We present a numerical scheme for efficiently extracting the higher-order moments and cumulants of various operators on spin systems represented as tensor product states, for both finite and infinite systems, and present several applications for such quantities. For example, the second cumulant of the energy of a state, $\langle \mathrm{\Delta }{H}^2\rangle$, gives a straightforward method to check the convergence of numerical ground-state approximation algorithms. Additionally, we discuss the use of moments and cumulants in the study of phase transitions. Of particular interest is the application of our method to calculate the so-called Binder cumulant, which we use to detect critical points and study the critical exponent of the correlation length with only small finite numerical calculations. We apply these methods to study the behavior of a family of one-dimensional models (the transverse Ising model, the spin-1 Ising model, and the spin-1 Ising model in a crystal field), as well as the two-dimensional Ising model on a square lattice. Our results show that in one dimension, cumulant-based methods can produce precise estimates of the critical points at a low computational cost. The method shows promise for two-dimensional systems as well.

Electronic spin systems with $\mathrm{S}>1/2$ provide an efficient method for dc vector magnetometry, since the conventional electron spin resonance spectra at a given magnetic field reflect not only the field strength but also orientation in the presence of strong spin-spin interactions. $S=1$ spins, e.g., the nitrogen-vacancy centers in diamond, have been intensively investigated for such a purpose. In this report, we compare $S=1$ and $3/2$ spins, and discuss how one can apply general principles for the use of high-spin systems as a vector magnetometer to the $S=3/2$ spin systems. We find analytical solutions which allow a reconstruction of the magnetic field strength and polar angle using the observed resonance transitions if a uniaxial symmetry exists for the spin-spin interaction as in $S=1$ systems. We also find that an ambiguity of determining the field parameters may arise due to the unique properties of $S=3/2$ systems, and present solutions for it utilizing additional transitions in the low-field region. The electronic spins of the silicon vacancy in silicon carbide will be introduced as a model for the $S=3/2$ dc vector magnetometer and the practical usage of it, including the magic-angle spinning type method, will be presented too.

Tin selenide (SnSe) and tin sulfide (SnS) have recently attracted particular interest due to their great potential for large-scale thermoelectric applications. A complete prediction of the thermoelectric performance and the understanding of underlying heat and charge transport details are the key to further improvement of their thermoelectric efficiency. We conduct comprehensive investigations of both thermal and electrical transport properties of SnSe and SnS using first-principles calculations combined with the Boltzmann transport theory. Due to the distinct layered lattice structure, SnSe and SnS exhibit similarly anisotropic thermal and electrical behaviors. The cross-plane lattice thermal conductivity ${\kappa }_L$ is $40–60\%$ lower than the in-plane values. Extremely low ${\kappa }_L$ is found for both materials because of high anharmonicity, while the average ${\kappa }_L$ of SnS is $\sim 8\%$ higher than that of SnSe from 300 to 750 K. It is suggested that nanostructuring would be difficult to further decrease ${\kappa }_L$ because of the short mean free paths of dominant phonon modes (1–30 nm at 300 K), while alloying would be efficient in reducing ${\kappa }_L$ considering that the relative ${\kappa }_L$ contribution $(\sim 65\%)$ of optical phonons is remarkably large. On the electrical side, the anisotropic electrical conductivities are mainly due to the different effective masses of holes and electrons along the $a, b$, and $c$ axes. This leads to the highest optimal $\mathit{ZT}$ values along the $b$ axis and lowest ones along the $a$ axis in both $p$-type materials. However, the $n$-type ones exhibit the highest $\mathit{ZT}\mathrm{s}$ along the $a$ axis due to the enhancement of power factor when the chemical potential gradually approaches the secondary conduction band valley that causes significant increase in electron mobility and density of states. Owing to the larger mobility and smaller ${\kappa }_L$ along the given direction, SnSe exhibits larger optimal ZTs compared with SnS in both $p$- and $n$-type materials. For both materials, the peak $\mathit{ZT}\mathrm{s}$ of $n$-type materials are much higher than those of $p$-type ones along the same direction. The predicted highest $\mathit{ZT}$ values at 750 K are 1.0 in SnSe and 0.6 in SnS along the $b$ axis for the $p$-type doping, while those for the $n$-type doping reach 2.7 in SnSe and 1.5 in SnS along the $a$ axis, rendering them among the best bulk thermoelectric materials for large-scale applications. Our calculations show reasonable agreements with the experimental results and quantitatively predict the great potential in further enhancing the thermoelectric performance of SnSe and SnS, especially for the $n$-type materials.

