We investigate the formation of edge states in graphene ribbons and flakes with proximity-induced valley-Zeeman and Rashba spin-orbit couplings in the presence of a perpendicular magnetic field $B$. Two types of edge states appear in the spin-orbit gap at the Fermi level at zero field: strongly localized pseudohelical (intervalley) states and weakly localized intravalley states. We show that if the magnetic field is stronger than a crossover field $B_c$, which is a few milliteslas for realistic systems such as $\mathrm{graphene}/\mathrm{W}{\mathrm{Se}}_2$, only the pseudohelical edge states remain in zigzag graphene ribbons; the intravalley states disappear. The crossover is directly related to the closing and reopening of the bulk gap formed between nonzero Landau levels. Remarkably, in finite flakes the pseudohelical states undergo perfect reflection at the armchair edges if $B>B_c$, forming standing waves at the zigzag edges. These standing waves comprise two counterpropagating pseudohelical states; so while they carry no charge current, they do carry (pure) spin current.

Inversion symmetry in bilayer graphene allows for layered opposite Rashba spin-orbit coupling (LO-RSOC)—the situation when the RSOC has the same magnitude but the opposite sign in two coupled spatially separated layers. We show that the LO-RSOC results in the loss of spin chirality in the momentum space, in contrast to the common uniform RSOC. This chirality loss makes it difficult to experimentally establish whether the LO-RSOC (on the scale of 10 meV) exists, because the band structure is insensitive to it. To solve this problem, we propose to identify the LO-RSOC either by gating to break the inversion symmetry or by magnetic field to break the time-reversal symmetry. Remarkably, we observe the transition between trivial and nontrivial band topology as the system deviates from the LO Rashba state. Ab initio calculations suggest that bilayer graphene encapsulated by two monolayers of Au is a candidate to be a LO Rashba system.

Universal fractionalization of quantum transport characteristics in Majorana quantum dot devices is expected to emerge for well separated Majorana bound states. We show that the Majorana universality of the differential shot noise $\partial S^{>}/\partial V$ and conductance $\partial I/\partial V$ at low bias voltages $V$ arises only in ideal setups with only one Majorana mode entangled with the quantum dot. In realistic devices, where both Majorana modes are entangled with the quantum dot, $\partial S^{>}/\partial V$ and $\partial I/\partial V$ become very sensitive to tunneling phases and their universal fractional values are hard to observe even for well separated Majorana bound states. In contrast, as revealed here, the ratio $(\partial S^{>}/\partial V)/(\partial I/\partial V)$ weakly depends on the tunneling phases and is fractional when the Majorana bound states are well separated or integer when they significantly overlap. Importantly, for very large $V$ we demonstrate that this ratio becomes fully independent of the tunneling phases and its universal fractional Majorana value may be observed in state-of-the-art experiments.

The rare-earth material ${\mathrm{LiHoF}}_4$ is believed to be an experimental realization of the celebrated (dipolar) Ising model and, upon the inclusion of a transverse field $B_x$, an archetypal quantum Ising model. Moreover, by substituting the magnetic Ho ions by nonmagnetic Y ions, disorder can be introduced into the system, giving rise to a dipolar disordered magnet and at high disorders to a spin glass. Indeed, this material has been scrutinized experimentally, numerically, and theoretically over many decades with the aim of understanding various collective magnetic phenomena. One of the to-date open questions is the discrepancy between the experimental and theoretical $B_x-T$ phase diagram at low fields and high temperatures. Here we propose a mechanism, backed by numerical results, that highlights the importance of quantum fluctuations induced by the off-diagonal dipolar terms, in determining the critical temperature of anisotropic dipolar magnets in the presence and in the absence of a transverse field. We thus show that the description as a simple Ising system is insufficient to quantitatively describe the full phase diagram of ${\mathrm{LiHoF}}_4$, for the pure as well as for the dilute system.

By classical and path integral molecular dynamics simulations, we study the pressure-temperature ($P\text{−}T$) phase diagram of ${\mathrm{LaH}}_{10}$ to clarify the impact of temperature and atomic zero-point motions. We calculate the XRD pattern and analyze the space group of the crystal structures. For 125 GPa $\le P\le$ 150 GPa and $T=300\mathrm{K}$, we show that a highly symmetric $Fm\overline{3}m$ structure, for which superconductivity is particularly favored, is stabilized only by the temperature effect. On the other hand, for $T=200\mathrm{K}$, the interplay between the temperature and quantum effects is crucial to realize the $Fm\overline{3}m$ structure. For $P=100\mathrm{GPa}$ and $T=300\mathrm{K}$, we find that the system is close to the critical point of the structural phase transition between the $Fm\overline{3}m$ structure and those with lower symmetries.

