We examine the properties of a one-dimensional (1D) Fermi gas with attractive intrinsic (Hubbard) interactions in the presence of spin-orbit coupling and Zeeman field by numerically computing the pair binding energy, excitation gap, and susceptibility to local perturbations using the density matrix renormalization group. Such a system can, in principle, be realized in a system of ultracold atoms confined in a 1D optical lattice. We note that, in the presence of spatial interfaces introduced by a smooth parabolic potential, the pair binding and excitation energy of the system decays exponentially with the system size, pointing to the existence of an exponential ground state degeneracy, and is consistent with recent works. However, the susceptibility of the ground state degeneracy of this number-conserving system to local impurities indicates that the energy gap vanishes as a power law with the system size in the presence of local perturbations. We compare this system with the more familiar system of an Ising antiferromagnet in the presence of a transverse field realized with Rydberg atoms and argue that the exponential splitting in the clean number-conserving 1D Fermi system is similar to a phase with only conventional order.

Lattice vibrations in materials induce perturbations on the electron dynamics in the form of long-range (dipole and quadrupole) and short-range (octopole and higher) potentials. The dipole Fröhlich term can be included in current first-principles electron-phonon (e-ph) calculations and is present only in polar materials. The quadrupole e-ph interaction is present in both polar and nonpolar materials, but currently it cannot be computed from first principles. Here we show an approach to compute the quadrupole e-ph interaction and include it in ab initio calculations of e-ph matrix elements. The accuracy of the approach is demonstrated by comparing with direct density functional perturbation theory calculations. We apply our method to silicon as a case of a nonpolar semiconductor and tetragonal ${\mathrm{PbTiO}}_3$ as a case of a polar piezoelectric material. In both materials we find that the quadrupole term strongly impacts the e-ph matrix elements. Analysis of e-ph interactions for different phonon modes reveals that the quadrupole term mainly affects optical modes in silicon and acoustic modes in ${\mathrm{PbTiO}}_3$, although the quadrupole term is needed for all modes to achieve quantitative accuracy. The effect of the quadrupole e-ph interaction on electron scattering processes and transport is shown to be important. Our approach enables accurate studies of e-ph interactions in broad classes of nonpolar, polar, and piezoelectric materials.

Intercalation of lithium atoms between layers of two-dimensional (2D) materials can alter their atomic and electronic structure. We investigate effects of Li intercalation in twisted bilayers of the transition metal dichalcogenide ${\mathrm{MoS}}_2$ through first-principles calculations, tight-binding parametrization based on the Wannier transformation, and analysis of moiré band structures through an effective continuum model. The energetic stability of different intercalation sites for Li between layers of ${\mathrm{MoS}}_2$ are classified according to the local coordination type and the number of vertically aligned Mo atoms, suggesting that the Li atoms will cluster in certain regions of the moiré superlattice. The proximity of a Li atom has a dramatic influence on the interlayer interaction between sulfur atoms, deepening the moiré potential well and leading to better isolation of the flat bands in the energy spectrum. These results demonstrate the importance of chemical intercalation as a powerful means for controlling moiré flat-band physics in 2D semiconductors.

Solid-state experimental realizations of Majorana bound states are based on materials with strong intrinsic spin-orbit interactions. In this paper, we explore an alternative approach where spin-orbit coupling is induced artificially through a nonuniform magnetic field that originates from an array of micromagnets. Using a recently developed optimization algorithm, we find suitable magnet geometries for the emergence of topological superconductivity in wires without intrinsic spin-orbit coupling. We confirm the robustness of Majorana bound states against disorder and periodic potentials whose amplitudes do not exceed the Zeeman energy. Furthermore, we identify low $g$-factor materials commonly used in mesoscopic physics experiments as viable candidates for Majorana devices.

