I propose monoradical nanographenes without $C_3$ symmetry as building blocks to design two-dimensional carbon crystals. As representative examples I study the honeycomb and kagome lattices, showing that by replacing the sites with olympicene radicals the band dispersion near the Fermi energy corresponds, respectively, to that of Kekulé/anti-Kekulé graphene and breathing kagome tight-binding models. As a consequence, finite islands of these crystals present corner states close to the Fermi energy, just like the parent models. In the case of Kekulé/anti-Kekulé graphene, such states are topologically protected, standing as examples of second-order topological insulators with a nonzero ${\mathbb{Z}}_2$- or ${\mathbb{Z}}_6$-Berry phase. Differently, those of the breathing kagome lattice are of trivial nature, but the ground state has been predicted to be a spin liquid in the antiferromagnetic $S=1/2$ Heisenberg model. Hence, two-dimensional systems made of low-symmetric nanographenes may be convenient platforms to explore exotic physics in carbon materials.

We study the correlations of a two-dimensional electron gas with Rashba spin-orbit coupling (SOC). We obtain the two-particle density matrix and use it to derive the exchange hole. We find a nontrivial correlation for electrons with opposite spin projections that does not occur without Rashba SOC. The two-particle density matrix allows us to further study the quantum correlations of the system. We use it to obtain the concurrence and the entanglement of formation in order to quantify the entanglement of the electron spins. Additionally, we calculate the quantum discord and compare it with the entanglement and classical correlations.

Two-dimensional inorganic molecular crystals (2D IMCs) consisting of compound molecules are emerging as a new branch of the 2D materials family. Based on first-principles calculations, here we propose a 2D IMC class assembled from diatomic molecules whose building blocks are derived from a single element, iodine. We reveal that 2D monolayers of halogen-bonded ${\mathrm{I}}_2$ molecules can be stabilized with distinct structures of $\alpha$-I, $\beta$-I, and $\gamma$-I, and these allotropes are collectively named iodene. Intriguingly, the intermolecular angle between two neighboring ${\mathrm{I}}_2$ units demonstrate magic angles of ${90}^{\circ },{120}^{\circ }$, and ${180}^{\circ }$ for $\alpha$-I, $\beta$-I, and $\gamma$-I, respectively, which serves as a degree of freedom to modulate the structural and electronic properties of iodene monolayers. The $\gamma$-I behaves as a quantum spin Hall insulator with a band gap of 0.18 eV, which offers a candidate for potential topological 2D IMCs. The $\alpha$- and $\beta$-I phases demonstrate trivial semiconductors with gaps of 2.30 and 1.94 eV. These findings broaden the scope of 2D IMCs stabilized by halogen bonding, with appealing application potentials in molecular physics and optoelectronics.

The diffusion of particles on surfaces subjected to a thermal gradient driven by phonons is numerically and theoretically investigated. Performing molecular dynamics (MD) simulations, we show that the thermal gradient induces a drift velocity of the adatom toward the cold regions. Beyond the bare study of the adatom trajectories for various thermal gradients, we propose to use a Massieu function as a thermodynamic potential that drives the adatom motion. We generalize the thermodynamic integration method to this out-of-equilibrium system to compute this thermodynamic potential. The thermal-gradient-induced effect is decorrelated from the stochastic diffusion from the analysis of the thermodynamic potential. Based on these results, we propose a model to evaluate the drift velocity and trajectory of an adatom that compares with a good agreement with trajectories provided by MD.

Belief propagation is a well-studied algorithm for approximating local marginals of multivariate probability distribution over complex networks, while tensor network states are powerful tools for quantum and classical many-body problems. Building on a recent connection between the belief propagation algorithm and the problem of tensor network contraction, we propose a block belief propagation algorithm for contracting two-dimensional (2D) tensor networks and approximating the ground state of 2D systems. The advantages of our method are threefold: (1) the same algorithm works for both finite and infinite systems; (2) it allows natural and efficient parallelization; and (3) given its flexibility, it would allow us to deal with different unit cells. As applications, we use our algorithm to study the 2D Heisenberg and transverse Ising models, and show that the accuracy of the method is on par with state-of-the-art results.

