Spin-orbit coupling in two-dimensional systems is usually characterized by Rashba and Dresselhaus spin-orbit coupling (SOC) linear in the wave vector. However, there is a growing class of materials which instead support dominant SOC cubic in the wave vector (cSOC), while their superconducting properties remain unexplored. By focusing on Josephson junctions in Zeeman field with superconductors separated by a normal cSOC region, we reveal a strongly anharmonic current-phase relation and complex spin structure. An experimental cSOC tunability enables both tunable anomalous phase shift and supercurrent, which flows even at the zero-phase difference in the junction. A fingerprint of cSOC in Josephson junctions is the $f$-wave spin-triplet superconducting correlations, important for superconducting spintronics and supporting Majorana bound states.

We report a study of the Mott insulator ${\mathrm{La}}_2{\mathrm{O}}_3{\mathrm{Fe}}_2{\mathrm{Se}}_2$ by means of ${}^{139}\mathrm{La}$ nuclear quadrupole resonance (NQR). The NQR spectra evidence a single La site in the paramagnetic phase and two inequivalent La sites, La1 and La2, in the antiferromagnetic phase. These two sites are characterized by different quadrupole couplings, indicative of distinct lattice configurations segregated in domains. The dependence of the quadrupole coupling for La2 on temperature suggests that the structural distortion is driven by the magnetic order parameter. The nuclear transverse relaxation rate $1/T_2$ evidences fluctuations in the paramagnetic phase with characteristic frequencies well below the Heisenberg exchange frequency and likely associated with nematic fluctuations.

Using first-principles calculations, we predict a unique $\mathrm{BiFe}{\mathrm{O}}_3$ (BFO) phase, which is coined $I$-BFO, with layered characteristics based on the ilmenite structure. The interactions between interlayer bismuth atoms make it easy to exfoliate monolayer BFO with a configuration in which Bi ions are above and below two-dimensional (2D) iron-oxygen octahedra sharing common edges. The calculated phonon spectra reveal the dynamic stability of both bulk and monolayer forms of $I$-BFO. Combining total energy computation and crystal structure search, we corroborate that the $I$-BFO monolayer maintains the lowest-energy ground state, as compared to other 2D BFO exfoliations. We also discover that monolayer $I$-BFO is a robust antiferromagnetic material with a Néel temperature ($T_N$) of 4 K in the fully relaxed case. Such $T_N$ can be prominently improved by strain, for example, $T_N=25\mathrm{K}$ at 6% tension. Furthermore, our electronic structure calculations with PBE and hybrid HSE functionals show the $I$-BFO monolayer to be an indirect-gap semiconductor. Finally, we indicate that other ternary $AB{\mathrm{O}}_3$ compounds also have the potential to produce layered materials from the ilmenite structure. This work thus provides guidance to explore unconventional layered materials, and further broadens the application of BFO and other promising ilmenite oxides in two dimensions.

We study static and dynamic properties of an electron coupled to dispersive quantum optical phonons in the framework of the Holstein model defined on a one-dimensional lattice. Calculations are performed using the Lanczos algorithm based on a highly efficient construction of the variational Hilbert space. Even small phonon dispersion has a profound effect on the low-energy optical response. While the upward phonon dispersion broadens the optical spectra due to single-phonon excitations, the downward dispersion has the opposite effect. With increasing dispersion, a multiphonon excitation (MPE) state becomes the lowest excited state of the system at zero momentum and determines the low-frequency response of the optical conductivity where the threshold for optical absorption moves below the single-phonon frequency. Multiphonon states form a well-defined bandlike feature just above the polaron band as clearly seen in the electron spectral function. Low-energy MPEs should be observable in systems with strong optical phonon dispersion in optical as well as angle-resolved photoemission experiments.

We investigate various magnetic configurations caused by the dipole–dipole interaction in thin-film magnets with perpendicular anisotropy under open boundary conditions. Two different approaches are simulated: one starts from a random magnetic configuration and decreases temperatures stepwisely; the other starts from the saturated out-of-plane ferromagnetic state to evaluate its metastability. As typical patterns of magnetic configuration, five typical configurations are found: an out-of-plane ferromagnetic, in-plane ferromagnetic, vortex, multidomain, and canted multidomain states. Notably, the canted multidomain forms a concentric magnetic-domain pattern with an in-plane vortex structure, resulting from the open boundary conditions. Concerning the coercivity, a comparison of the magnetic configurations in both processes reveals that the out-of-plane ferromagnetic state exhibits metastability in the multidomain state, but not in the vortex state. We also confirm that the so-called Neel-cap magnetic-domain-wall structure, which is originally discussed in the in-plane anisotropy system, appears at the multidomain state.

