We analyze possible nonlinear exciton-exciton correlation effects in the optical response of semiconductors by using a time-dependent density-functional theory (TDDFT) approach. For this purpose we derive the nonlinear (third-order) TDDFT equation for the excitonic polarization. In this equation the nonlinear time-dependent effects are described by the time-dependent (nonadiabatic) part of the effective exciton-exciton interaction, which depends on the exchange-correlation (XC) kernel. We apply the approach to study the nonlinear optical response of a GaAs quantum well. In particular, we calculate the two-dimensional Fourier spectrum (2DFS) of the system and compare it with experimental data. We find that the memory effects play a crucial role in this response, and in particular that it is necessary to use a nonadiabatic XC kernel to describe excitonic bound states, biexcitons, which are formed due to the retarded TDDFT exciton-exciton interaction.

We establish, through numerical calculations and comparisons with a recursive Green's-function based implementation of the Landauer-Büttiker formalism, an efficient method for studying Anderson localization in quasi-one-dimensional and two-dimensional systems using the Kubo-Greenwood formalism. Although the recursive Green's-function method can be used to obtain the localization length of a mesoscopic conductor, it is numerically very expensive for systems that contain a large number of atoms transverse to the transport direction. On the other hand, linear scaling has been achieved with the Kubo-Greenwood method, enabling the study of effectively two-dimensional systems. While the propagating length of the charge carriers will eventually saturate to a finite value in the localized regime, the conductances given by the Kubo-Greenwood method and the recursive Green's-function method agree before the saturation. The converged value of the propagating length is found to be directly proportional to the localization length obtained from the exponential decay of the conductance.

We theoretically investigate the magnetically controllable Casimir force between a parallel metal plate and a superparamagnetic metametamaterial (MMM) plate based on Mie scattering and effective medium theory. A type of MMM composed of superparamagnetic nanoparticles is proposed to fulfill the high frequency magnetic effect to gain Casimir repulsion when interacting with the metal plate. The permeability of such MMM depends on an external magnetic field, which makes it possible to adjust the magnitude of Casimir force. The effects of size, filling ratio, and magnetic property of the superparamagnetic particles on the tuning range are also investigated. Construction of such MMM using the micro/nanofabrication technology is promising to achieve magnetically controllable repulsive Casimir force.

We study the properties of the two-dimensional Fermi polaron model in which an impurity attractively interacts with a Fermi sea of particles in the zero-range limit. We use a diagrammatic Monte Carlo (DiagMC) method which allows us to sample a Feynman diagrammatic series to very high order. The convergence properties of the series and the role of multiple particle-hole excitations are discussed. We study the polaron and molecule energy as a function of the coupling strength, revealing a transition from a polaron to a molecule in the ground state. We find a value for the critical interaction strength which complies with the experimentally measured one and predictions from variational methods. For all considered interaction strengths, the polaron $Z$ factor from the full diagrammatic series almost coincides with the one-particle-hole result. We also formally link the DiagMC and the variational approaches for the polaron problem at hand.

We propose that the contrasting low-temperature behaviors observed experimentally among isostructural and isoelectronic materials, like nonsuperconducting and nonmagnetic MgFeGe, magnetically ordered NaFeAs, and superconducting LiFeAs, can be well understood from itinerant weak-coupling limit. We find that stronger $(\pi ,\pi )$ instability appearing in the $d_{x^2-y^2}$ orbital of NaFeAs is responsible for the occurrence of weak magnetism, while weaker but still prominent $(\pi ,\pi )$ instability in LiFeAs leads to a superconducting state. In contrast, multiple competing instabilities coexisting in orbital-resolved momentum-dependent susceptibilities, serving as magnetic frustrations from itinerant electrons, may account for the nonmagnetic state in MgFeGe, while poorer Fermi surface nesting leads to a nonsuperconducting state. Based on above findings, we predict a possible way to make MgFeGe a new Fe-based superconductor.