We study a classical model of fully packed loops on the square lattice, which interact through attractive loop segment interactions between opposite sides of plaquettes. This study is motivated by effective models of interacting quantum matter arising in frustrated magnets or Rydberg atom arrays, for which loop degrees of freedom appear at low energy. Through the combination of Monte Carlo simulations and of an effective height field theory, we find that the critical point known to occur at infinite temperature gives rise to a high-temperature critical phase with floating exponents. At lower temperature, the system transitions via a Kosterlitz-Thouless phase transition to a nematic phase where lattice rotation symmetry is broken. We discuss consequences for the phase diagram of the quantum loop model on the same lattice.

We show that the rainbow state, which has volume-law entanglement entropy for most choices of bipartitions, can be embedded in a many-body localized spectrum. For a broad range of disorder strengths in the resulting model, we numerically find a narrow window of highly entangled states in the spectrum, embedded in a sea of area law entangled states. The construction hence embeds mobility edges in many-body localized systems. This can be thought of as the complement to many-body scars, an “inverted quantum many-body scar,” providing a further type of setting where the eigenstate thermalization hypothesis is violated.

The skin effect, which is unique to non-Hermitian systems, can generate an extensive number of eigenstates localized near the boundary in an open geometry. Here, we propose that in two dimensions (2D) and three dimensions (3D) other quantities besides charge density are susceptible to the skin effect. We show that 2D and 3D models that are a hybrid between topological insulators and skin-effect systems can have a topological skin effect where an extensive number of topological modes, and the corresponding bulk topological invariant, are pinned to the surface. A key example, which we call the quantum skin Hall effect is constructed from layers of Chern insulators and exhibits an extensive Hall conductance and number of chiral modes bound to surfaces normal to the stack of layers. The same procedure is further extended to other symmetry classes to illustrate that a variety of one-dimensional and 2D topological invariants ($\mathbb{Z}$ or ${\mathbb{Z}}_2)$ are subject to the skin effect. Indeed, we also propose a hybrid 2D system that exhibits an extensive number of topological corner modes and may be more easily realized in metamaterial experiments.

The use of moiré patterns to manipulate two-dimensional materials has facilitated new possibilities for controlling material properties. The moiré patterns in the two-dimensional magnets can cause peculiar spin texture, as shown by previous studies focused on twisted bilayer systems. In our study, we develop a theoretical model to investigate the magnetic structure of twisted trilayer magnets. Unlike the twisted bilayer, the twisted trilayer magnet has four different local stacking structures distinguished by the interlayer couplings between the three layers. Our results show that the complex interlayer coupling effects in the moiré superlattice can lead to the stabilization of rich magnetic domain structures; these structures can be significantly manipulated by adjusting the twist angle. Additionally, external magnetic fields can easily manipulate these domain structures, indicating potential applications in magnetic devices.

Band gap is known as an effective parameter for tuning the Landé $g$ factor in semiconductors and can be manipulated in a wide range through the bowing effect in ternary alloys. In this work, using the recently developed virtual substrate technique, high-quality InAsSb alloys throughout the whole Sb composition range are fabricated and a large $g$ factor of $g\approx -90$ at the minimum band gap of $\sim 0.1$ eV, which is almost twice that in bulk InSb, is found. Further analysis to the zero gap limit reveals a possible gigantic $g$ factor of $g\approx -200$ with a peculiar relativistic Zeeman effect that disperses as the square root of magnetic field. Such a $g$-factor enhancement toward the narrow gap limit cannot be quantitatively described by the conventional Roth formula, as the orbital interaction effect between the nearly triply degenerated bands becomes the dominant source for the Zeeman splitting. These results may provide insights into realizing large $g$ factors and spin-polarized states in semiconductors and topological materials.

We elucidate the properties of a robust transverse polarization mode in heterostructures of transition metal dichalcogenides. This trapped-photon mode arises from strong interband light-matter coupling, but its nature is fundamentally distinct from extensively studied exciton polaritons, as well as photon-cavity modes. It can be viewed as a transverse counterpart to the longitudinal two-dimensional Dirac plasmon mode found in doped graphene, characterized by much greater oscillatory strength. Furthermore, the trapped photon is easily tunable by adjusting the number of semiconducting layers, allowing for enhanced photon-electron-hole binding strength. In addition, we devise a near-field microscopy simulation that paves the way for future experimental characterization, which could lead to exciting applications in optoelectronics, sensing, and quantum information processing.

