The mutual interplay between superlattice structures, band filling factors, and spin-orbit coupling results in a highly correlated electronic spin and charge state found for an array of atomic Pb wires grown on Si(557). By means of spin- and angle-resolved photoemission spectroscopy, the spin texture close to the Fermi surface was found to be alternating and equidistant; thus, Fermi nesting occurs in between bands with the same spin helicity, giving rise to spin-polarized charge-density waves in the direction across the wires. An out-of-phase superposition of both Rashba channels is manifested by an extraordinary large Rashba splitting of $\Delta k_0=0.2{\AA }^{-1}=g/2$, where $g$ is a reciprocal lattice vector defined by the interwire distance and fits into the model of spin-density waves in antiferromagnetically ordered chain structures. The implications towards spin-polarized transport along the wires will be discussed.

We investigate theoretically the low-energy physics of semiconductor Majorana wires in the vicinity of a magnetic field-driven topological quantum phase transition (TQPT). The local density of states at the end of the wire, which is directly related to the differential conductance in the limit of point-contact tunneling, is calculated numerically. We find that the dependence of the end-of-wire local density of states on the magnetic field is nonuniversal and that the signatures associated with the closing of the superconducting gap at the Majorana TQPT are essentially invisible within a significant range of experimentally relevant parameters. Our results provide a possible explanation for the recent observation of the apparent nonclosure of the gap at the Majorana TQPT in semiconductor nanowires.

A hierarchical equations of motion based numerical approach is developed for accurate and efficient evaluation of dynamical observables of strongly correlated quantum impurity systems. This approach is capable of describing quantitatively Kondo resonance and Fermi-liquid characteristics, achieving the accuracy of the latest high-level numerical renormalization group approach, as demonstrated on single-impurity Anderson model systems. Its application to a two-impurity Anderson model results in differential conductance versus external bias, which correctly reproduces the continuous transition from Kondo states of individual impurity to singlet spin states formed between two impurities. The outstanding performance on characterizing both equilibrium and nonequilibrium properties of quantum impurity systems makes the hierarchical equations of motion approach potentially useful for addressing strongly correlated lattice systems in the framework of dynamical mean-field theory.

We show that the exact exchange-correlation potential of time-dependent density-functional theory displays dynamical step structures that have a spatially nonlocal and time nonlocal dependence on the density. Using one-dimensional two-electron model systems, we illustrate these steps for a range of nonequilibrium dynamical situations relevant for modeling of photochemical or physical processes: field-free evolution of a nonstationary state, resonant local excitation, resonant complete charge transfer, and evolution under an arbitrary field. A lack of these steps in the usual approximations yields inaccurate dynamics, for example, predicting faster dynamics and incomplete charge transfer.

We theoretically investigate the possibility of establishing ferromagnetism in the topological insulator ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ via magnetic doping of $3d$ transition metal elements. The formation energies, charge states, band structures, and magnetic properties of doped ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ are studied using first-principles calculations within density functional theory. Our results show that Bi substitutional sites are energetically more favorable than interstitial sites for single impurities. Detailed electronic structure analysis reveals that Cr and Fe doped materials are still insulating in the bulk but the intrinsic band gap of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ is substantially reduced due to the strong hybridization between the $d$ states of the dopants and the $p$ states of the neighboring Se atoms. The calculated magnetic coupling suggests that Cr doped ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ is possible to be both ferromagnetic and insulating, while Fe doped ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ tends to be weakly antiferromagnetic.

By scanning tunneling microscopy and spectroscopy, we study nearly free electron band formation of the ${\sigma }^{*}$ lowest unoccupied molecular orbital of ${\mathrm{C}}_6{\mathrm{F}}_6$ on a Cu(111) surface. In fractal islands, the lowest unoccupied molecular orbital energy systematically stabilizes with the number of interacting near-neighbor ${\mathrm{C}}_6{\mathrm{F}}_6$ molecules. Density functional theory calculations reveal the origin of effective intermolecular orbital overlap in the previously unrecognized superatom character of the ${\sigma }^{*}$ orbital of ${\mathrm{C}}_6{\mathrm{F}}_6$ molecules. The discovery of superatom orbitals in planar molecules offers a new universal principle for effective band formation, which can be exploited in designing organic semiconductors with nearly free electron properties.