We study the stability of nucleated topological phases that can emerge when interacting non-Abelian anyons form a regular array. The studies are carried out in the context of Kitaev's honeycomb model, where we consider three distinct types of perturbations in the presence of a lattice of Majorana mode binding vortices—spatial anisotropy of the vortices, dimerization of the vortex lattice, and local random disorder. While all the nucleated phases are stable with respect to weak perturbations of each kind, strong perturbations are found to result in very different behavior. Anisotropy of the vortices stabilizes the strong-pairing-like phases, while dimerization can recover the underlying non-Abelian phase. Local random disorder, on the other hand, can drive all the nucleated phases into a gapless thermal metal state. We show that all these distinct behaviors can be captured by an effective staggered tight-binding model for the Majorana modes. By studying the pairwise interactions between the vortices, i.e., the amplitudes for the Majorana modes to tunnel between vortex cores, the locations of phase transitions and the nature of the resulting states can be predicted. We also find that, due to oscillations in the Majorana tunneling amplitude, lattices of Majorana modes may exhibit a Peierls-like instability, where a dimerized configuration is favored over a uniform lattice. As the nature of the nucleated phases depends only on the Majorana tunneling, our results are expected to apply also to other system supporting localized Majorana mode arrays, such as Abrikosov lattices in $p$-wave superconductors, Wigner crystals in Moore-Read fractional quantum Hall states, or arrays of topological nanowires.

We present a new method to formulate equations of motion for open quantum many-particle systems. Our approach allows for a numerically exact treatment as well as for approximations necessary in large systems and can be applied to systems involving both bosonic and fermionic particles. The method generalizes the cluster expansion technique by using expectation values instead of correlation functions. The use of expectation values not only makes the equations more transparent but also considerably reduces the amount of algebraic effort to derive the equations. The proposed formulation offers a unified view on various approximation techniques presented recently in the literature. The microscopic semiconductor model for quantum-dot-based microcavity lasers is extended to higher-order photon-autocorrelation functions and the validity of the cluster expansion is shown for this system. We study photon-autocorrelation functions up to fifth order and monitor the onset of lasing in quantum-dot-based microcavity lasers. We observe a successive vanishing of photon bunching in the higher-order photon-autocorrelation functions with increasing pump rates. Our results reveal that the laser threshold is not only softened in microcavity laser systems but is centered around different pump rates with respect to the photon-autocorrelation functions.

We study nonlocal resistance in an H-shaped two-dimensional HgTe/CdTe quantum well consisting of an injector and a detector, both of which can be tuned in the quantum spin Hall or metallic spin Hall regime. Because of strong spin-orbit interaction, there always exists the spin Hall effect and nonlocal resistance in the HgTe/CdTe quantum well. We find that when both the detector and the injector are in the quantum spin Hall regime, the nonlocal resistance is quantized at $0.25\frac{h}{e^2}$, which is robust against weak disorder scattering and small magnetic field. When the detector or injector is beyond this regime, the nonlocal resistance decreases rapidly and will be strongly suppressed by disorder and magnetic field. In the presence of a strong magnetic field, the quantum spin Hall regime will be switched into the quantum Hall regime, and the nonlocal resistance will disappear. The nonlocal signal and its various manifestations in different hybrid regimes originate from the special band structure of the HgTe/CdTe quantum well, and they can be considered as the fingerprint of the helical quantum spin Hall edge states in a two-dimensional topological insulator.

We report preparation of large area quasi-one-dimensional (1D) monolayer graphene superlattices on a prototypical high-index surface Cu(410)-O and characterization by Raman spectroscopy, Auger electron spectroscopy, low-energy electron diffraction, scanning tunneling microscopy, and scanning tunneling spectroscopy. The periodically stepped substrate gives a 1D modulation to graphene, forming a superlattice of the same superperiodicity. Consequently, the moiré pattern is also quasi-1D, with a different periodicity. Scanning tunneling spectroscopy measurements revealed new Dirac points formed at the superlattice Brillouin zone boundary as predicted by theories.

A combination of systematic density-functional theory (DFT) calculations and machine learning techniques has a wide range of potential applications. This study presents an application of the combination of systematic DFT calculations and regression techniques to the prediction of the melting temperature for single and binary compounds. Here we adopt the ordinary least-squares regression, partial least-squares regression, support vector regression, and Gaussian process regression. Among the four kinds of regression techniques, SVR provides the best prediction. The inclusion of physical properties computed by the DFT calculation to a set of predictor variables makes the prediction better. In addition, limitation of the predictive power is shown when extrapolation from the training dataset is required. Finally, a simulation to find the highest melting temperature toward the efficient materials design using kriging is demonstrated. The kriging design finds the compound with the highest melting temperature much faster than random designs. This result may stimulate the application of kriging to efficient materials design for a broad range of applications.