A continuum approach to study magnetoelectric multiferroic ${\mathrm{BiFeO}}_3$ (BFO) is proposed. Our modeling effort marries the ferroelectric (FE) phase field method and micromagnetic simulations to describe the entire multiferroic order parameter sector (polarization, oxygen antiphase tilts, strain, and magnetism) self-consistently on the same time- and length scale. In this paper, we discuss our choice of FE and magnetic energy terms and demonstrate benchmarks against known behavior. We parametrize the lowest order couplings of the structural distortions against previous predictions from density functional theory calculations giving access to simulations of the FE domain wall (DW) topology. This allows us to estimate the energetic hierarchy and thicknesses of the numerous structural DWs. We then extend the model to the canted antiferromagnetic order and demonstrate how the FE domain boundaries influence the resulting magnetic DWs. We also highlight some capabilities of this model by providing two examples relevant for applications. We demonstrate spin-wave transmission through the multiferroic domain boundaries which identify rectification in qualitative agreement with recent experimental observations. As a second example of application, we model fully dynamical magnetoelectric switching, where we find a sensitivity on the Gilbert damping with respect to switching pathways. We envision that this modeling effort will set the basis for further work on properties of arbitrary 3D nanostructures of BFO (and related multiferroics) at the mesoscale.

We analyze theoretically the demagnetization dynamics in a ferromagnetic model system due to the interplay of Rashba-type spin-orbit coupling and electron-electron Coulomb scattering. We compute the $k$-resolved electronic reduced spin-density matrix, including precessional dynamics around internal spin-orbit and exchange fields as well as the electron-electron Coulomb scattering for densities and spin coherences. Based on a comparison with numerical solutions of the full Boltzmann scattering integrals, we establish that the $k$-resolved reduced spin-density matrix dynamics are well described using a simpler generalized relaxation-time ansatz for the reduced spin-density matrix. This ansatz allows one to relate the complicated scattering dynamics underlying the demagnetization dynamics to a physically meaningful momentum relaxation time $\tau$. Our approach reproduces the behavior of the demagnetization time ${\tau }_{\text{m}}\propto 1/\tau$ and ${\tau }_{\text{m}}\propto \tau$ for the limits of short and long $\tau$, respectively, and is also valid for the intermediate regime. The ansatz is not limited to the specific form of spin-orbit coupling considered here and provides a tool to include the correct demagnetization behavior in approaches that treat other contributions to the magnetization dynamics such as transport or magnon/phonon dynamics.

We report on magnetic and magnetotransport studies of the kagome ferromagnetic metal ${\mathrm{Fe}}_3\mathrm{Sn}$. Our studies reveal a large anomalous Hall conductivity ${\sigma }_{zx}$ in this system, mainly contributed by temperature-independent intrinsic Hall conductivity (${\sigma }_{zx}^{\mathrm{int}}=485\pm 60\mathrm{S}{\mathrm{cm}}^{-1}$) and temperature-dependent extrinsic Hall conductivity ${\sigma }_{zx}^{\mathrm{ext}}$ due to skew scattering. Although the ${\sigma }_{zx}^{\mathrm{ext}}$ value is large and almost equivalent to the intrinsic Hall conductivity at low temperatures, it drastically decreases with increasing temperature, following the relation ${\sigma }_{zx}^{\mathrm{ext}}=\frac{{\sigma }_{zx0}^{\mathrm{ext}}}{{(aT+1)}^2}$, under the influence of electron-phonon scattering. The presence of electron-phonon scattering in this system is also confirmed by the linear dependence of the longitudinal electrical resistivity at higher temperatures $\left[\rho \right(T)\propto T]$. We further find that ${\mathrm{Fe}}_3\mathrm{Sn}$ is a soft ferromagnet with an easy axis of magnetization lying in the $\mathit{ab}$ plane of the crystal with a magnetocrystalline anisotropy energy density as large as $1.02\times {10}^6\mathrm{J}{\mathrm{m}}^{-3}$.

