We investigate the impact of mechanical strain, stacking order, and external electric fields on the magnetic interactions of a two-dimensional (2D) van der Waals heterostructure in which a 2D ferromagnetic metallic ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ monolayer is deposited on germanene. Three distinct computational approaches based on ab initio methods are used, (i) the Green's function method, (ii) the generalized Bloch theorem, and (iii) the supercell approach, and a careful comparison is given. First, the shell-resolved exchange constants are calculated for the three Fe atoms within the unit cell of the freestanding ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ monolayer. We find that the results obtained with approaches (i) and (ii) are in good qualitative agreement and also in good qualitative agreement with previously reported values. An electric field of $\mathcal{E}=\pm 0.5$ V/Å applied perpendicular to the ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$/germanene heterostructure leads to significant changes in the exchange constants. We show that the Dzyaloshinskii-Moriya interaction (DMI) in ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$/germanene is mainly dominated by the nearest neighbors, resulting in a good quantitative agreement between approaches (i) and (ii). Furthermore, we demonstrate that the DMI is highly tunable by strain, stacking, and electric field, leading to a large DMI comparable to that of ferromagnetic/heavy metal interfaces, which have been recognized as prototypical multilayer systems to host isolated skyrmions. The geometrical change and hybridization effect explain the origin of the high tunability of the DMI at the interface. The electric-field-driven DMI obtained by approach (iii) is in qualitative agreement with the more accurate ab initio method used in approach (ii). However, the field effect on the DMI is overestimated by approach (iii) by about 50%. This discrepancy is attributed to the different implementations of the electric field and basis sets used in the ab initio methods applied in approaches (ii) and (iii). The magnetocrystalline anisotropy energy (MAE) can also be drastically changed by the application of compressive or tensile strain in the ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$/germanene heterostructure. The application of an electric field, in contrast, leads only to relatively small changes in the MAE for electric fields of up to 1 V/Å.

Generally speaking, for a fractional quantum Hall (FQH) state, the electronic occupation number for each Landau orbit could be obtained by numerical methods such as exact diagonalization, density matrix renormalization group, matrix product state, or algebraic recursive schemes (Jack polynomial). In this paper, we apply a Metropolis Monte Carlo method to calculate the occupation numbers of several FQH states in cylinder geometry. The convergent occupation numbers for more than 40 particles are used to verify the chiral bosonic edge theory and determine topological quantities from momentum polarization or dipole moments. The guiding center spin, central charge, and topological spin of different topological sectors are consistent with theoretical values and other numerical studies. In particular, we obtain the topological spin of a $e/4$ quasihole in Moore-Read and 331 states. Lastly, we calculate the electron edge Green's functions and analyze the position dependence of the non-Fermi liquid behavior.

Particles obeying non-Abelian braid statistics have been predicted to emerge in the fractional quantum Hall effect. In particular, a model Hamiltonian with short-range three-body interaction (${\widehat{V}}_3^{\text{Pf}}$) between electrons confined to the lowest Landau level provides exact solutions for quasiholes, and thereby allows a proof of principle for the existence of quasiholes obeying non-Abelian braid statistics. We construct, in terms of two- and three-body Haldane pseudopotentials, a model Hamiltonian that can be solved exactly for both quasiholes and quasiparticles, and provide evidence of non-Abelian statistics for the latter as well. The structure of the quasiparticle states of this model is in agreement with that predicted by the bipartite composite-fermion model of quasiparticles. We further demonstrate, for systems for which exact diagonalization is possible, adiabatic continuity for the ground state, the ordinary neutral excitation, and the topological exciton as we deform our model Hamiltonian continuously into the lowest Landau-level ${\widehat{V}}_3^{\text{Pf}}$ Hamiltonian.

Josephson junctions based on quantum dots offer a convenient tunability by means of local gates. Here we analyze a Josephson junction based on a serial double quantum dot in which the two dots are individually gated by phase-shifted microwave tones of equal frequency. We calculate the time-averaged current across the junction and determine how the phase shift between the drives modifies the current-phase relation of the junction. Breaking particle-hole symmetry on the dots is found to give rise to a finite average anomalous Josephson current with phase bias between the superconductors fixed to zero. This microwave gated weak link thus realizes a tunable “Floquet ${\phi }_0$ junction” with maximum critical current achieved for driving frequencies slightly off resonance with the subgap excitation energy. We provide numerical results supported by an analytical analysis for infinite superconducting gap and weak interdot coupling. We identify an interaction-driven $0\text{−}\pi$ transition of anomalous Josephson current as a function of driving phase difference. Finally, we show that this junction can be tuned so as to provide for complete rectification of the time-averaged Josephson current-phase relation.

