlike lattice change of the Cu-O-Cu chain in the $b$ axis, and that the peculiar dependence arises from the local spin correlation. This idea is supported by DFT+$U$ calculations simulating the lattice change and a finite-size calculation of the spin correlation, indicating that the recently proposed coupled-trimer model is a plausible one.

The main question we address is how to probe the fractionalized excitations of a quantum spin liquid (QSL), for example, in the Kitaev honeycomb model. By analyzing the energy spectrum and entanglement entropy, for antiferromagnetic couplings and a field along either [111] or [001], we find a gapless QSL phase sandwiched between the non-Abelian Kitaev QSL and polarized phases. Increasing the field strength towards the polarized limit destroys this intermediate QSL phase, resulting in a considerable reduction in the number of frequency modes and the emergence of a beating pattern in the local dynamical correlations, possibly observable in pump-probe experiments.

Recent experiments on strongly coupled microwave and ferromagnetic resonance modes have focused on large volume bulk crystals such as yttrium iron garnet, typically of millimeter-scale dimensions. We extend these experiments to lower volumes of magnetic material by exploiting low-impedance lumped-element microwave resonators. The low impedance equates to a smaller magnetic mode volume, which allows us to couple to a smaller number of spins in the ferromagnet. Compared to previous experiments, we reduce the number of participating spins by two orders of magnitude, while maintaining the strength of the coupling rate. Strongly coupled devices with small volumes of magnetic material may allow the use of spin orbit torques, which require high current densities incompatible with existing structures.

All ensembles of statistical mechanics are equivalent in the sense that they give the equivalent thermodynamic functions in the thermodynamic limit. However, when investigating microscopic structures in the first-order phase transition region, one must choose an appropriate statistical ensemble. The appropriate choice is particularly important when one investigates finite systems, for which even the equivalence of ensembles does not hold. We propose a class of statistical ensembles, which always give the correct equilibrium state even in the first-order phase transition region. We derive various formulas for this class of ensembles, including the one by which temperature is obtained directly from energy without knowing entropy. Moreover, these ensembles are convenient for practical calculations because of good analytic properties. We also derive formulas which relate statistical-mechanical quantities of different ensembles, including the conventional ones, for finite systems. The formulas are useful for obtaining results with smaller finite-size effects, and for improving the computational efficiency. The advantages of the squeezed ensembles are confirmed by applying them to the Heisenberg model and the frustrated Ising model.

We discuss the polarization amplitude of quantum spin systems in one dimension. In particular, we closely investigate it in gapless phases of those systems based on the two-dimensional conformal field theory. The polarization amplitude is defined as the ground-state average of a twist operator which induces a large gauge transformation attaching the unit amount of the $U\left(1\right)$ flux to the system. We show that the polarization amplitude under the periodic boundary condition is sensitive to perturbations around the fixed point of the renormalization-group flow rather than the fixed point itself even when the perturbation is irrelevant. This dependence is encoded into the scaling law with respect to the system size. In this paper, we show how and why the scaling law of the polarization amplitude encodes the information of the renormalization-group flow. In addition, we show that the polarization amplitude under the antiperiodic boundary condition is determined fully by the fixed point in contrast to that under the periodic one and that it visualizes clearly the nontriviality of spin systems in the sense of the Lieb-Schultz-Mattis theorem.