The standard model of enhanced ionic conductivities in solid electrolyte heterostructures follows from a continuum mean-field description of defect distributions that makes no reference to crystalline structure. To examine ionic transport and defect distributions while explicitly accounting for ion-ion correlations and lattice effects, we have performed molecular dynamics simulations of a model coherent fluorite heterostructure without any extrinsic defects, with a difference in standard chemical potentials of mobile fluoride ions between phases induced by an external potential. Increasing the offset in fluoride ion standard chemical potentials across the internal interfaces decreases the activation energies for ionic conductivity and diffusion and strongly enhances fluoride ion mobilities and defect concentrations near the heterostructure interfaces. Non-charge-neutral “space-charge” regions, however, extend only a few atomic spacings from the interface, suggesting a continuum model may be inappropriate. Defect distributions are qualitatively inconsistent with the predictions of the continuum mean-field model, and indicate strong lattice-mediated defect-defect interactions. We identify an atomic-scale “Frenkel polarization” mechanism for the interfacial enhancement in ionic mobility, where preferentially oriented associated Frenkel pairs form at the interface and promote local ion mobility via concerted diffusion processes.

The magnetic and ferroelectric properties of the multiferroic system ${\text{Mn}}_{1-x}$${\text{Co}}_x$${\text{WO}}_4$ ($x=0.135$, 0.15, and 0.17) are studied in magnetic fields $H_c$ oriented along the monoclinic $c$ axis. ${\text{Mn}}_{0.85}$${\text{Co}}_{0.15}$${\text{WO}}_4$, which is right at the phase boundary between two helical spin structures, exhibits a spontaneous sign change of the ferroelectric polarization when cooled in fields $H_c>$ 25 kOe. The origin of the ferroelectric polarization is studied and two magnetic exchange interactions contributing to the polarization are identified. In ${\text{Mn}}_{0.85}$${\text{Co}}_{0.15}$${\text{WO}}_4$, domains of the characteristic helical spin structures, known for $x<0.15$ and $x>0.15$, coexist and form domain boundaries. The contributions of the different domains to the global polarization are determined. The polarization reversal in ${\text{Mn}}_{0.85}$${\text{Co}}_{0.15}$${\text{WO}}_4$ can be explained by a combination of various contributions to the polarization and a strong correlation between magnetic domains of different helical spin orders resulting in a smooth transition across the domain walls, which preserves the chirality of the spin spiral.

We propose a method to measure the nonadiabatic spin-transfer torque parameter $\beta$ and the spin-polarization rate $P$ independently. These quantities are crucial for current-driven magnetization processes, but their value could so far hardly be measured. It is shown that the motion of transverse domain walls in cylindrical nanowires, driven by a magnetic field and by an electric current, can be used to extract those values. This domain wall type propagates with a precessional motion around the wire, where the domain wall acts as a magnetic dipole rotating at well-defined frequency. The spin-polarization rate $P$ can be deduced from the current-induced axial motion of the domain wall, while the rotational frequency of the domain wall and its variation with an external field allows one to determine the nonadiabatic spin-transfer torque. This proposal for an experiment to directly measure these quantities is based on analytical calculations and micromagnetic simulations.

In the antiferromagnetic (AF) heavy-fermion system CePdAl the magnetic Ce ions form a network of equilateral triangles in the $\left(001\right)$ plane, similar to the kagomé lattice, with one third of the Ce moments not participating in the long-range order. The Néel temperature $T_{\mathrm{N}}=2.7\mathrm{K}$ is reduced upon replacing Pd by Ni in ${\text{CePd}}_{1-x}{\text{Ni}}_x\text{Al}$, with $T_{\mathrm{N}}\to 0$ for $x=0.144$, where the specific heat $C$ exhibits a $C/T\propto -logT$ dependence. Within the Hertz-Millis-Moriya model of quantum criticality, this behavior might indicate 2D critical antiferromagnetic fluctuations arising from the decoupling of 3D magnetic order by frustration. On the other hand, the simultaneous presence of Kondo effect and geometric frustration might entail a different route to quantum criticality.