By first principles atomistic analysis we demonstrate how controlled localized doping distributions in nanoscale Si transistors can suppress leakage currents. We consider dopants (B and P atoms) to be randomly confined to a $\approx 1\mathrm{nm}$ width doping region in the channel. If this region is located away from the electrodes, roughly 20% of the channel length $L$, the tunneling leakage is reduced $2\times$ compared to the case of uniform doping and shows little variation. Oppositely, we find the leakage current increases by orders of magnitude and may result in large device variability. We calculate the maximum and minimum conductance ratio that characterizes the tunnel leakage for various values of $L$. We conclude that doping engineering provides a possible approach to resolve the critical issue of leakage current in nanotransistors.

We propose and analyze a physical system that naturally admits two-dimensional topological nearly flat bands. Our approach utilizes an array of three-level dipoles (effective $S=1$ spins) driven by inhomogeneous electromagnetic fields. The dipolar interactions produce arbitrary uniform background gauge fields for an effective collection of conserved hard-core bosons, namely, the dressed spin flips. These gauge fields result in topological band structures, whose band gap can be larger than the corresponding bandwidth. Exact diagonalization of the full interacting Hamiltonian at half-filling reveals the existence of superfluid, crystalline, and supersolid phases. An experimental realization using either ultracold polar molecules or spins in the solid state is considered.

We design three-dimensional models of topological insulator thin films, showing a tunability of the odd number of Dirac cones driven by the atomic-scale geometry at the boundaries. A single Dirac cone at the $\Gamma$-point can be obtained as well as full suppression of quantum tunneling between Dirac states at geometrically differentiated surfaces. The spin texture of surface states changes from a spin-momentum-locking symmetry to a surface spin randomization upon the introduction of bulk disorder. These findings illustrate the richness of the Dirac physics emerging in thin films of topological insulators and may prove utile for engineering Dirac cones and for quantifying bulk disorder in materials with ultraclean surfaces.

We investigate diffusive transport through a number of domain wall (DW) profiles of the important magnetic alloy Permalloy taking into account simultaneously noncollinearity, alloy disorder, and spin-orbit-coupling fully quantum mechanically, from first principles. In addition to observing the known effects of magnetization mistracking and anisotropic magnetoresistance, we discover a not-previously identified contribution to the resistance of a DW that comes from spin-orbit-coupling-mediated spin-flip scattering in a textured diffusive ferromagnet. This adiabatic DW resistance, which should exist in all diffusive DWs, can be observed by varying the DW width in a systematic fashion in suitably designed nanowires.

We present an element selective resonant magnetic x-ray scattering study of ${\mathrm{NdFe}}_3({\mathrm{BO}}_3{)}_4$ as a function of temperature and applied magnetic field. Our measurements show that the magnetic order of the Nd sublattice is induced by the Fe spin order. When a magnetic field is applied parallel to the hexagonal basal plane, the helicoidal spin order is suppressed and a collinear ordering, where the moments are forced to align in a direction perpendicular to the applied magnetic field, is stabilized. This result excludes a noncollinear spin order as the origin of the magnetically induced electric polarization in this compound. Instead our data imply that magnetic frustration results in a phase competition, which is the origin of the magnetoelectric response.

We consider the Ising model in a transverse field with long-range antiferromagnetic interactions that decay as a power law with their distance. We study both the phase diagram and the entanglement properties as a function of the exponent of the interaction. The phase diagram can be used as a guide for future experiments with trapped ions. We find two gapped phases, one dominated by the transverse field, exhibiting quasi-long-range order, and one dominated by the long-range interaction, with long-range Néel ordered ground states. We determine the location of the quantum critical points separating those two phases. We determine their critical exponents and central charges. In the phase with quasi-long-range order the ground states exhibit exotic corrections to the area law for the entanglement entropy coexisting with gapped entanglement spectra.

Neutron diffraction has been used to investigate antiferromagnetism since 1949. Here, we show that antiferromagnetic reflections can also be seen in transmission electron diffraction patterns from NiO. The diffraction patterns taken here came from regions as small as 10.5 nm, and such patterns could be used to form an image of the antiferromagnetic structure with a nanometer resolution.

We have determined the temperature profile in magnetic nanocontacts under applied current densities typical of spin-torque oscillators ($\sim {10}^8\mathrm{A}/{\mathrm{cm}}^2$). The study combines experimental measurements of the electrical and magnetic properties of the nanocontacts and full three-dimensional simulations of the heat and current flow in these systems. It is found that the quadratic current-induced increase of the resistance due to Joule heating is independent of the applied temperature from 6 to 300 K. In terms of magnetization dynamics, the measured current-induced vortex nucleation, a thermally activated process, is found to be consistent with local temperatures increases of between 147 and 225 K. Simulations reproduce the experimental findings and show that significant thermal gradients exist out to 450 nm from the nanocontact.