The global magnetic phase diagram for fused azulene oligomers is obtained by using a fermionic Hubbard model, which is an intermediate between the molecular Pariser-Parr-Pople empiric Hamiltonian and the spin-$1/2$ antiferromagnetic Heisenberg model. We employ the density matrix renormalization group (DMRG) approach to explore the ground state properties of azulene-like molecules as a function of the electronic correlation and the oligomer size. It is shown that, depending on the length of the oligomer, fused azulene transitions from a singlet ($S=0$) to a higher-spin ($S=1,2$) ground state. Near the quantum magnetic phase transition the electric dipole moment, present on fused azulene molecules, couples with the magnetic moment leading to a divergent magnetoelectric susceptibility at the boundary lines of the magnetic phase diagram. These spontaneous electric and magnetic polarizations, together with the magnetoelectric coupling between them, indeed corroborate that these fused azulene oligomers can be viewed as a purely organic multiferroic material, being a magnetoelectric molecule.

Polarization, the precession direction with respect to the background magnetization, is an intrinsic degree of freedom of spin wave. Introducing symmetry-breaking mechanisms lies in the heart of lifting the degeneracy between polarized spin-wave modes and is essential in constructing polarization-based magnonic devices. Here we show that polarized spin waves can be naturally harnessed in a curved antiferromagnetic wire via tuning its curvature and torsion. Specifically, we investigate evolution of polarized spin wave in a spin-wave rotator and a spin-wave interferometer based on magnetic circular helices and correlate these curvilinear effects to the Berry phase accumulated along the wire.

To better understand the electronic structure of a single vacancy in graphene, we study the ground-state property of an effective Anderson model, consisting of three dangling $s{p}^2$ orbitals of the surrounding carbon atoms around the vacancy and the $\pi$ orbitals of carbon atoms that form the honeycomb lattice with a single vacancy. This model possesses ${\mathcal{C}}_3$ point group symmetry around the vacancy and thereby the local multiplets can be characterized by their irreducible representations. Employing the block-Lanczos density-matrix renormalization group (DMRG) scheme proposed by the present authors [T. Shirakawa and S. Yunoki, Phys. Rev. B 90, 195109 (2014)], we show that there are two phases in the relevant parameter space, i.e., a nonmagnetic phase in the weak-coupling region and a free magnetic moment phase in the realistic parameter region. The systematic analysis finds that, in the free magnetic moment phase, local multiplets of the doubly degenerate irreducible representation with spin 1 become dominant in the ground state, and approximately half of this local spin 1 is screened by electrons in the surrounding $\pi$ orbitals, indicating the emergence of the residual spin-1/2 free magnetic moment. The symmetry of this local multiplets is compatible with the occurrence of the in-plane Jahn-Teller distortion to lift the degeneracy, found in the previous ab initio calculations based on the density functional theory. Furthermore, we find that the emergence of the free magnetic moment is robust against carrier doping, which is in sharp contrast to the case of graphene with an adatom, thus explaining the qualitative difference observed experimentally in these two classes of systems. We also find the enhancement of the spin correlation function between $\pi$ electrons around the vacancy and those in the conduction band away from the vacancy in the undoped case, as compared to that in the doped case, while the spin correlation function between the $\sigma$ electrons in the $s{p}^2$-dangling orbitals around the vacancy and the $\pi$ electrons in the conduction band remains large in both undoped and doped cases. This implies that there is an additional contribution for the free magnetic moment from the $\pi$ electrons, which is fragile against the carrier doping, besides the free magnetic moment due to the $\sigma$ electrons in the $s{p}^2$-dangling orbitals, which is robust against the carrier doping. Our calculations thus support qualitatively the previous experiment that suggests the emergence of free magnetic moment with two distinct origins.

Metamagnetic transitions are analogs of a pressure-driven gas-liquid transition in water. In insulators, they are marked by a superlinear increase in the magnetization that occurs at a field strength set by the spin exchange interactions. Here we study topological metamagnets, in which the magnetization is itself a topological quantity and for which we find a single transition line for two materials with substantially different magnetic interactions: the spin ices ${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ and ${\mathrm{Ho}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$. We study single crystals under magnetic field and stress applied along the [001] direction and show that this transition, of the Kasteleyn type, has a magnetization versus field curve with upward convexity and a distinctive asymmetric peak in the susceptibility. We also show that the dynamical response of ${\mathrm{Ho}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ is sensitive to changes in the ${\mathrm{Ho}}^{3+}$ environment induced by compression along [001]. Uniaxial compression may open up experimental access to equilibrium properties of spin ice at lower temperatures.

