We investigate relations between topology and the quantum metric of two-dimensional Chern insulators. The quantum metric is the Riemannian metric defined on a parameter space induced from quantum states. Similar to the Berry curvature, the quantum metric provides a geometrical structure associated to quantum states. We consider the volume of the parameter space measured with the quantum metric, which we call the quantum volume of the parameter space. We establish an inequality between the quantum volume of the Brillouin zone and that of the twist-angle space. Exploiting this inequality and the inequality between the Chern number and the quantum volume, we investigate how the quantum volume can be used as a good measure to infer the Chern number. The inequalities are found to be saturated for fermions filling Landau levels. Through various concrete models, we elucidate conditions when the quantum volume gives a good estimate of the topology of the system.

We study Chern insulators from the point of view of Kähler geometry, i.e., the geometry of smooth manifolds equipped with a compatible triple consisting of a symplectic form, an integrable almost complex structure, and a Riemannian metric. The Fermi projector, i.e., the projector onto the occupied bands, provides a map to a Kähler manifold. The quantum metric and Berry curvature of the occupied bands are then related to the Riemannian metric and symplectic form, respectively, on the target space of quantum states. We find that the minimal volume of a parameter space with respect to the quantum metric is $\pi \left|\mathcal{C}\right|$, where $\mathcal{C}$ is the first Chern number. We determine the conditions under which the minimal volume is achieved both for the Brillouin zone and the twist-angle space. The minimal volume of the Brillouin zone, provided the quantum metric is everywhere nondegenerate, is achieved when the latter is endowed with the structure of a Kähler manifold inherited from the one of the space of quantum states. If the quantum volume of the twist-angle torus is minimal, then both parameter spaces have the structure of a Kähler manifold inherited from the space of quantum states. These conditions turn out to be related to the stability of fractional Chern insulators. For two-band systems, the volume of the Brillouin zone is naturally minimal provided the Berry curvature is everywhere non-negative or nonpositive, and we additionally show how the latter, which in this case is proportional to the quantum volume form, necessarily has zeros due to topological constraints.

We report on the study of the magnetic ratchet effect in AlGaN/GaN heterostructures superimposed with a lateral superlattice formed by a dual-grating gate structure. We demonstrate that irradiation of the superlattice with a terahertz beam results in the direct ratchet current, which shows giant magneto-oscillations in the regime of Shubnikov–de Haas oscillations. The oscillations have the same period and are in phase with the resistivity oscillations. Remarkably, their amplitude is greatly enhanced as compared with the ratchet current at zero magnetic field, and the envelope of these oscillations exhibits large beatings as a function of the magnetic field. We demonstrate that the beatings are caused by the spin-orbit (SO) splitting of the conduction band. We develop a theory which gives a good qualitative explanation of all experimental observations and allows us to extract the SO splitting constant ${\alpha }_{\mathrm{SO}}=7.5\pm 1.5$ meVÅ. We also discuss how our results are modified by plasmonic effects and show that these effects become more pronounced with decreasing the period of the grating gate structures down to submicrons.

We present a theoretical study of the effects of heterostrain and lattice relaxation on the optical conductivity of twisted bilayer graphene (TBG) at small twist angle, based on the band structures obtained from a continuum model. We find that heterostrain, lattice relaxation, and their combination give rise to very distinctive spectroscopic features in the optical conductivity, which can be used to probe and distinguish these effects. From the spectrum at various Fermi energies, important features in the strain- and relaxation-modified band structure, such as the band gap, bandwidth, and van Hove singularities, can be directly measured. The peak associated with the transition between the flat bands in the optical conductivity with twist angle $\theta =1.{05}^{\circ }$ are highly sensitive to the direction of the strain, which can provide direct information on the strain-modified flat bands. Moreover, discussing $\theta =1.{47}^{\circ }$ and $1.{81}^{\circ }$ as two more examples, we show that the qualitative changes of optical conductivity under the influence of strain and lattice relaxation are quite general in small-angle TBG.