We study the band structure and transport property of a zigzag silicene nanoribbon when electric fields are applied to the edges. It is found that band bending could be induced and controlled by the antisymmetric edge fields, which can be understood based on the wave functions of the edge states. The highest valence band and the lowest conduction band coexist in the band-bending region. With the narrowing of edge potentials, the bending increases gradually. When the edge fields become symmetric, an asymmetric band gap at the Dirac points can be obtained due to the intrinsic spin-orbit interaction, suggesting a valley-polarized quantum spin Hall state. The gap could reach a maximum value rapidly and then decrease slowly as the electric fields increase. Due to the combining effect of the band bending, band-selective rule, and resonant states, many zero-conductance resonances and resonance peaks appear in different regions, which could be described by the Fano resonance effect. Furthermore, the band bending and zero-conductance resonances are robust against the Hubbard interaction. The Hubbard interaction could work as a spin-dependent edge field, together with the edge electric fields, leading to a spin-dependent band gap and various quantum phases such as metal and half-metal.

We use polarized light microscopy in situ with an externally applied electric field to induce square-net birefringence patterns in top-seeded single crystals of barium titanate above the Curie temperature ($T_C$). The patterns occur under a wide range of electric field magnitudes larger than $\sim 0.2$ kV/mm and at temperatures up to $6{}^{\circ }\mathrm{C}$ above $T_C$. We mapped this behavior on a pseudophase diagram showing the region in electric field and temperature space where this domain configuration is stable. We observed the electric field induced transformation into the periodically ordered structure from both the cubic structure above $T_C$ and the tetragonal structure below $T_C$. Synchrotron x-ray reciprocal space maps indicate the presence of ferroelastic domains perpendicular to the electric field direction at a range of electric field magnitudes similar to those required to induce the periodic domain ordering we observe using polarized light microscopy. Combined with a simple model of the optical retardation, we show that the periodic domain ordering responsible for the square-net birefringence occurs only at the surfaces of the crystals and that these domain structures are unexpectedly invariant with respect to the electric field that induces them.

Isothermal equations of state were determined for the open-framework silicon allotrope ${\mathrm{Si}}_{24}$ and its sodium-filled precursor $\left({\mathrm{Na}}_4{\mathrm{Si}}_{24}\right)$ using different pressure media including hydrogen and argon, and with no pressure medium. ${\mathrm{Si}}_{24}$ does not transform into diamond-cubic silicon under compression, and the low-density phase possesses a bulk modulus of 91(2) GPa. The sodium-filled precursor exhibits a comparable volumetric compressibility with different axial trends that are explained by the crystallographic structure. Above 11 GPa, ${\mathrm{Si}}_{24}$ transforms to the β-tin structure, followed by other high-pressure silicon allotropes similar to diamond-cubic silicon, driven by a large increase in density. Small molecules such as ${\mathrm{H}}_2$ do not enter the channels of ${\mathrm{Si}}_{24}$ during compression at room temperature, however, hydrostaticity strongly influences the transformation pressure and range of coexistence with other phases including β-Sn, $Imma$, and simple-hexagonal Si.

We present a phenomenological theory for coupled spin-charge dynamics in magnetic van der Waals (vdW) heterostructures. The system studied consists of a layered antiferromagnet inserted into a capacitive vdW heterostructure. It has been recently demonstrated that charge doping in such layered antiferromagnets can modulate the strength, and even the sign, of exchange coupling between the layer magnetizations. This provides a mechanism for electrically generating magnetization dynamics. The central result we predict here is that the magnetization dynamics reciprocally results in inducing charge flows. Such dynamics makes magnetic van der Waals heterostructures interesting candidates for spintronics applications. To this end, we also show that these systems can be used to convert subterahertz-radiation-induced magnetization dynamics into electrical signals.

We report magnetic properties of a $3d^9$ $\left({\mathrm{Cu}}^{2+}\right)$ magnetic insulator ${\mathrm{Cu}}_2{\mathrm{OSO}}_4$ measured on both powder and single crystal. The magnetic atoms of this compound form layers whose geometry can be described either as a system of chains coupled through dimers or as a kagome lattice where every third spin is replaced by a dimer. Specific heat and DC susceptibility show a magnetic transition at 20 K, which is also confirmed by neutron scattering. Magnetic entropy extracted from the specific heat data is consistent with an $S=1/2$ degree of freedom per ${\mathrm{Cu}}^{2+}$, and so is the effective moment extracted from DC susceptibility. The ground state has been identified by means of neutron diffraction on both powder and single crystal and corresponds to an $\sim {120}^{\circ }$ spin structure in which ferromagnetic intradimer alignment results in a net ferrimagnetic moment. No evidence is found for a change in lattice symmetry down to 2 K. Our results suggest that ${\mathrm{Cu}}_2{\mathrm{OSO}}_4$ represents a type of model lattice with frustrated interactions where interplay between magnetic order, thermal and quantum fluctuations can be explored.