We report x-ray diffraction studies of the electronic ordering instabilities in the kagome material ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ as a function of temperature and applied magnetic field. Our zero-field measurements between 10 and 120 K reveal an unexpected reorganization of the three-dimensional electronic order in the bulk of ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$: At low temperatures, a $2\times 2\times 2$ superstructure modulation due to electronic order is observed, which upon warming changes to a $2\times 2\times 4$ superstructure at 60 K. The electronic order-order transition discovered here involves a change in the stacking of electronically ordered ${\mathrm{V}}_3{\mathrm{Sb}}_5$ layers, which coincides with anomalies previously observed in magnetotransport measurements. This implies that the temperature-dependent three-dimensional electronic order plays a decisive role for transport properties, which are related to the Berry curvature of the V bands. We also show that the bulk electronic order in ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ breaks the sixfold rotational symmetry of the underlying $P6/mmm$ lattice and perform a crystallographic analysis of the $2\times 2\times 2$ phase. The latter yields two possible superlattices, namely a staggered star-of-David and a staggered inverse star-of-David structure. Applied magnetic fields up to 10 T have no effect on the x-ray diffraction signal. This, however, does not rule out time-reversal symmetry breaking in ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$.

The interband optical absorption of linearly polarized light by two-dimensional (2D) semimetals hosting tilted and anisotropic Dirac cones in the band structure is analysed theoretically. Supercritically tilted (type-II) Dirac cones are characterized by an absorption that is highly dependent on the incident photon polarization and frequency and is tunable by changing the Fermi level with a back-gate voltage. Type-II Dirac cones exhibit open Fermi surfaces and large regions of the Brillouin zone where the valence and conduction bands sit either above or below the Fermi level. As a consequence, unlike their subcritically tilted (type-I) counterparts, type-II Dirac cones have many states that are Pauli blocked even when the Fermi level is tuned to the level crossing point. We analyze the interplay of the tilt parameter with the Fermi velocity anisotropy, demonstrating that the optical response of a Dirac cone cannot be described by its tilt alone. As a special case of our general theory, we discuss the proposed 2D type-I semimetal 8-$Pmmn$ borophene. Guided by our in-depth analytics, we develop an optical recipe to fully characterize the tilt and Fermi velocity anisotropy of any 2D tilted Dirac cone solely from its absorption spectrum. We expect our paper to encourage Dirac cone engineering as a major route to create gate-tunable thin-film polarizers.

We theoretically demonstrate that the non-Abelian braiding operation can be realized through the scattering between chiral Dirac edge modes (CDEMs) in quantum anomalous Hall insulators by analytically deriving its $S$ matrix. Based on the analytical model, we propose a viable device for the experimental realization and detection of the non-Abelian braiding operations. Through investigating the tunneling conductance in a discretized lattice model, the non-Abelian properties of CDEMs could also be verified in a numerical way. Our proposal for CDEM-based braiding provides an avenue for realizing topologically protected quantum gates.

We present the exact dimer ground state of a quantum antiferromagnet on the maple-leaf lattice. A coupling anisotropy for one of the three inequivalent nearest-neighbor bonds is sufficient to stabilize the dimer state. Together with the Shastry-Sutherland Hamiltonian, we show that this is the only other model with an exact dimer ground state for all two-dimensional lattices with uniform tilings.

The interplay of superconductivity with charge density wave (CDW) in metallic transition-metal dichalcogenides has been widely debated, and viable strategies manipulating these quantum states in the two-dimensional (2D) limit remain unclear. Using the ab initio anisotropic Migdal-Eliashberg theory, we successfully explain the superconductivity observed in monolayer $1H\text{−}{\mathrm{TaS}}_2$ by simultaneously determining its precise CDW structure and treating the marked modification of electron-phonon interaction and critical temperature $T_{\mathrm{c}}$ by spin-orbit coupling effects. With this paradigm, we further show that electron doping weakens the CDW order leading to increased $T_{\mathrm{c}}$ up to 11 K, along with a single-gap to two-gap superconductivity transition due to the suppression of the CDW gap. By contrast, a low hole doping barely affects the CDW but still yields a significantly enhanced superconducting order, implying their good coexistence. Combined with the synergistic behavior of CDW and superconductivity, which cooperate upon ${\mathrm{TaS}}_2$ thickness reduction causing an unusual rise of $T_{\mathrm{c}}$, our results unravel diversified interactions between the two collective orders in ultrathin ${\mathrm{TaS}}_2$, being competition, coexistence or cooperation depending on external stimuli, which provide key clues for controlling correlated states in devices based on 2D CDW superconductors.