Topological magnons are bosonic analogues of topological fermions in electronic systems. They have been studied extensively by theory but rarely realized by experiment. Here, by performing inelastic neutron scattering measurements on single crystals of a two-dimensional ferromagnet ${\mathrm{CrBr}}_3$, which was classified as Dirac magnon semimetal featured by the linear bands crossing at the Dirac points, we fully map out the magnetic excitation spectra, and reveal that there is an apparent gap of $\sim 3.5$ meV between the acoustic and optical branches of the magnons at the K point. By collaborative efforts between experiment and theoretical calculations using a five-orbital Hubbard model obtained from first-principles calculations to derive the exchange parameters, we find that a Hamiltonian with Heisenberg exchange interactions, next-nearest-neighbor Dzyaloshinskii-Moriya (DM) interaction, and single-ion anisotropy is more appropriate to describe the system. Calculations using the model show that the lower and upper magnon bands separated by the gap exhibit Chern numbers of $\pm 1$. These results indicate that ${\mathrm{CrBr}}_3$ is a topological magnon insulator, where the nontrivial gap is a result of the DM interaction.

We discuss nonergodic dynamics of interacting spinless fermions in a tilted optical lattice as modeled by a XXZ spin chain in a magnetic (or electric) field changing linearly across the chain. The time dynamics is studied using exact propagation for small chains and matrix product state techniques for larger system sizes. We consider both the initial Néel separable state and the quantum quench scenario, in which the initial state may be significantly entangled. We show that the entanglement dynamics is significantly different in both cases. In the former a rapid initial growth is followed by a saturation for sufficiently large tilt $F$. In the latter case the dynamics seems to be dominated by pair tunneling, and the effective tunneling rate scales as $1/F^2$. In the presence of an additional harmonic potential the imbalance is found to be entirely determined by a local effective tilt $F_{\text{loc}}$; the entanglement entropy growth is modulated with frequency that follows $1/F_{\mathrm{loc}}^2$ scaling first, but at long time the dynamics is determined rather by the curvature of the harmonic potential. Only for large tilts or sufficiently large curvatures, corresponding to the deeply localized regime, do we find logarithmic entanglement growth for the Néel initial state. The same curvature determines the long-time imbalance for large $F$, which reveals strong revival phenomena associated with the manifold of equally spaced states, degenerate in the absence of the harmonic potential.

In this paper, the interplay of the non-Herimiticity and the cascade of delocalization transition in a quasiperiodic chain are studied. The study is applied in the non-Hermitian interpolating Aubry-André-Fibonacci (IAAF) model, which combines the non-Hermitian Aubry-André (AA) model and the non-Hermitian Fibonacci model through a varying parameter, and the non-Hermiticity in this model is introduced by nonreciprocal hopping. In the non-Hermitian AA limit, the system undergoes a delocalization transition by tuning the potential strength. At the critical point, the spatial distribution of the critical state shows a self-similar structure with the relative distance between the peaks being the Fibonacci sequence, and the finite-size scaling of the inverse participation ratios $\left(\mathrm{IPRs}\right)$ of the critical ground state with lattice size $L$ shows that ${\mathrm{IPR}}_g\propto L^{-0.1189}$. In the non-Hermitian Fibonacci limit, we find that the system is always in the extended phase. Along the continuous deformation from the non-Hermitian AA model into the non-Hermitian Fibonacci model in the IAAF model, the cascade of the delocalization transition is found, but only a few plateaux appear. Moreover, the self-similar structure of spatial distribution for the critical modes along the cascade transition is also found. In addition, we find that the delocalization transition and the real-complex transition for the excited states happen at almost the same parameter. Our results show that the non-Hermiticity provides an additional knob to control the cascade of the delocalization transition besides the on-site potential.