We theoretically investigate multiple-$Q$ spin textures, which are composed of superpositions of spin density waves with different wave numbers, for an effective spin model of centrosymmetric itinerant magnets. Our focus is on the interplay between biquadratic interactions arising from the spin-charge coupling and magnetic anisotropy caused by the spin-orbit coupling. Taking into account two types of the magnetic anisotropy, single-ion anisotropy and bond-dependent anisotropy, we elucidate magnetic phase diagrams for an archetypal triangular-lattice system in the absence and presence of an external magnetic field. In the case of the single-ion anisotropy, we find a plethora of multiple-$Q$ instabilities depending on the strength and the sign of the anisotropy (easy plane or easy axis), including a noncoplanar triple-$Q$ state regarded as a skyrmion crystal with topological number of two, and coplanar and noncoplanar double-$Q$ states. In an external magnetic field, we find that another noncoplanar triple-$Q$ state, a skyrmion crystal with topological number of one, is stabilized by the in-plane (out-of-plane) magnetic field under the easy-plane (easy-axis) anisotropy. A part of the results, especially for the relatively large biquadratic interaction, qualitatively reproduce those in the Kondo lattice model, which explicitly includes itinerant electrons [S. Hayami and Y. Motome, Phys. Rev. B 99, 094420 (2019)]. We also examine the stability of the field-induced skyrmion crystal by rotating the field direction. As a by-product, we show that a different triple-$Q$ state with nonzero chirality appears in the presence of the biquadratic interaction and the easy-axis anisotropy. Meanwhile, we find that the bond-dependent anisotropy also stabilizes both types of skyrmion crystals. We show that, however, for the skyrmion crystal with topological number of one, Bloch- and Néel-type skyrmion crystals are selectively realized depending on the sign of the bond-dependent anisotropy, since this anisotropy selects a particular set of the helicity and vorticity. Moreover, we find yet another multiple-$Q$ states with nonzero spin scalar chirality, including two types of meron crystals with the skyrmion numbers of one and two. The systematic investigation of multiple-$Q$ instabilities in triangular itinerant magnets will provide a reference to complex magnetic textures in centrosymmetric magnetic metals.

The formation of charge density wave (CDW) is attributed to Fermi-surface nesting in textbooks, but this common paradigm is challenged by recent studies that reveal the pronounced effects of electron-phonon interaction and defects. Transition-metal dichalcogenide $\mathrm{Ta}{\mathrm{Te}}_2$, being a prototype of charge density wave at around 170 K, is an ideal playground for exploring the mechanism of CDW. In this work, we reveal the subtle effect of defects on the CDW through studying a series of $\mathrm{Ta}{\mathrm{Te}}_{2-\delta }$ ($\delta =0.028-0.123$) crystals. Transport measurements show that $\mathrm{Ta}{\mathrm{Te}}_{1.972}$, being close to the stoichiometric compound, have a resistivity-kink feature (fingerprint of CDW) around 160 K along both $a$- and $b$ axes; $\mathrm{Ta}{\mathrm{Te}}_{1.933}$ only has a resistivity-kink feature along the $b$ axis. Remarkably, the resistivity kink completely disappears in $\mathrm{Ta}{\mathrm{Ta}}_{1.877}$. Raman spectroscopy not only confirms the corresponding structural phase transition, but also verifies decreased electron-phonon interaction at the Γ point of the Brillouin zone from $\mathrm{Ta}{\mathrm{Te}}_{1.972}$ to $\mathrm{Ta}{\mathrm{Te}}_{1.933}$ based on analysis of theoretical Fermi surface of 1 $T^{\prime }$ phase of $\mathrm{Ta}{\mathrm{Te}}_2$ before CDW phase transition. We propose that the CDW of $\mathrm{Ta}{\mathrm{Te}}_{2-\delta }$ ($\delta =0.028-0.067$) along the $a$ axis is mainly due to electron-phonon interaction, while CDW along the $b$ axis is the synergetic effect of Fermi-surface nesting and electron-phonon interaction; if dopant concentration is high enough $(\delta =0.123)$, CDW is completely quenched by disorder induced by doping. Our study reveals the subtle effects of doping on CDW, and may give more hints on the interplay between CDW and high-temperature superconductor in the doped Mott insulators.