The quest for new transition metal dichalcogenides (TMDs) with outstanding electronic properties is a particularly significant and interesting subject. The use of nonconventional methods of materials synthesis, especially pressure engineering, shows great potential for breakthrough discoveries in TMDs. Here, we employ the high-pressure techniques to successfully realize the transformation of two-dimensional semiconductor into three-dimensional superconducting states in $1T\text{−}{\mathrm{HfSe}}_2$. We unambiguously demonstrate that the enhancement of the interlayer coupling and the bonding between interlayer Se-Se atoms contribute to the emergence of nonlayered $C2/m$ and $I4/mmm$ phases. The discovered three-dimensional (3D) structures present excellent superconductivity compared to the original layered structure, and the superconducting critical temperature reaches a maximum of 5.8 K at around 50 GPa. Theoretical calculations reveal that the realization of superconductivity in these two 3D structures is related to the increase in the density of states at the Fermi surface $\left[N\left({\varepsilon }_f\right)\right]$. The present results in ${\mathrm{HfSe}}_2$ may provide a platform for our deep understanding of the relationship among dimensionality, structure, and superconductivity phenomena in TMDs.

The quadrupole topological insulator (QTI) has attracted intense studies as a prototype of symmetry-protected higher-order topological phases of matter with a quantized quadrupole moment. The realization of QTIs has been reported in various static settings with periodic structures. Here, we theoretically investigate topological phase transitions and establish the QTI phase in a periodically driven system with disorder. In the clean limit, the Floquet QTI phase emerges from a topologically trivial band structure driven by elliptically polarized irradiation. More strikingly, starting from a pure and static system with trivial topology, we unveil an intriguing QTI phase which necessitates the simultaneous presence of disorder and periodic driving. Furthermore, we reveal that particle-hole symmetry is sufficient to protect the QTI. Our work not only establishes a strategy to design QTIs but also enriches the symmetry-protected mechanism of higher-order topology.

We theoretically explore mechanisms that can potentially give rise to the steady-state and transient negative capacitance in a uniaxial ferroelectric film stabilized by a dielectric layer. The analytical expressions for the steady-state capacitance of a single-domain and polydomain states are derived within the Landau-Ginzburg-Devonshire approach and used to study the state stability vs the domain splitting as a function of dielectric layer thickness. Analytical expressions for the critical thickness of the dielectric layer, polarization amplitude, equilibrium domain period, and susceptibility are obtained and corroborated by finite element modeling. We further explore the possible effects of nonlinear screening by two types of screening charges at the ferroelectric-dielectric interface and show that if at least one of the screening charges is very slow, the total polarization dynamics can exhibit complex time- and voltage-dependent behaviors that can be interpreted as an observable negative capacitance. In this setting, the transient negative capacitance effect is accompanied by almost zero dielectric susceptibility in a wide voltage range and low frequencies. These results may help to elucidate the observation of the transient negative capacitance in thin ferroelectric films, and identify materials systems that can give rise to the behavior.

Nanoscale magnetic skyrmions are potential candidates for information carriers, for which the nonvolatility under external stimuli is critical to the stability of recorded bits. Here, we present a micromagnetic study on the annihilation dynamics of a two-dimensional skyrmion lattice under a transverse magnetic field and the recoverability of the topological charge after removing the field. The temporal and spatial correlation functions and their Fourier transforms of the spin system reveal position-dependent dynamics under the transverse field. The slow modes $(<10\mathrm{GHz})$ hosted by all spins determine the spin configurations, and the fast ones $(>10\mathrm{GHz})$ around the skyrmion core region control the dynamics of topological properties. A dynamic critical time $t_{\mathrm{cri}}$, when the field-induced ferromagnetic nuclei begin to be long-range correlated, is proved by statistical analyses of their spatial distribution over time. If turning off the transverse field before $t_{\mathrm{cri}}$, the collective motion of the spin system can restore the previously lost topological charge. Our results guide the realization of nonvolatile information storage in skyrmion lattice, thus widening the possibility of skyrmion-based devices for future spintronics-based nanocomputing.

We study the spatiotemporal spreading of correlations in an ensemble of spins due to dissipation characterized by short- and long-range spatial profiles. Such emission channels can be synthesized with tunable spatial profiles in lossy cavity QED experiments using a magnetic field gradient and a Raman drive with multiple sidebands. We consider systems initially in an uncorrelated state, and find that correlations widen and contract in a novel pattern intimately related to both the dissipative nature of the dynamical channel and its spatial profile. Additionally, we make a methodological contribution by generalizing nonequilibrium spin-wave theory to the case of dissipative systems and derive equations of motion for any translationally invariant spin chain whose dynamics can be described by a combination of Hamiltonian interactions and dissipative Lindblad channels. Our work aims at extending the study of correlation dynamics to purely dissipative quantum simulators and compare them with the established paradigm of correlations spreading in Hamiltonian systems.