We generalize the classical one-dimensional Potts model to the case where the symmetry group is a non-Abelian finite group. It turns out that this model has a quantum nature in that its spectrum of energy eigenstates consists of entangled states. We determine the complete energy spectrum, i.e., the ground states and all the excited states with their degeneracy structure. We calculate the partition function by two different algebraic and combinatorial methods. We also determine the entanglement properties of its ground states.

The electronic stopping power is a crucial quantity for ion irradiation: it governs the deposited heat, the damage profile, and the implantation depth. Whereas experimental data are readily available for elemental solids, the data are much more scarce for compounds. Here we develop a fully ab initio computational scheme based on linear response time-dependent density-functional theory to predict the random electronic stopping power (RESP) of materials without any empirical fitting. We show that the calculated RESP compares well with experimental data, when at full convergence, with the inclusion of the core states and of the exchange correlation. We evaluate the unexpectedly limited magnitude of the nonlinear terms in the RESP by comparing with other approaches based on the time propagation of time-dependent density-functional theory. Finally, we check the validity of a few empirical rules of thumbs that are commonly used to estimate the electronic stopping power.

We combine several numerical and semianalytical methods to study the $5d$ double perovskites ${\mathrm{Sr}}_2{\mathrm{YIrO}}_6$ and ${\mathrm{Ba}}_2{\mathrm{YIrO}}_6$, which were recently proposed to exhibit excitonic magnetism. Starting from the density-functional theory and the constrained random-phase approximation, we construct effective multiband Hubbard models. These are analyzed by means of static and dynamical mean-field theories and strong-coupling expansion. We find both materials to be insulators, but, contrary to the experimental claims, with a large spin gap of several hundreds of meV preventing the formation of an ordered state at low temperature.

We present measurements of thermal interface conductance as a function of metal alloy composition. Composition spread alloy films of $\mathrm{A}{\mathrm{u}}_x\mathrm{C}{\mathrm{u}}_{1-x}$ and $\mathrm{A}{\mathrm{u}}_x\mathrm{P}{\mathrm{d}}_{1-x}$ solid solutions were deposited on single crystal sapphire substrates via dual electron-beam evaporation. High throughput measurements of thermal interface conductance across the (metal alloy)-sapphire interfaces were made by positional scanning of frequency domain thermoreflectance measurements to sample a continuum of Au atomic fractions $(x\sim 0\to 1)$. At a temperature of 300 K, the thermal interface conductance at the $\mathrm{A}{\mathrm{u}}_x\mathrm{C}{\mathrm{u}}_{1-x}$-sapphire interfaces monotonically decreased from $197\pm 39\mathrm{MW}{\mathrm{m}}^{-2}{\mathrm{K}}^{-1}$ to $74\pm 11\mathrm{MW}{\mathrm{m}}^{-2}{\mathrm{K}}^{-1}$ for $x=0\to 0.95\pm 0.02$ and at the $\mathrm{A}{\mathrm{u}}_x\mathrm{P}{\mathrm{d}}_{1-x}$-sapphire interfaces from $167\pm 35\mathrm{MW}{\mathrm{m}}^{-2}{\mathrm{K}}^{-1}$ to $60\pm 10\mathrm{MW}{\mathrm{m}}^{-2}{\mathrm{K}}^{-1}$ for $x=0.03\to 0.97\pm 0.02$. To shed light on the phonon physics at the interface, a Diffuse Mismatch Model for thermal interface conductance with alloys is presented and agrees reasonably with the thermal interface conductance data.

Energy-dependent apparent step heights of two-dimensional ultrathin Pb islands grown on the Si(111)$6\times 6\text{−}\mathrm{Au}$ surface have been investigated by a combination of scanning tunneling microscopy, first-principles density-functional theory, and the particle-in-a-box model calculations. The apparent step height shows the thickness- and energy-dependent oscillatory behaviors, which are directly related to the spilling of electron states into the vacuum exhibiting a quantum size effect. This has been unambiguously proven by extensive first-principles scanning tunneling microscopy and spectroscopy simulations. An electronic contribution to the apparent step height is directly determined. At certain energies it reaches values as high as a half of the atomic contribution. The applicability of the particle-in-a-box model to the spilling of electron states is also discussed.