After quantum quenches in many-body systems, finite subsystems evolve nontrivially in time, eventually approaching a stationary state. In typical situations, the reduced density matrix of a given subsystem begins and ends this endeavor as a low-entangled vector in the space of operators. This means that if its entanglement in the operator space initially grows (which is generically the case), it must eventually decrease, describing a barrier-shaped curve. Understanding the shape of this “entanglement barrier” is interesting for three main reasons: (i) it quantifies the dynamics of entanglement in the (open) subsystem; (ii) it gives information on the approximability of the reduced density matrix by means of matrix product operators; and (iii) it shows qualitative differences depending on the type of dynamics undergone by the system, signaling quantum chaos. Here we compute exactly the shape of the entanglement barriers described by different Rényi entropies after quantum quenches in dual-unitary circuits initialized in a class of solvable matrix product states (MPS)s. We show that, for free (SWAP-like) circuits, the entanglement entropy behaves as in rational conformal field theories (CFT)s. On the other hand, for completely chaotic dual-unitary circuits, it behaves as in holographic CFTs, exhibiting a longer entanglement barrier that drops rapidly when the subsystem thermalizes. Interestingly, the entanglement spectrum is nontrivial in the completely chaotic case. Higher Rényi entropies behave in an increasingly similar way to rational CFTs, such that the free and completely chaotic barriers are identical in the limit of infinite replicas (i.e., for the so called min-entropy). We also show that, upon increasing the bond dimension of the MPSs, the barrier maintains the same shape. It simply shifts to the left to accommodate for the larger initial entanglement.

We report the Ni-doping effect on magnetism and superconductivity (SC) in an Eu-containing 112-type system $\mathrm{Eu}\left({\mathrm{Fe}}_{1-x}{\mathrm{Ni}}_x\right){\mathrm{As}}_2$ ($0\le x\le 0.15$) by the measurements of resistivity, magnetization, and specific heat. The undoped ${\mathrm{EuFeAs}}_2$ undergoes a spin-density-wave (SDW) transition at $T_{\mathrm{SDW}}\sim 105\mathrm{K}$ in the Fe sublattice and a magnetic ordering at $T_{\mathrm{m}}\sim 40\mathrm{K}$ in the Eu sublattice. Complex Eu-spin magnetism is manifested by a spin-glass reentrance at $T_{\mathrm{SG}}\sim 15\mathrm{K}$ and an additional spin reorientation at $T_{\mathrm{SR}}\sim 7\mathrm{K}$. With Ni doping, the SDW order is rapidly suppressed, and SC emerges in the Ni-doping range of 0.01 $\le x\le$ 0.1 where a maximum of the superconducting transition temperature $T_{\mathrm{c}}^{\max }=17.6\mathrm{K}$ shows up at $x=0.04$. On the other hand, $T_{\mathrm{m}}$ decreases very slowly, yet $T_{\mathrm{SG}}$ and $T_{\mathrm{SR}}$ hardly change with the Ni doping. The phase diagram has been established, which suggests a very weak coupling between SC and Eu spins. The complex Eu-spin magnetism is discussed in terms of the Ruderman-Kittel-Kasuya-Yosida interactions mediated by the conduction electrons from both layers of FeAs and As surrounding ${\mathrm{Eu}}^{2+}$ ions.

The spin chirality, created by magnetic atoms, has been comprehensively understood to generate and control the magneto-optical effects. In comparison, the role of the crystal chirality that relates to nonmagnetic atoms has received much less attention. Here, we theoretically discover the crystal chirality magneto-optical (CCMO) effects, which depend on the chirality of crystal structures that originates from the rearrangement of nonmagnetic atoms. We show that the CCMO effects exist in many collinear antiferromagnets, such as ${\mathrm{RuO}}_2$ and ${\mathrm{CoNb}}_3{\mathrm{S}}_6$, which has a local and global crystal chirality, respectively. The key character of the CCMO effects is the sign change if the crystal chirality reverses. The magnitudes of the CCMO spectra can be effectively manipulated by reorienting the Néel vector with the help of an external electric field, and the spectral integrals are strongly correlated to magnetocrystalline anisotropy energy bridging by orbital magnetic moments.