Higher-order topological states that possess gapped bulk energy bands and exotic topologically protected boundary states with at least two dimensions lower than the bulk have opened a significant and new perspective for understanding topological quantum matter. Here, we propose to generate two-dimensional (2D) topological boundary states for implementing a synthetic magnetic flux of ultracold atoms trapped in bilayer optical lattices. It is shown that a Chern insulator, Dirac semimetals, and a second-order topological phase (SOTP) are generated by the interplay of the two-photon detuning and effective Zeeman shift. These observed topological phases can be well characterized by the energy gap of the bulk, the Wilson loop spectra, and the spin textures at the high-symmetry points of the system. We show that the SOTP exhibits a pair of $0\mathrm{D}$ boundary states. Meanwhile, the phases of the Dirac semimetals and Chern insulator support the conventional $1\mathrm{D}$ boundary states due to the principle of bulk-boundary correspondence. Strikingly, the boundary states that emerge for Dirac semimetals and the SOTP are topologically protected by $\mathcal{P}T$ symmetry and chiral-mirror symmetry (${\tilde{\mathcal{M}}}_{\alpha }$), respectively. In particular, the location of $0\mathrm{D}$ corner states for the SOTP which are associated with ${\tilde{\mathcal{M}}}_{\alpha }$ symmetry are highly manipulable by tuning the magnetic flux. Our scheme herein provides a platform for emerging exotic topological boundary states, which may facilitate the study of higher-order topological phases in ultracold atomic gases.

Two-dimensional (2D) ferromagnetic semiconductors hold great interest due to their potential applications for nanoscale electronic devices. In this paper, the Janus $2H\text{−}\mathrm{Gd}XY$ $(X, Y=\mathrm{Cl},\mathrm{Br},\mathrm{I},X\ne Y)$ monolayers with rare-earth element Gd ($4f^7+5d^1$) are predicted by first-principles calculations. Small exfoliation energy of less than $0.25 \mathrm{J}/{\mathrm{m}}^2$ and excellent dynamical/thermal stabilities can be confirmed for the Janus $2H\text{−}\mathrm{Gd}XY$ monolayers, which exhibit the bipolar magnetic semiconductor character with high Curie temperatures above 260 K and large spin-orbit coupling effect, and can be further transformed into the half-semiconductor phase under proper tensile strains (5–6%). In addition, in-plane magnetic anisotropy can be observed in the $2H$-GdICl and $2H$-GdIBr monolayers. On the contrary, the $2H$-GdBrCl monolayer exhibits perpendicular magnetic anisotropy character, which originates from the competition between Gd-$p/d$ and halogen atom-$p$ orbitals. Calculated valley optical actions of the Janus $2H\text{−}\mathrm{Gd}XY$ monolayers exhibit distinguished valley-selective circular dichroisms, which is expected to realize the special valley excitation by polarized light. Spontaneously, valley-Zeeman effect in the valance band for the Janus $2H\text{−}\mathrm{Gd}XY$ monolayers induces a giant valley splitting of 60–120 meV, which is also robust against various external biaxial strains. A tunable valley degree of freedom in Janus $2H\text{−}\mathrm{Gd}XY$ systems is very necessary for encoding and processing information.

In quantum spin-1 chains, there is a nonlocal unitary transformation known as the Kennedy-Tasaki transformation $U_{\mathrm{KT}}$, which defines a duality between the Haldane phase and the ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ symmetry-breaking phase. In this paper, we find that $U_{\mathrm{KT}}$ also defines a duality between a topological Ising critical phase and a trivial Ising critical phase, which provides a “hidden symmetry breaking” interpretation of the topological criticality. Moreover, since the duality relates different phases of matter, we argue that a model with self-duality (i.e., invariant under $U_{\mathrm{KT}}$) is natural to be at a critical or multicritical point. We study concrete examples to demonstrate this argument. In particular, when $H$ is the Hamiltonian of the spin-1 antiferromagnetic Heisenberg chain, we prove that the self-dual model $H+U_{\mathrm{KT}}H{U}_{\mathrm{KT}}$ is exactly equivalent to a gapless spin-$1/2$ XY chain, which also implies an emergent quantum anomaly. On the other hand, we show that the topological and trivial Ising critical phases that are dual to each other meet at a multicritical point which is indeed self-dual.

The Mott transition is observed experimentally in materials that are magnetically frustrated so that long-range order does not hide the Mott transition at finite temperature. The Hubbard model on the triangular lattice at half filling is a paradigmatic model to study the interplay of interactions and frustration on the normal-state phase diagram. We use the dynamical cluster approximation with continuous-time auxiliary-field quantum Monte Carlo to solve this model for 1-, 4-, 6-, 12-, and 16-site clusters with detailed analysis performed for the 6-site cluster. We show that (a) for every cluster there is an inflection point in the double occupancy as a function of interaction, defining a Widom line that extends above the critical point of the first-order Mott transition; (b) the presence of this line and the cluster size dependence argue for the observability of the Mott transition at finite temperature in the thermodynamic limit; and (c) the loss of spectral weight in the metal-to-Mott-insulator transition as a function of temperature and for strong interactions is momentum dependent, the hallmark of a pseudogap. That pseudogap spans a large region of the phase diagram near the Mott transition.