We have performed far-field extinction measurements and near electric field measurements on gold bowtie antennas resonant at THz frequencies. These measurements show a very large shift between the resonant frequencies of the near-field and the far-field spectra. We use the established damped-driven harmonic oscillator model for resonators to model the far-field response of the antennas from the near-field spectrum and show that there is a large discrepancy between the predicted and measured far-field response. We were able to explain this discrepancy by improving the oscillator model with a Fano model. This large shift makes the prediction of the near-field response of resonant structures at THz frequencies very imprecise, provided that only information of the far-field response is available and establishes the necessity of measuring near fields for a correct and accurate characterization of these structures.

The Zak phase labels the topological property of one-dimensional Bloch bands. Here we propose a scheme and experimentally measure the Zak phase in a photonic system. The Zak phase of a bulk band is related to the topological properties of the two band gaps sandwiching this band, which in turn can be inferred from the existence or absence of an interface state. Using a reflection spectrum measurement, we determined the existence of interface states in the gaps and then obtained the Zak phases. The knowledge of Zak phases can also help us predict the existence of interface states between a metasurface and a photonic crystal. By manipulating the property of the metasurface, we can further tune the excitation frequency and the polarization of the interface state.

We study the many-body electronic state created by a time-dependent drive of a mesoscopic contact. The many-body state is expressed manifestly in terms of single-electron and electron-hole quasiparticle excitations with the amplitudes and probabilities of creation which depend on the details of the applied voltage. We experimentally probe the time dependence of the constituent electronic states by using an analog of the optical Hong-Ou-Mandel correlation experiment where electrons emitted from the terminals with a relative time delay collide at the contact. The electron wave packet overlap is directly related to the current noise power in the contact. We have confirmed the time dependence of the electronic states predicted theoretically by measurements of the current noise power in a tunnel junction under harmonic excitation.

We theoretically investigate the dynamical Franz-Keldysh effect in femtosecond time resolution, that is, the time-dependent modulation of a dielectric function at around the band gap under an irradiation of an intense laser field. We develop a pump-probe formalism in two distinct approaches: first-principles simulation based on real-time time-dependent density functional theory and analytic consideration of a simple two-band model. We find that, while time-average modulation can be reasonably described by the static Franz-Keldysh theory, a remarkable phase shift is found to appear between the dielectric response and the applied electric field.

The magnetic properties of FeGe and FeSi are studied in a unified way on the basis of the realistic model derived from the first principle calculations. We can show that, with decreasing the temperature, the transition from the paramagnetic metallic state to the ferromagnetic metallic state takes place for FeGe, while the transition of FeSi from the paramagnetic metal to the paramagnetic insulator is a continuous crossover, consistent with experiments. It is shown that the distinct magnetic behaviors in FeGe and FeSi are attributed to the difference of the strength of the electron correlation effects, controlled by the effective bandwidth.

Using the semiclassical neutral atom theory, we extend to fourth order the modified gradient expansion of the exchange energy of density functional theory. This expansion can be applied both to large atoms and solid-state problems. Moreover, we show that it can be employed to construct a simple and nonempirical generalized gradient approximation (GGA) exchange-correlation functional competitive with state-of-the-art GGAs for solids, but also reasonably accurate for large atoms and ordinary chemistry.