In this paper, we investigate the dynamical quantum phase transitions appearing in the Loschmidt echo and the time-dependent order parameter of a quantum system of harmonically coupled degenerate bosons as a function of the power-law decay $\sigma$ of long-range interactions. Following a sudden quench, the nonequilibrium dynamics of this system are governed by a set of nonlinear coupled Ermakov equations. To solve them, we develop an analytical approximation valid at late times. Based on this approximation, we show that the emergence of a dynamical quantum phase transition hinges on the generation of a finite mass gap following the quench, starting from a massless initial state. In general, we can define two distinct dynamical phases characterized by the finiteness of the post-quench mass gap. The Loschmidt echo exhibits periodical nonanalytic cusps whenever the initial state has a vanishing mass gap and the final state has a finite mass gap. These cusps are shown to coincide with the maxima of the time-dependent long-range correlations.

The quantum-spin $S=1/2$ chain system ${\mathrm{Cs}}_2\mathrm{Cu}{\mathrm{Cl}}_4$ is of high interest due to competing antiferromagnetic intrachain $J$ and interchain exchange $J^{\prime }$ interactions and represents a paramount example for Bose-Einstein condensation of magnons [R. Coldea et al., Phys. Rev. Lett. 88, 137203 (2002)]. Substitution of chlorine by bromine allows tuning the competing exchange interactions and corresponding magnetic frustration. Thereby, anisotropic exchange contributions may be decisive for the resulting ground state. Here we report on electron spin resonance (ESR) in single crystals of ${\mathrm{Cs}}_2\mathrm{Cu}{\mathrm{Cl}}_{4-x}{\mathrm{Br}}_x$ with the aim to analyze the evolution of these anisotropic exchange contributions. The main source of the ESR linewidth is attributed to the uniform Dzyaloshinskii-Moriya interaction. The vector components of the Dzyaloshinskii-Moriya interaction are determined from the angular dependence of the ESR spectra using a high-temperature approximation. The obtained results support the site selectivity of the Br substitution suggested from the evolution of lattice parameters and magnetic susceptibility dependent on the Br concentration.

The interaction energy of the indirect-exchange or Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between magnetic spins localized on lattice sites of the $\alpha \text{−}{\mathcal{T}}_3$ model is calculated using linear response theory. In this model, the AB-honeycomb lattice structure is supplemented with C atoms at the centers of the hexagonal lattice. This introduces a parameter $\alpha$ for the ratio of the hopping integral from hub to rim and that around the rim of the hexagonal lattice. A valley and $\alpha$-dependent retarded Green's function matrix is used to form the susceptibility. Analytic and numerical results are obtained for undoped $\alpha \text{−}{\mathcal{T}}_3$ when the chemical potential is finite and also in the presence of an applied magnetic field. We demonstrate the anisotropy of these results when the magnetic impurities are placed on the A, B, and C sublattice sites. Additionally, a comparison of the behavior of the susceptibility of $\alpha \text{−}{\mathcal{T}}_3$ with graphene shows that there is a phase transition at $\alpha =0$.

We report a theoretic study of the topological properties of the $\alpha \text{−}{T}_3$ lattice by taking the intrinsic spin orbit interaction into account. It is shown that when $0<\alpha <1$, the electronic band structure is spin-valley split and the original flat band is distorted to display a nonzero dispersion that imparts the system to be metallic. The gapped valence or conduction band shows the quantum spin Hall phase and experiences a topological phase transition from the spin Chern number $C_s=1$ to $C_s=2$ at the critical point $\alpha =\frac{1}{2}$. When a staggered magnetization order is considered in the system, a bunch of topological phases appear such as the quantum spin quantum anomalous Hall phase with variation of $\alpha$ or the magnetization strength.

Electrons on the liquid helium surface form an extremely clean two-dimensional system where different plasmon excitations can coexist. Under a magnetic field, time-reversal symmetry is broken, and all the bulk magnetoplasmons become gapped at frequencies below cyclotron resonance while chiral one-dimensional edge magnetoplasmons appear at the system perimeter. We theoretically show that the presence of a homogeneous density gradient in the electron gas leads to the formation of a delocalized magnetoplasmon mode in the same frequency range as the lowest-frequency edge-magnetoplasmon mode. We experimentally confirm its existence by measuring the corresponding resonance peak in frequency dependence of the admittance of the electron gas. This allows us to realize a prototype system to investigate the coupling between a chiral one-dimensional mode and a single delocalized bulk mode. Such a model system can be important for the understanding of transport properties of topological materials where states of different dimensionality can coexist.