The past decade has seen the emergence of ab initio computational methods for calculating phonon-limited carrier mobilities in semiconductors with predictive accuracy. More realistic calculations ought to take into account additional scattering mechanisms such as, for example, impurity and grain-boundary scattering. In this paper, we investigate the effect of ionized-impurity scattering on the carrier mobility. We model the analytical impurity potential parameterized from first principles by a collection of randomly distributed Coulomb scattering centers, and we include this relaxation channel into the ab initio Boltzmann transport equation, as implemented in the EPW code. We demonstrate this methodology by considering silicon, silicon carbide, and gallium phosphide, for which detailed experimental data are available. Our calculations agree well with experiments over a broad range of temperatures and impurity concentrations. For each compound investigated here, we compare the relative importance of electron-phonon scattering and ionized-impurity scattering, and we critically assess the reliability of Matthiessen's rule. We also show that an accurate description of dielectric screening and carrier effective masses can improve quantitative agreement with experiments.

The quantum skyrmionic phase is modeled in a two-dimensional helical spin lattice. This topological skyrmionic phase retains its nature in a large parameter space before moving to a ferromagnetic phase. Next-nearest-neighbor interaction improves the stability and it also causes a shift of the topological phase in the parameter space. Nonanalytic behavior of the rate function observed, when the system which is initially in a quantum skyrmion phase is quenched to a trivial quantum ferromagnetic phase, indicates a dynamical quantum phase transition. Dynamical quantum phase transition is absent when the system initially in a skyrmion phase is quenched to a helical phase.

The time evolution of a quantum state with short-range correlations after a quench to a one-dimensional critical Hamiltonian can be understood using the quasiparticle picture, which states that local entanglement spreads as if it was carried by quasiparticles which separate at a fixed speed. We extend the quasiparticle picture using the recently introduced link representation of entanglement, allowing us to apply it to initial states presenting long-range correlations. The entanglement links are current correlators, and therefore follow a wave equation on the appropriate configurational space which allows us to predict the time evolution of the entanglement entropies. Our results are checked numerically for free fermionic chains with different initial entanglement patterns.

Floquet engineering, the concept of tailoring a system by a periodic drive, is increasingly exploited to design and manipulate topological phases of matter. In this work we study periodically driven higher-order topological Dirac semimetals associated with a $k$-dependent quantized quadrupole moment by applying circularly polarized light. The undriven Dirac semimetals feature gapless higher-order hinge Fermi arc states which are the consequence of the higher-order topology of the Dirac nodes. Floquet Weyl semimetal phases with hybrid-order topology, characterized by both a $k$-dependent quantized quadrupole moment and a $k$-dependent Chern number, emerge when illumining circularly polarized light. Such Floquet Weyl semimetals support both hinge Fermi arc states and topological surface Fermi arc states. In addition, Floquet Weyl semimetals with tilted Weyl cones in higher-order topological Dirac semimetals are also discussed. Considering numerous higher-order topological Dirac semimetal materials were recently proposed, our findings can be testable soon.

Electron irradiation-induced damage is often the limiting factor in imaging materials prone to ionization or electronic excitations due to inelastic electron scattering. Quantifying the related processes at the atomic scale has only become possible with the advent of aberration-corrected (scanning) transmission electron microscopes and two-dimensional materials that allow imaging each lattice atom. While it has been shown for graphene that pure knock-on damage arising from elastic scattering is sufficient to describe the observed damage, the situation is more complicated with two-dimensional semiconducting materials such as ${\mathrm{MoS}}_2$. Here, we measure the displacement cross section for sulfur atoms in ${\mathrm{MoS}}_2$ with primary beam energies between 55 and 90 keV, and correlate the results with existing measurements and theoretical models. Our experimental data suggests that the displacement process can occur from the ground state, or with single or multiple excitations, all caused by the same impinging electron. The results bring light to reports in the recent literature, and add necessary experimental data for a comprehensive description of electron irradiation damage in a two-dimensional semiconducting material. Specifically, the results agree with a combined inelastic and elastic damage mechanism at intermediate energies, in addition to a pure elastic mechanism that dominates above 80 keV. When the inelastic contribution is assumed to arise through impact ionization, the associated excitation lifetime is on the order of picoseconds, on par with expected excitation lifetimes in ${\mathrm{MoS}}_2$, whereas it drops to some tens of femtoseconds when direct valence excitation is considered.