We give a detailed physical argument for the area law for entanglement entropy in gapped phases of matter arising from local Hamiltonians. Our approach is based on renormalization group (RG) ideas and takes a resource oriented perspective. We report four main results. First, we argue for the “weak area law”: any gapped phase with a unique ground state on every closed manifold obeys the area law. Second, we introduce an RG based classification scheme and give a detailed argument that all phases within the classification scheme obey the area law. Third, we define a special subclass of gapped phases, topological quantum liquids, which captures all examples of current physical relevance, and we rigorously show that topological quantum liquids obey an area law. Fourth, we show that all topological quantum liquids have MERA representations which achieve unit overlap with the ground state in the thermodynamic limit and which have a bond dimension scaling with system size $L$ as $e^{c{log}^{d(1+\delta )}\left(L\right)}$ for all $\delta >0$. For example, we show that chiral phases in $d=2$ dimensions have an approximate MERA with bond dimension $e^{c{log}^{2(1+\delta )}\left(L\right)}$. We discuss extensively a number of subsidiary ideas and results necessary to make the main arguments, including field theory constructions. While our argument for the general area law rests on physically motivated assumptions (which we make explicit) and is therefore not rigorous, we may conclude that “conventional” gapped phases obey the area law and that any gapped phase which violates the area law must be a dragon.

We study the temperature-dependent quantum correction to conductivity due to the interplay of spin density fluctuations and weak disorder for a two-dimensional metal near an antiferromagnetic (AFM) quantum critical point. AFM spin density fluctuations carry large momenta around the ordering vector $\mathbf{Q}$ and, at lowest order of the spin-fermion coupling, only scatter electrons between “hot spots” of the Fermi surface which are connected by $\mathbf{Q}$. Earlier, it was seen that the quantum interference between AFM spin density fluctuations and soft diffusive modes of the disordered metal is suppressed, a consequence of the large-momentum scattering. The suppression of this interference results in a nonsingular temperature dependence of the corresponding interaction correction to conductivity. However, at higher order of the spin-fermion coupling, electrons on the entire Fermi surface can be scattered successively by two spin density fluctuations and, in total, suffer a small momentum transfer. This higher-order process can be described by composite modes which carry small momenta. We show that the interference between formally subleading composite modes and diffusive modes generates singular interaction corrections which ultimately dominate over the nonsingular first-order correction at low temperatures. We derive an effective low-energy theory from the spin-fermion model which includes the above-mentioned higher-order process implicitly and show that for weak spin-fermion coupling the small-momentum transfer is mediated by a composite propagator. Employing the conventional diagrammatic approach to impurity scattering, we find the correction $\delta \sigma \propto +{ln}^{2}T$ for temperatures above an exponentially small crossover scale.

We study the spectral properties of a family of quantum antiferromagnets on two-dimensional (2D) lattices. This family of models is obtained by a deformation of the well-studied 2D quantum antiferromagnetic model of Affleck, Kennedy, Lieb, and Tasaki (AKLT); they are described by two-body, frustration-free Hamiltonians on a three-colorable lattice of spins. Although the existence of a spectral gap in the 2D AKLT model remains an open question, we rigorously prove the existence of a gap for a subset of this family of quantum antiferromagnets. Along with providing progress for the gap problem in AKLT-type antiferromagnets in 2D, this result has implications for the theory of quantum computation as it provides a family of two-body Hamiltonians for which the ground state is a resource for universal quantum computation and for which a spectral gap is proven to exist.

The circular photon drag effect is observed in a bulk semiconductor. The photocurrent caused by a transfer of both translational and angular momenta of light to charge carriers is detected in tellurium in the midinfrared frequency range. Dependencies of the photocurrent on the light polarization and on the incidence angle agree with the symmetry analysis of the circular photon drag effect. Microscopic models of the effect are developed for both intra- and intersubband optical absorption in the valence band of tellurium. The shift contribution to the circular photon drag current is calculated. An observed decrease of the circular photon drag current with the increase of the photon energy is explained by the theory for intersubband optical transitions. Theoretical estimates of the circular photon drag current agree with the experimental data.