We use cluster mean-field theory, multiple block-product state, and nested cluster methods to study the ground state of a frustrated spin-½ Heisenberg antiferromagnetically stacked square lattice at zero temperature. By analyzing the magnetic order parameter and the geometric measure of entanglement, we find that the stacked model produces a new ordered magnetic phase because of the competition between the interlayer coupling, $J_c$, and the frustrated interaction, $J_2$. The interlayer coupling, $J_c$, strengthens the long-range Néel phase, the new phase, and the collinear phase and destroys the disordered quantum paramagnetic (QP) phase. Increasing $J_c$ results in the new phase gradually replacing the QP phase. The QP phase disappears at the critical point $J_2^{*}$ = 0.5 and $J_c^{*}$ = 0.12.

Thermally induced spin-dependent transport across magnetic tunnel junctions (MTJs) is theoretically investigated. We analyze the thermal analog of Slonczewski's model (as well as its limiting case—Julliere's model) of tunneling magnetoresistance and obtain analytical expressions for the junction thermopower and the tunneling magnetothermopower (TMT). The analytical model is tested numerically for the special case of an ${\text{Al}}_2$${\text{O}}_3$-based MTJ, for which we analyze the dependence of the thermopower and TMT on the relative magnetization orientations, as well as on the barrier height and thickness. We show that at a certain barrier height TMT vanishes, separating the region of positive and negative TMT. As its electrical prototype, this thermal spin transport model should serve as a phenomenological benchmark for analyzing experimental and first-principles calculations of thermopower in magnetic tunnel junctions. The analytical expressions can be used as a first estimate of the magnetothermopower of the junctions using ab initio band structure data of the junction ferromagnets.

Thermal Hall conductivity of magnons described by a noninteracting boson Hamiltonian is derived by the linear response theory. The thermal Hall conductivity is expressed by the Berry curvature in momentum space, which also has the prevailing form for bosonic systems. This theory covers various spin waves, such as spin waves in antiferromagnets and magnetostatic spin waves. As an example, we calculate the thermal Hall conductivity by the magnetostatic spin wave in yttrium iron garnet and reveal its dependence on a magnetic field and temperature.

We report a theoretical study of coherent collective quantum dynamic effects in an array of $N$ qubits (two-level systems) incorporated into a low-dissipation resonant cavity. Individual qubits are characterized by energy level differences ${\Delta }_i$ and a spread of ${\Delta }_i$ is taken into account. Noninteracting qubits display coherent quantum beatings with $N$ different frequencies, i.e., ${\omega }_i={\Delta }_i/\hslash$. Virtual emission and absorption of cavity photons provides a long-range interaction between qubits. In the presence of such interaction we analyze quantum correlation functions of individual qubits $C_i\left(t\right)$ to obtain two collective quantum-mechanical coherent oscillations, characterized by frequencies ${\omega }_1=\overline{\Delta }/\hslash$ and ${\omega }_2={\tilde{\omega }}_R$, where ${\tilde{\omega }}_R$ is the resonant frequency of the cavity renormalized by interaction. The amplitude of these oscillations can be strongly enhanced in the resonant case when ${\omega }_1\simeq {\omega }_2$. These collective quantum oscillations can be directly observed, e.g., by measurements of frequency dependent transmission coefficient $D\left(\omega \right)$ of electromagnetic field propagating in a transmission line coupled to the system.

Superconducting correlations which are long ranged in magnetic systems have attracted much attention due to their spin-polarization properties and potential use in spintronic devices. Whereas experiments have demonstrated the slow decay of such correlations, it has proven more difficult to obtain a smoking gun signature of their odd-frequency character which is responsible, e.g., for their gapless behavior. Here we demonstrate that the magnetic susceptibility response of a normal metal in contact with a superconducting spin valve provides precisely this signature, namely, in the form of an anomalous positive Meissner effect, which may be tuned back to a conventional negative Meissner response simply by altering the magnetization configuration of the spin valve.