Thin films and heterostructures of hexagonal manganites as promising multiferroic materials have attracted a considerable interest. We report structural transformations of high-quality strain-stabilized epitaxial hexagonal ${\mathrm{TbMnO}}_3/\mathrm{yttria}$ stabilized zirconia(111) (h-TMO) films, analyzed by means of various characterization techniques. A reversible structural phase transition from $P{6}_{3}cm$ to $P{6}_3/mmc$ structure at $T_{\mathrm{C}}\sim 800\mathrm{K}$ was observed in stoichiometric h-TMO films by temperature-dependent Raman spectroscopy and optical ellipsometry. The latter, directly probing the electronic system, indicates its modification at the structural phase transition, likely due to charge transfer from oxygen to Mn. A partially reversible phase transformation and stress relaxation was observed in h-TMO films with Tb excess after temperature cycling (300-1000-300 K) during Raman and ellipsometry. An inhomogeneous microstructure, containing ferroelectric and paraelectric nanodomains, was revealed by transmission electron microscopy in the Tb-rich film after annealing. The results obtained indicate a strong influence of stress, induced by temperature and by constrained sample geometry, onto the structure and ferroelectricity of strain-stabilized h-TMO thin films.

A recent experiment [, , , , , , , and , Nat. Phys. 15, 1168 (2019)] has realized a dynamical gauge system with a ${\mathbb{Z}}_2$ gauge symmetry in a double-well potential. In this work we propose a method to generalize this model from a single double well to a one-dimensional chain. We show that although there are no disordered potentials in the original model, the phenomenon of many-body localization can occur. The key ingredient is that different symmetry sectors with different local gauge charges play the role of different disorder configurations, which becomes clear after exactly mapping our model to a transverse Ising model in a random longitudinal field. We show that both the ergodic regime and the many-body localized regime exist in this model from four different metrics, which include level statistics, volume law versus area law of entanglement entropy of eigenstates, quench dynamics of entanglement entropy, and physical observables.

Spin-$1/2$ antiferromagnetic triangular lattice models are paradigms of geometrical frustration, revealing very different ground states and quantum effects depending on the nature of anisotropies in the model. Due to strong spin orbit coupling and crystal field effects, rare-earth ions can form pseudospin-$1/2$ magnetic moments with anisotropic single-ion and exchange properties. Thus, rare-earth-based triangular lattices enable the exploration of this interplay between frustration and anisotropy. Here we study one such case, the rare-earth double vanadate glaserite material ${\mathrm{K}}_3\mathrm{Er}{\left({\mathrm{VO}}_4\right)}_2$, which is a quasi-two-dimensional (2D) isosceles triangular antiferromagnet. Our specific heat and neutron powder diffraction data from ${\mathrm{K}}_3{\mathrm{Er}(\mathrm{VO}}_4{)}_2$ reveal a transition to long range magnetic order at $T_N=155\pm 5$ mK which accounts for all $Rln2$ entropy. We observe what appears to be a coexistence of three-dimensional (3D) and quasi-2D order below $T_N$. The quasi-2D order leads to an anisotropic Warren-like peak profile for $\left(hk0\right)$ reflections, while the 3D order is best-described by layers of antiferromagnetic $b$-aligned moments alternating with layers of zero moment. Our magnetic susceptibility data reveal that ${\mathrm{Er}}^{3+}$ takes on a strong $XY$ single-ion anisotropy in ${\mathrm{K}}_3\mathrm{Er}{\left({\mathrm{VO}}_4\right)}_2$, leading to vanishing moments when pseudospins are oriented along $c$. Thus, the magnetic structure, when considered from the pseudospin point of view could comprise of alternating layers of $b$-axis and $c$-axis aligned antiferromagnetism.