Reduction of cross-plane thermal conductivity and understanding of the mechanisms of heat transport in nanostructured metal/semiconductor superlattices are crucial for their potential applications in thermoelectric and thermionic energy conversion devices, thermal management systems, and thermal barrier coatings. We have developed epitaxial (Ti,W)N/(Al,Sc)N metal/semiconductor superlattices with periodicity ranging from 1 nm to 240 nm that show significantly lower thermal conductivity compared to the parent TiN/(Al,Sc)N superlattice system. The (Ti,W)N/(Al,Sc)N superlattices grow with [001] orientation on the MgO(001) substrates with well-defined coherent layers and are nominally single crystalline with low densities of extended defects. Cross-plane thermal conductivity (measured by time-domain thermoreflectance) decreases with an increase in the superlattice interface density in a manner that is consistent with incoherent phonon boundary scattering. Thermal conductivity values saturate at $1.7\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ for short superlattice periods possibly due to a delicate balance between long-wavelength coherent phonon modes and incoherent phonon scattering from heavy tungsten atomic sites and superlattice interfaces. First-principles density functional perturbation theory based calculations are performed to model the vibrational spectrum of the individual component materials, and transport models are used to explain the interface thermal conductance across the (Ti,W)N/(Al,Sc)N interfaces as a function of periodicity. The long-wavelength coherent phonon modes are expected to play a dominant role in the thermal transport properties of the short-period superlattices. Our analysis of the thermal transport properties of (Ti,W)N/(Al,Sc)N metal/semiconductor superlattices addresses fundamental questions about heat transport in multilayer materials.

Using first-principles calculations, we investigate the electronic and vibrational properties of monolayer As and AsSb. While the pristine monolayers are semiconductors (direct band gap at the $\mathrm{\Gamma }$ point), fluorination results in Dirac cones at the K points. Fluorinated monolayer As shows a band gap of 0.16 eV due to spin-orbit coupling, and fluorinated monolayer AsSb a larger band gap of 0.37 eV due to inversion symmetry breaking. Spin-orbit coupling induces spin splitting similar to monolayer ${\mathrm{MoS}}_2$. Phonon calculations confirm that both materials are dynamically stable. Calculations of the edge states of nanoribbons by the tight-binding method demonstrate that fluorinated monolayer As is topologically nontrivial in contrast to fluorinated monolayer AsSb.

We propose a theoretical model of magnetization switching in a ferromagnetic multilayer by both electric current and microwaves. The electric current gives a spin transfer torque on the magnetization, while the microwaves induce a precession of the magnetization around the initial state. Based on numerical simulation of the Landau-Lifshitz-Gilbert (LLG) equation, it is found that the switching current is significantly reduced compared with the switching caused solely by the spin transfer torque when the microwave frequency is in a certain range. We develop a theory of switching from the LLG equation averaged over a constant energy curve. It was found that the switching current should be classified into four regions, depending on the values of the microwave frequency. Based on the analysis, we derive an analytical formula of the optimized frequency minimizing the switching current, which is smaller than the ferromagnetic resonance frequency. We also derive an analytical formula of the minimized switching current. Both the optimized frequency and the minimized switching current decrease with increasing the amplitude of the microwave field. The results will be useful to achieve high thermal stability and low switching current in spin torque systems simultaneously.