Using magnetic, thermal, and neutron measurements on single-crystal samples, we show that ${\mathrm{Ba}}_3{\mathrm{CoSb}}_2{\mathrm{O}}_9$ is a spin-$1/2$ triangular-lattice antiferromagnet with the $c$ axis as the magnetic easy axis and two magnetic phase transitions bracketing an intermediate up-up-down phase in magnetic field applied along the $c$ axis. A pronounced extensive neutron-scattering continuum above spin-wave excitations, observed below $T_{\mathrm{N}}$, implies that the system is in close proximity to one of two spin-liquid states that have been predicted for a 2D triangular lattice.

The magnetic state and magnetic coupling of individual atoms in nanoscale structures relies on a delicate balance between different interactions with the atomic-scale surroundings. Using scanning tunneling microscopy, we resolve the self-assembled formation of highly ordered bilayer structures of Fe atoms and organic linker molecules (T4PT) when deposited on a Au(111) surface. The Fe atoms are encaged in a three-dimensional coordination motif by three T4PT molecules in the surface plane and an additional T4PT unit on top. Within this crystal field, the Fe atoms retain a magnetic ground state with easy-axis anisotropy, as evidenced by x-ray absorption spectroscopy and x-ray magnetic circular dichroism. The magnetization curves reveal the existence of ferromagnetic coupling between the Fe centers.

We measure the ferroelectric polarization of ${\mathrm{BiFeO}}_3$ films down to 3.6 nm using low energy electron and photoelectron emission microscopy. The measured polarization decays strongly below a critical thickness of 5–7 nm predicted by continuous medium theory whereas the tetragonal distortion does not change. We resolve this apparent contradiction using first-principles-based effective Hamiltonian calculations. In ultrathin films, the energetics of near open circuit electrical boundary conditions, i.e., an unscreened depolarizing field, drive the system through a phase transition from single out-of-plane polarization to nanoscale stripe domains. It gives rise to an average polarization close to zero as measured by the electron microscopy while maintaining the relatively large tetragonal distortion imposed by the nonzero polarization state of each individual domain.

Ab initio computations are performed to investigate properties of bulk material and epitaxial films made of ${\mathrm{EuTiO}}_3$ (ETO). A whole family of nanoscale twinned phases, that present complex oxygen octahedra tilting (OOT) and unusual antiferroelectricity, is found to be degenerate in energy with simpler phases (all possessing typical OOT) in bulk ETO. Such degeneracy provides a successful explanation of recently observed anomalous phenomena. The calculations also lead to revisiting the (rich) phase diagram of ETO films.

We introduce a bipartite, diluted and frustrated, network as a sparse restricted Boltzmann machine and we show its thermodynamical equivalence to an associative working memory able to retrieve several patterns in parallel without falling into spurious states typical of classical neural networks. We focus on systems processing in parallel a finite (up to logarithmic growth in the volume) amount of patterns, mirroring the low-level storage of standard Amit-Gutfreund-Sompolinsky theory. Results obtained through statistical mechanics, the signal-to-noise technique, and Monte Carlo simulations are overall in perfect agreement and carry interesting biological insights. Indeed, these associative networks pave new perspectives in the understanding of multitasking features expressed by complex systems, e.g., neural and immune networks.

Different formulations of modified Newtonian dynamics predict somewhat different rotation curves for the same mass distribution. Here I consider a global attribute of the rotation curve that might provide a convenient discriminant between theories when applied to isolated, pure-disk galaxies that are everywhere deep in the modified Newtonian dynamics regime. This parameter is $\mathcal{Q}\equiv ⟨V^2⟩/V_{\infty }^2$, where $⟨V^2⟩\equiv M^{-1}\int 2\pi r\Sigma (r)V^2(r)dr$, with $\Sigma (r)$ the disk’s surface density, $M$ its total mass, and $V_{\infty }$ the asymptotic (constant) rotational speed. The comparison between the observed and predicted values of $\mathcal{Q}$ is oblivious to the distance, the inclination, the mass, and the size of the disk, and to the form of the interpolating function. For the known modified-gravity theories $\mathcal{Q}$ is predicted to be a universal constant [independent of $\Sigma (r)$]: $\mathcal{Q}=2/3$. The predicted $\mathcal{Q}$ value for modified-inertia theories does depend on the form of $\Sigma$. However, surprisingly, I find here that it varies only little among a very wide range of mass distributions, $\mathcal{Q}\approx 0.73\pm 0.01$. While the difference between the theories amounts to only about 5% in the predicted rms velocity, a good enough sample of galaxies may provide the first discerning test between the two classes of theories.