Spontaneous symmetry breaking is responsible for rich phenomena in equilibrium physics. Driving a system out-of-equilibrium can significantly enrich the possibility of spontaneous symmetry breaking, which occurs not only in space, but also in the time domain. This study investigates a driven-dissipative frustrated magnetic system with alternate ferromagnetic and antiferromagnetic coupling. Results show that frustration in such a far-from-equilibrium system could lead to nonequilibrium phases with intriguing space-time symmetry breaking, e.g., a discrete time crystal accompanied by a time-dependent magnetism with alternating tripartite stripe and ferromagnetic orders.

Recently, single-site observables have been shown to be useful for probing critical slowing down in sudden quench dynamics [Dağ et al., Phys. Rev. B 107, L121113 (2023)]. Here, we demonstrate the potential of single-site magnetization as a probe of quantum phase transitions in integrable and nonintegrable transverse-field Ising chains (TFIC). We analytically prove the requirement of zero modes for the quasistationary regime to emerge at a probe site near the edge, and show how this regime gives rise to a nonanalytic behavior in the dynamical order profiles. Our $\mathit{t}$-DMRG calculations verify the results of the quench mean-field theory for near-integrable TFIC both with finite-size and finite-time scaling analyses. We find that both finite-size and finite-time analyses suggest a dynamical critical point for a strongly nonintegrable and locally connected TFIC. We finally demonstrate the presence of a quasistationary regime in the power-law interacting TFIC, and extract local dynamical order profiles for TFIC in the long-range Ising universality class with algebraic light cones.

The quantum effect of light nuclei in materials is usually considered as lattice vibration and zero-point motion from an ab initio perspective. Here we start from full-quantized particles and take the muon as an example, considering the two-body quantized system of the muon and the electrons within two-component density functional theory, which can calculate the related two-body wave functions directly and automatically taking into account the quantum effect of the muon. We first simulate the two-body correlation energy and the pair-correlation function by quantum Monte Carlo, then construct a two-body self-consistent loop to solve the two-body density and then the hyperfine couplings are estimated. This is an attempt to reveal the quantum effect of light nuclei in materials from a different perspective. We finally find this fundamental method agrees better with experiments and shows good potential for further such calculations.

${\mathrm{Mn}}^{4+}$, ${\mathrm{Cr}}^{3+}$, and ${\mathrm{Fe}}^{3+}$ electron paramagnetic resonance and ${}^{47,49}\mathrm{Ti}$ and ${}^{207}\mathrm{Pb}$ nuclear magnetic resonance (NMR) measurements are carried out in $\mathrm{PbTi}{\mathrm{O}}_3$ single crystals at temperatures from 300 K down to 20 K. It was found that the tetragonal crystal-field parameter of the ${\mathrm{Mn}}^{4+}$ and ${\mathrm{Cr}}^{3+}$ impurity ions undergoes an unexpected change in its temperature dependence at $T<170$ K: it increases with decreasing temperature to 150–170 K and then strongly decreases with further temperature lowering. Electric-field gradient at Ti site measured from ${}^{47,49}\mathrm{Ti}$ NMR shows nonuniform change with decreasing temperature: it sharply increases with decreasing temperature to 150–170 K and is practically temperature independent below these temperatures. Moreover, substantial broadening of NMR linewidth is seen for Ti and Pb nuclei at $T<170$ K due to essential increase of lattice parameters fluctuations. All these facts may indicate proximity of a transition to another phase with barely perceptible crystal-structure modification as reported in the paper by Kobayashi et al. [Phys. Rev. B 28, 3866 (1983)] while, actually, it was not detected in NMR. The experimental data are compared with those obtained from ab initio calculations.

A crystal field level scheme of a uniaxial chiral helimagnet $\mathrm{Yb}{\mathrm{Ni}}_3{\mathrm{Al}}_9$, exhibiting a chiral magnetic soliton lattice state by Cu substitution for Ni, has been determined by inelastic neutron scattering. The ground and the first excited doublets are separated by 44 K and are simply expressed as $\alpha |\pm 7/2\rangle +\beta |\mp 5/2\rangle$, with $\alpha$ and $\beta$ nearly equal to $\pm 1/\sqrt{2}$. The easy axis of the crystal field anisotropy is the $c$ axis when the excited levels are populated at high temperatures and high magnetic fields. On the other hand, the magnetism at low temperatures and low magnetic fields, where only the ground doublet is populated, is described by an easy-plane anisotropy which may be treated as an $S=1/2$ system with an anisotropic $g$ factor, $g_{xy}=3.02$ and $g_z=1.14$. An orbital-dependent exchange interaction is also discussed to explain the temperature dependence of the magnetic susceptibility based on this level scheme.