Magnetic skyrmions are nanosized topological spin textures stabilized by a delicate balance of magnetic energy terms. The chemical substitution of the underlying crystal structure of skyrmion-hosting materials offers a route to manipulate these energy contributions but also introduces additional effects such as disorder and pinning. While the effects of doping and disorder have been well studied in B20 metallic materials such as ${\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x\mathrm{Si}$ and ${\mathrm{Mn}}_{1-x}{\mathrm{Fe}}_x\mathrm{Si}$, the consequences of chemical substitution in the magnetoelectric insulator ${\mathrm{Cu}}_2\mathrm{O}\mathrm{Se}{\mathrm{O}}_3$ have not been fully explored. In this work we utilize a combination of AC magnetometry and small-angle neutron scattering to investigate the magnetic phase transition dynamics in pristine and Zn-substituted ${\mathrm{Cu}}_2\mathrm{O}\mathrm{Se}{\mathrm{O}}_3$. The results demonstrate that the first-order helical-conical phase transition exhibits two thermally separated behavioral regimes: at high temperatures, the helical and conical domains transform by large-scale, continuous rotations, while at low temperatures, the two phases coexist. Remarkably, the effects of pinning in the substituted sample are less prevalent at low temperatures compared to high temperatures, despite the reduction of available thermal activation energy. We attribute this behavior to the large, temperature-dependent, cubic anisotropy unique to ${\mathrm{Cu}}_2\mathrm{O}\mathrm{Se}{\mathrm{O}}_3$, which becomes strong enough to overcome the pinning energy at low temperatures. Consideration and further exploration of these effects will be crucial when engineering skyrmion materials towards future applications.

In the presence of mass anisotropy, anisotropic interaction, or in-plane magnetic field, quantum Hall droplets can exhibit shape deformation and an internal geometrical degree of freedom. We characterize the geometry of quantum Hall states by principal component analysis, which is a statistical technique that emphasizes variation in a data set. We first test the method in an integer quantum Hall droplet with dipole-dipole interaction in disk geometry. In the subsequent application to fractional quantum Hall systems with anisotropic Coulomb interaction in torus geometry, we demonstrate that the principal component analysis can quantify the metric degree of freedom and predict the collapse of a $\nu =1/3$ state. We also calculate the metric response to interaction anisotropy at filling fractions $\nu =1/5$ and $2/5$ and show that the response is roughly the same within the same Jain sequence but can differ at large anisotropy for different sequences.

The recent accessibility of high-quality, charge-neutral monolayer transition metal dichalcogenides with narrow exciton linewidths at the homogeneous limit provides an ideal platform to study excitonic many-body interactions. In particular, the possibility to manipulate coherent exciton-exciton interactions, which govern the ultrafast nonlinear optical response, by applying an external magnetic field has not been considered so far. We address this discrepancy by presenting a nonlinear microscopic theory in the coherent limit for optical excitations in the presence of out-of-plane, in-plane, and tilted magnetic fields. Specifically, we explore the magnetic-field-induced exciton and biexciton fine structure and calculate their oscillator strengths based on a Heisenberg equations-of-motion formalism. Our microscopic evaluations of pump-probe spectra allow to interpret and predict coherent signatures in future wave-mixing experiments.

We study the electronic structure and topological properties of monolayer and the ABC-stacked multilayer of graphyne-$N$, which are a family of planar carbon sheets consisting of $sp$ and $s{p}_2$-bonding. By using the density-functional theory and the effective continuum model, we find a striking even-odd effect in the dependence of the band structure on $N$ (the number of carbon-carbon triple bonds between neighboring benzene rings). Specifically, the even-$N$ graphyne monolayer has doubly degenerate conduction and valence bands near the Fermi energy, and in its ABC multilayer, the band inversion of the doubly degenerate bands leads to a nodal-line semimetal phase with nontrivial ${\mathbb{Z}}_2$ monopole charge. In contrast, the odd-$N$ monolayer has singly degenerate bands in separate valleys, and its ABC multilayer can have only ${\mathbb{Z}}_2$-trivial nodal lines. ABC graphynes with larger $N$ tend to be trivial insulators because of smaller interlayer coupling, while the external pressure induces a topological phase transition from the trivial phase to the nodal line semimetal phase.