The frustrated double perovskite $\mathrm{L}{\mathrm{a}}_2\mathrm{LiOs}{\mathrm{O}}_6$, based on $\mathrm{O}{\mathrm{s}}^{5+}\left(5d^3,{\mathrm{t}}_2^3\right)$ is studied using magnetization, elastic neutron scattering, heat capacity, and muon spin relaxation (μSR) techniques and compared with isostructural $\left(P{2}_1/n\right)\mathrm{L}{\mathrm{a}}_2\mathrm{LiRu}{\mathrm{O}}_6,\mathrm{R}{\mathrm{u}}^{5+}\left(4d^3,{\mathrm{t}}_2^3\right)$. While previous studies of $\mathrm{L}{\mathrm{a}}_2\mathrm{LiOs}{\mathrm{O}}_6$ showed a broad susceptibility maximum $\left({\chi }_{\max }\right)$ near 40 K, heat capacity data indicate a sharp peak at 30 K, similar to $\mathrm{L}{\mathrm{a}}_2\mathrm{LiRu}{\mathrm{O}}_6$ with ${\chi }_{\max }\sim 30\mathrm{K}$ and a heat capacity peak at 24 K. Significant differences between the two materials are seen in powder neutron diffraction where the magnetic structure is described by $\mathit{k}=\left(1/21/20\right)$ for $\mathrm{L}{\mathrm{a}}_2\mathrm{LiOs}{\mathrm{O}}_6$, while $\mathrm{L}{\mathrm{a}}_2\mathrm{LiRu}{\mathrm{O}}_6$ has been reported with $\mathit{k}=\left(000\right)$, structure for face centered lattices. For the $\mathit{k}=\left(1/21/20\right)$ structure, one has antiferromagnetic layers stacked antiferromagnetically, while for $\mathit{k}=\left(000\right)$ structure, ferromagnetic layers are stacked antiferromagnetically. In spite of these differences, both can be considered as type I fcc antiferromagnetic structures. For $\mathrm{L}{\mathrm{a}}_2\mathrm{LiOs}{\mathrm{O}}_6$, the magnetic structure is best described in terms of linear combinations of basis vectors belonging to irreducible representations ${\mathrm{\Gamma }}_2$ and ${\mathrm{\Gamma }}_4$. The combinations ${\mathrm{\Gamma }}_2–{\mathrm{\Gamma }}_4$ and ${\mathrm{\Gamma }}_2+{\mathrm{\Gamma }}_4$ could not be distinguished from refinement of the data. In all cases, the $\mathrm{O}{\mathrm{s}}^{5+}$ moments lie in the $yz$ plane with the largest component along $y$. The total moment is 1.81(4) ${\mu }_{\mathrm{B}}$. For $\mathrm{L}{\mathrm{a}}_2\mathrm{LiRu}{\mathrm{O}}_6$, the $\mathrm{R}{\mathrm{u}}^{5+}$ moments are reported to lie in the $xz$ plane. In addition, while neutron diffraction, μSR and NMR data indicate a unique $T_{\mathrm{N}}=24\mathrm{K}$ for $\mathrm{L}{\mathrm{a}}_2\mathrm{LiRu}{\mathrm{O}}_6$, the situation for $\mathrm{L}{\mathrm{a}}_2\mathrm{LiOs}{\mathrm{O}}_6$ is more complex, with heat capacity, neutron diffraction, and μSR indicating two ordering events at 30 and 37 K, similar to the cases of cubic $\mathrm{B}{\mathrm{a}}_2\mathrm{YRu}{\mathrm{O}}_6$ and monoclinic $\mathrm{S}{\mathrm{r}}_2\mathrm{YRu}{\mathrm{O}}_6$.

We examine theoretically the dynamics of two vortex shells in pinning-free superconducting thin disks in the Corbino geometry. In the first considered case, the inner shell is composed of vortices and the outer one of antivortices, corresponding to a state induced by the stray field of an off-plane magnetic dipole placed on top of the superconductor. In the second considered case, both shells comprise vortices induced by a homogeneous external field. We derive the equation of motion for each shell within the Bardeen-Stephen model and study the dynamics analytically by assuming both shells are rigid and commensurate. In both cases, two distinct regimes for vortex shell motion are identified: For low applied currents the entire configuration rotates rigidly, while above a threshold current the shells decouple from each other and rotate at different angular velocities. Analytical expressions for the decoupling current, the recombination time in the decoupled phases, as well as the voltage-current characteristics are presented. Our analytical results are in excellent agreement with numerical molecular dynamics simulations of the full many-vortex problem.