We predict, through first-principles calculations, a different class of Janus two-dimensional (2D) materials $X{\mathrm{Sn}}_{2}Y$ ($X, Y=\mathrm{P}$, As, Sb, and Bi; $X\ne Y$). It has found that these 2D monolayers have intrinsic polarization effect owing to presence of mirror-symmetry breaking. $\mathrm{Sb}{\mathrm{Sn}}_2\mathrm{Bi}, \mathrm{As}{\mathrm{Sn}}_2\mathrm{Sb}$, and $\mathrm{P}{\mathrm{Sn}}_2\mathrm{As}$ have a semiconducting feature, however $\mathrm{As}{\mathrm{Sn}}_2\mathrm{Bi}, \mathrm{P}{\mathrm{Sn}}_2\mathrm{Bi}$, and $\mathrm{P}{\mathrm{Sn}}_2\mathrm{Sb}$ have a metallic feature with inverted band structure. When the spin-orbit coupling (SOC) is considered, the double Rashba effects are found in $\mathrm{Sb}{\mathrm{Sn}}_2\mathrm{Bi}$. Band inversion coupling with SOC leads to unexpected spin-valley splitting characteristics in $\mathrm{As}{\mathrm{Sn}}_2\mathrm{Bi}, \mathrm{P}{\mathrm{Sn}}_2\mathrm{Bi}$, and $\mathrm{P}{\mathrm{Sn}}_2\mathrm{Sb}$, showing a circle-type Berry curvature. The electronic and spin properties of Janus $X{\mathrm{Sn}}_{2}Y$ monolayers are tunable via applying external strain and electric field, resulting in Rashba-type spin-splitting, $p_z/p_{xy}$ band inversion, and a Dirac cone. In particular, the sombrero band dispersion and Van Hove singularity are revealed in $\mathrm{P}{\mathrm{Sn}}_2\mathrm{As}$ by exerting tensile strain. We therefore investigate the Lifshitz transition and inverse Edelstein effect (also referred as spin-charge conversion) of the strained $\mathrm{P}{\mathrm{Sn}}_2\mathrm{As}$. On the basis of the k·p model in the clean limit, the Drude coefficient for spin-charge conversion is estimated to be about 0.086 $e$/Å as tensile strain of +3%. Finally, the synergic effect of tensile strain and electric field is considered to manipulate the spin-charge conversion. Our results provide a class of 2D materials to investigate the Rashba effect, Lifshitz transition, and spin-charge conversion.

The two-orbital Hubbard model on a square lattice at quarter filling (electron number per site $n=1$) is investigated by the variational Monte Carlo method. For the variational wave function, we include short-range doublon-holon binding factors. We find that the energy of this wave function is lower than that of the density-density Jastrow wave function partially including long-range correlations used in a previous study. We introduce frustration to the model by the next-nearest-neighbor hopping $t^{\prime }$ in addition to the nearest-neighbor hopping $t$. For $t^{\prime }=0$, a ferromagnetic state with staggered orbital order occurs by increasing the Coulomb interaction $U$ before the Mott transition takes place. By increasing $t^{\prime }$, the region of this ferromagnetic phase shrinks, and the Mott transition without magnetic order occurs.

The mechanisms underlying the paramagnetic metal to paramagnetic insulator (PM-PI) and antiferromagnetic insulator (PM-AFI) transitions in the archetypical correlated oxide of ${\mathrm{V}}_2{\mathrm{O}}_3$ are long-standing yet not completely resolved topics in condensed matter physics. Herein, utilizing large differences of thermal expansion coefficient between ${\mathrm{V}}_2{\mathrm{O}}_3$ and ${\mathrm{Al}}_2{\mathrm{O}}_3$, a large variation of trigonal distortion in a continuous way is realized in pure ${\mathrm{V}}_2{\mathrm{O}}_3$ thin films grown on $c$-plane ${\mathrm{Al}}_2{\mathrm{O}}_3$ substrates by changing the substrate temperature during deposition. The PM-PI transition is successfully reproduced in pure ${\mathrm{V}}_2{\mathrm{O}}_3$ thin films through enhancing trigonal distortion. Furthermore, the PM phase cannot be taken for granted to exhibit identical orbital occupations and consequently, play a negligible role in triggering the PM-AFI transitions. Instead, the $a_{1g}$ orbital occupation gauged by the $A_{1g}$ phonon mode in the PM phase strongly varies with the trigonal distortion and directly determines the PM-AFI transition characteristics. Our findings unambiguously demonstrate the essential role of trigonal distortion for understanding the multiple metal-insulator transitions and open up an opportunity for manipulating them by trigonal distortion in ${\mathrm{V}}_2{\mathrm{O}}_3$.