Skyrmions in chiral magnetic materials are topologically stable and energetically balanced spin configurations appearing under the presence of ferromagnetic interaction (FMI) and Dzyaloshinskii-Moriya interaction (DMI). Much of the current interest has focused on the effects of magnetoelastic coupling on these interactions under mechanical stimuli, such as uniaxial stresses for future applications in spintronics devices. Recent studies suggest that skyrmion shape deformations in thin films are attributed to an anisotropy in the coefficient of DMI, such that $D_x\ne D_y$, which makes the ratio $\lambda /D$ anistropic, where the coefficient of FMI $\lambda$ is isotropic. It is also possible that ${\lambda }_x\ne {\lambda }_y$ while $D$ is isotropic for $\lambda /D$ to be anisotropic. In this paper, we study this problem using a modeling technique constructed based on Finsler geometry (FG). Two possible FG models are examined: In the first (second) model, the FG modeling prescription is applied to the FMI (DMI) Hamiltonian. We find that these two different FG models' results are consistent with the reported experimental data for skyrmion deformation. We also study responses of helical spin orders under lattice deformations corresponding to uniaxial extension/compression and find a clear difference between these two models in the stripe phase, elucidating which interaction of FMI and DMI is deformed to be anisotropic by uniaxial stresses.

Here, we report the possible origin of natural and magnetic field induced polar order near room temperature (RT) in $\mathrm{Pr}{\mathrm{Fe}}_{1/2}{\mathrm{Cr}}_{1/2}{\mathrm{O}}_3$. The temperature-dependent Raman spectroscopy (RS) and synchrotron x-ray diffraction experiments disregard any change in the structure at low temperatures, which is not compatible with the emergence of natural ferroelectricity in this sample. Further, inelastic neutron scattering, neutron Compton scattering, neutron resonance transmission analysis and magnetic field-dependent RS experiments, suggest an increase in the delocalization of ${\mathrm{Pr}}^{3+}$ ions in $\mathrm{Pr}{\mathrm{Fe}}_{1/2}{\mathrm{Cr}}_{1/2}{\mathrm{O}}_3$ with respect to the parent compound $\mathrm{PrFe}{\mathrm{O}}_3$. The evaluation of the present results reveals that more delocalized ${\mathrm{Pr}}^{3+}$ ions and strong spin-phonon coupling in $\mathrm{Pr}{\mathrm{Fe}}_{1/2}{\mathrm{Cr}}_{1/2}{\mathrm{O}}_3$ seem to be a driving force for the observed natural and magnetic field induced switchable polar order in $\mathrm{Pr}{\mathrm{Fe}}_{1/2}{\mathrm{Cr}}_{1/2}{\mathrm{O}}_3$. The present results provide a significant contribution in understanding the ferroelectric polarization and progress in the search for RT magnetodielectric materials.

Distortions of the oxygen octahedra influence the fundamental electronic structure of perovskite oxides, such as their bandwidth and exchange interactions. Utilizing a fully ab initio methodology based on density functional theory plus dynamical mean field theory $(\mathrm{DFT}+\mathrm{DMFT})$, we study the crystal and magnetic structure of ${\mathrm{SrMoO}}_3$. Comparing our results with $\mathrm{DFT}+U$ performed on the same footing, we find that $\mathrm{DFT}+U$ overestimates the propensity for magnetic ordering, as well as the octahedral rotations, leading to a different ground-state structure. This demonstrates that structural distortions can be highly sensitive to electronic correlation effects and to the considered magnetic state, even in a moderately correlated metal such as ${\mathrm{SrMoO}}_3$. Moreover, by comparing different downfolding schemes, we demonstrate the robustness of the $\mathrm{DFT}+\mathrm{DMFT}$ method for obtaining structural properties, highlighting its versatility for applications to a broad range of materials.