The quantification of materials' dynamical responses to external electromagnetic fields is central to understanding their physical properties. Here we present an implementation of the density functional perturbation theory for the computation of linear susceptibilities using the projector augmented wave method. The Sternheimer equations are solved self-consistently through a nested iterative procedure to compute the first-order wave functions, from which the linear susceptibilities are obtained. As a demonstration, we compute the spin-wave spectral functions of two magnetic metals. The computed magnon spectra for half-metallic ${\mathrm{CrO}}_2$ and a Heusler intermetallic ${\mathrm{Cu}}_2\mathrm{MnAl}$ show gapless Goldstone modes when spin-rotation symmetry is preserved and display reasonable agreement with available experimental data. The Landau damping is computed to be small in ${\mathrm{CrO}}_2$, but significant in ${\mathrm{Cu}}_2\mathrm{MnAl}$, producing an asymmetric Lorentzian spectral line shape. The access to linear susceptibilities as well as first-order wave functions offers a range of novel possibilities in the quantitative understanding of materials' electronic properties from ab initio methods.

For ultrathin films of manganites, it is commonly observed that the first several layers exhibit no magnetic signal, which are referred to as magnetic “dead layer.” The existence of such a magnetic dead layer hinders the exploration of two-dimensional (2D) magnetism in strongly correlated systems. Various approaches including modulations of lattice, charge, and orbital of the ultrathin films have been used to reduce or even remove the magnetic dead layer. Although complete removal of the dead layer has not been achieved, noticeable success has been made in a model system of ultrathin films of ${\mathrm{La}}_{0.7}{\mathrm{Sr}}_{0.3}\mathrm{Mn}{\mathrm{O}}_3/\mathrm{SrTi}{\mathrm{O}}_3$ (001), where the dead layer is reduced from 10 to 3 unit cells. In this work, we demonstrate that the dead layer can be further reduced to 1 unit cell with significantly enhanced magnetic moment and Curie temperature $\left(T_{\mathrm{C}}\right)$ using a strong spin-orbit coupling (SOC) effect. Specifically, we put two unit cells of $\mathrm{SrIr}{\mathrm{O}}_3$ (SIO) either as the buffer or capping layers for the LSMO ultrathin films and similar results have been obtained. Density functional theory (DFT) calculations demonstrate that SIO dramatically enhances the magnetic anisotropy energy, in which the strong SOC effect of Ir atoms plays an important role. Our work indicates that enhancing spin-orbit coupling is an effective way to boost magnetism in 2D strongly correlated systems.

We experimentally demonstrate rarely observed fully compensated ferrimagnetic behavior in the half-Heusler compound $\left({\mathrm{Co}}_{0.5}{\mathrm{Mn}}_{0.5}\right)\mathrm{MnAl}$. A comprehensive structural investigation at room temperature was carried out using x-ray and neutron diffraction techniques, which indicated that the sample exhibited a $C{1}_b$ structure with B2-type disorder. The magnetic measurement on this compound reveals that the sample has a completely compensated ferrimagnetic behavior with a very low saturation magnetization of $0.09 {\mu }_{\mathrm{B}}/\text{f.u.}$ and a Curie temperature of 634 K. This finding was further verified by neutron diffraction techniques. Around 200 K, a change in the sign of the magnetic moment and anomalous Hall resistivity was observed, resulting from sublattice spin crossing. The resistivity measurement indicates an unusual temperature dependence with a negative temperature coefficient, revealing the possibility of alternative mechanisms for electronic transport observed in materials such as semimetals or gapless/spin-gapless semiconductors. The compensated ferrimagnetic behavior is analyzed and substantiated by carrying out fixed spin moment calculations within the framework of density functional theory. The electronic structure analysis predicts a spin semimetallic quantum phase for this half-Heusler compound.

The discovery of two-dimensional magnets with intrinsic ferromagnetic or antiferromagnetic orders has opened up promising prospects for exploring magnetism at the desired thickness, paving the way for novel spintronic applications. In practice, the manipulation of the magnetic state in van der Waals ferromagnets is highly demanding but remains a significant challenge. In this work, we demonstrate that the magnetic states of the ${\mathrm{Fe}}_5{\mathrm{GeTe}}_2$ (FGT)-based heterostructures can be substantially tuned through a natural oxidation process. During this process, the exchange bias effect is observed in the naturally oxidized FGT flakes, confirming the existence of exchange coupling between the ferromagnetic FGT layer and antiferromagnetic oxide layer. Through the exchange coupling, the formed oxide layer affects the magnetic ordering of the Fe1 sites and magnetic anisotropy, which is evidenced by the increment of hard magnetic temperature. Theoretical calculations shed light on the crucial role of the oxide layer in the magnetic state transitions. These results provide valuable insights into the understanding and manipulation of the emergent magnetic states, leading to significant advances in the realization of practical two-dimensional spintronics.