Plasmonic sensors based on metallic nanorings benefit from resonances covering a wide spectral range and homogeneous cavity fields. Here, we explore the potential for nanorings in active plasmonics by examining the tunability of plasmon resonances due to external magnetic fields. Within the electrostatic approximation, we compute plasmon resonances and their shifts in magnetic fields for both solid and planar nanorings. In particular, solid nanorings of circular, elliptical, and disk-shaped cross sections are critically examined and compared to planar rings. Overall, we find that magnetoplasmon shifts in nanorings are greatly reduced compared to standard nanoparticles. However, flat geometries are found to be preferable and allow for relatively large shifts.

Recent lightwave-STM experiments have shown space and time resolution of single molecule vibrations directly on their intrinsic length and timescales. We address here theoretically the electronic dynamics of a copper-phthalocyanine in a lightwave-STM explored within a pump-probe cycle scheme. The spin-orbit interaction in the metallic center induces beatings of the electric charge flowing through the molecule as a function of the delay time between the pump and the probe pulses. Interference between the quasidegenerate anionic states of the molecule and the intertwined dynamics of the associated spin and pseudospin degrees of freedom are the key aspects of such phenomenon. We study the dynamics directly in the time domain within a generalized master-equation approach.

Double-perovskite iridates A${}_2{\mathrm{ZnIrO}}_6$ (A=alkaline or lanthanide) show complex magnetic behaviors ranging from weak ferromagnetism to successive antiferromagnetic transitions. Here we report the static (dc) and dynamic (ac) magnetic susceptibility and neutron powder diffraction measurements for A=La and Nd compounds to elucidate the magnetic ground state. Below 10 K, the A=La compound is best described as canted iridium moments in an antiferromagnet arrangement with a propagation vector k = 0 and a net ferromagnetic component along the c axis. On the other hand, ${\mathrm{Nd}}_2{\mathrm{ZnIrO}}_6$ is described well as an antiferromagnet with a propagation vector k = ($\frac{1}{2}\frac{1}{2}0$) below $T_{\mathrm{N}}\sim$ 17 K. Scattering from both the Nd and Ir magnetic sublattices was required to describe the data, and both were found to lie almost completely within the ab plane. The dc susceptibility revealed a bifurcation between the zero-field-cooled and field-cooled curves below $\sim 13$ K in ${\mathrm{Nd}}_2{\mathrm{ZnIrO}}_6$. A glassy state was ruled out by ac susceptibility but detailed magnetic isotherms revealed the opening of the loop below 13 K. These results suggest a delicate balance exists between the Dzyaloshinskii-Moriya, crystal field schemes, and d-f interaction in this series of compounds.

We investigate near-Fermi-energy ($E_F$) element-specific electronic and spin states of ferromagnetic van der Waals (vdW) metal ${\mathrm{Fe}}_5\mathrm{Ge}{\mathrm{Te}}_2$. The soft x-ray angle-resolved photoemission spectroscopy (SX-ARPES) measurement provides spectroscopic evidence of localized Fe $3d$ band. We also find prominent hybridization between the localized Fe $3d$ band and the delocalized Ge/Te $p$ bands. This picture is strongly supported from direct observation of the remarkable spin polarization of the ligand $p$ bands near $E_F$, using x-ray magnetic circular dichroism (XMCD) measurements. The strength of XMCD signal from ligand element Te shows the highest value, as far as we recognize, among literature reporting finite XMCD signal for nonmagnetic element in any systems. Combining SX-ARPES and elemental selective XMCD measurements, we collectively point to an important role of giant spin polarization of the delocalized ligand Te states for realizing itinerant long-range ferromagnetism in ${\mathrm{Fe}}_5\mathrm{Ge}{\mathrm{Te}}_2$. Our finding provides a fundamental elemental selective viewpoint for understanding mechanism of itinerant ferromagnetism in low-dimensional compounds, which also leads to insight for designing exotic magnetic states by interfacial band engineering in heterostructures.