The dependence of the Hall and bend resistances on a perpendicular magnetic field and on vacancy defects in a four-terminal phosphorene single layer Hall bar is investigated. A tight-binding model in combination with the Landauer-Büttiker formalism is used to calculate the energy spectrum, the lead-to-lead transmissions, and the Hall and bend resistances of the system. It is shown that the terminals with zigzag edge orientation are responsible for the absence of quantized plateaus in the Hall resistance and peaks in the longitudinal resistance. A negative bend resistance in the ballistic regime is found due to the presence of high- and low-energy transport modes in the armchair and zigzag terminals, respectively. The system density of states, with single vacancy defects, shows that the presence of in-gap states is proportional to the number of vacancies. Quantized plateaus in the Hall resistance are only formed in a sufficiently clean system. The effects of different kinds of vacancies where the plateaus are destroyed and a diffusive regime appears in the bend resistance are investigated.

The measurement of Friedel oscillations (FOs) is conventionally used to recover the energy dispersion of electronic structure. Besides the energy dispersion, the modern electronic structure also embodies other key ingredients such as the geometrical and topological properties; it is one promising direction to explore the potential of FOs for the relevant measurement. Here, we present a comprehensive study of FOs in substrate-supported graphene under off-resonant circularly polarized light, in which a valley-contrasting feature and topological phase transition occur due to the combined breaking of inversion ($\mathcal{P}$) and time reversal ($\mathcal{T}$) symmetries. Depending on the position of the Fermi level, FOs may be contributed by electronic backscattering in one single valley or two valleys. In the single-valley regime, the oscillation periods of FOs can be used to determine the topological phase boundary of electronic structure, while the amplitudes of FOs distinguish trivial insulators and topological insulators in a quantitative way. In the two-valley regime, the unequal Fermi surfaces lead to a beating pattern (robust two-wave-front dislocations) of FOs contributed by intravalley (intervalley) scattering. This study implies the great potential of FOs in characterizing topological and geometrical properties of the electronic structure of two-dimensional materials.

We study the phase diagram of an effective model of competing nematic and antiferromagnetic orders of interacting electrons on the Bernal-stacked honeycomb bilayer, as relevant for bilayer graphene. In the noninteracting limit, the model features a semimetallic ground state with quadratic band touching points at the Fermi level. Taking the effects of short-range interactions into account, we demonstrate the existence of an extended region in the mean-field phase diagram characterized by coexisting nematic and antiferromagnetic orders. By means of a renormalization group approach, we reveal that the quantum phase transition from nematic to coexistent nematic-antiferromagnetic orders is continuous and characterized by emergent Lorentz symmetry. It falls into the $(2+1)$-dimensional relativistic Gross-Neveu-Heisenberg quantum universality class, which has recently been much investigated in the context of interacting Dirac systems in two spatial dimensions. The coexistence-to-antiferromagnetic transition, by contrast, turns out to be weakly first order as a consequence of the absence of the continuous spatial rotational symmetry on the honeycomb bilayer. Implications for experiments in bilayer graphene are discussed.

The common sense regarding twisting or untwisting a ribbon is that it requires the application of an external rotation to happen. However, at nanoscale, the application of precise amounts of rotation on a nanoribbon is not a trivial task. Here, the concept of an alternative method to add twist to or remove twist from a twisted graphene nanoribbon (TGNR) without rotation is presented and computationally demonstrated. The method consists of suspending a TGNR on two separate substrates and, by changing only their distance, the total amount of twist of the TGNR is shown to change. The possibility of fine-tuning the amount of twist of a TGNR is also shown. The concept is demonstrated through fully atomistic molecular dynamics simulations and numerical calculations of the topological parameters twist and writhe of a TGNR. It is shown that the above process satisfies the so-called linking number theorem of space curves. Besides being capable of precisely determining the total twist of a TGNR, this concept reveals a twist to writhe transition phenomenon that is tension-free and does not require controlling either the nanoribbon end-to-end distance or its critical twist density.