We report the observation of an unusually large number of consecutive spin pairs in a weakly coupled many-electron $\text{GaAs/AlGaAs}$ quantum dot. The pairs are identified due to pairwise parallel shifts of Coulomb resonances in a perpendicular magnetic field. Using a nearby quantum point contact for time-resolved charge detection, the tunneling rates are investigated as a function of gate voltage and magnetic field. We compare our experimental data to a single-level transport model and discuss possible reasons for deviations.

A combination of neutron diffraction and angle-resolved photoemission spectroscopy measurements on a pure antiferromagnetic stripe ${\mathrm{Rb}}_{1-\delta }{\mathrm{Fe}}_{1.5-\sigma }{\mathrm{S}}_2$ is reported. A neutron diffraction experiment on a powder sample shows that a $98\%$ volume fraction of the sample is in the antiferromagnetic stripe phase with rhombic iron vacancy order and a refined composition of ${\mathrm{Rb}}_{0.66}{\mathrm{Fe}}_{1.36}{\mathrm{S}}_2$, and that only $2\%$ of the sample is in the block antiferromagnetic phase with $\sqrt{5}\times \sqrt{5}$ iron vacancy order. Furthermore, a neutron diffraction experiment on a single crystal shows that there is only a single phase with the stripe antiferromagnetic order with the refined composition of ${\mathrm{Rb}}_{0.78}{\mathrm{Fe}}_{1.35}{\mathrm{S}}_2$, while the phase with block antiferromagnetic order is absent. Angle-resolved photoemission spectroscopy measurements on the same crystal with the pure stripe phase reveal that the electronic structure is gapped at the Fermi level with a gap larger than 0.325 eV. The data collectively demonstrate that the extra $10\%$ iron vacancies in addition to the rhombic iron vacancy order effectively impede the formation of the block antiferromagnetic phase; the data also suggest that the stripe antiferromagnetic phase with rhombic iron vacancy order is a Mott insulator.

A linear response theory for electron-hole pair density is developed, which constitutes a theoretical method, and a definition of exciton density in a first-principles context is derived by considering both the electron-hole attractive interaction and the screening effect. This allows the exciton time evolution to be examined. This formulation is applied to a jellium model in order to prove the existence of a transient exciton, and to observe crossover from a transient to a stable exciton in response to decreased electron density. The exciton formation mechanism is also revealed.

A definition of topological phases of density matrices is presented. The topological invariants in case of both noninteracting and interacting systems are extended to nonzero temperatures. The influence of electron interactions on topological insulators at finite temperatures is investigated. A correlated topological insulator is described by the Kane-Mele model, which is extended by the interaction term of the Falicov-Kimball type. Within the Hartree-Fock and the Hubbard I approximations, thermodynamic and topological phase diagrams are determined where the long-range order is included. The results show that correlation effects lead to a strong suppression of the existence of the nontrivial topological phase. In the homogeneous phase, we find a purely correlation driven phase transition into the topologically trivial Mott insulator.

The conditions for both the stability and the breakdown of the topological classification of gapped ground states of noninteracting fermions, the tenfold way, in the presence of quartic fermion-fermion interactions are given for any dimension of space. This is achieved by encoding the effects of interactions on the boundary gapless modes in terms of boundary dynamical masses. Breakdown of the noninteracting topological classification occurs when the quantum nonlinear $\sigma$ models for the boundary dynamical masses favor quantum disordered phases. For the tenfold way, we find that (i) the noninteracting topological classification ${\mathbb{Z}}_2^{}$ is always stable, (ii) the noninteracting topological classification $\mathbb{Z}$ in even dimensions is always stable, and (iii) the noninteracting topological classification $\mathbb{Z}$ in odd dimensions is unstable and reduces to ${\mathbb{Z}}_N^{}$ that can be identified explicitly for any dimension and any defining symmetries. We also apply our method to the three-dimensional topological crystalline insulator SnTe from the symmetry class $\mathrm{AII}+R$, for which we establish the reduction $\mathbb{Z}\to {\mathbb{Z}}_8^{}$ of the noninteracting topological classification.

We report on the nontrivial field dependence of charge-carrier recombination in an organic blend at low temperatures. A new microwave resonance technique for monitoring charge recombination in organic semiconductors at low temperatures is applied in bulk heterojunction poly(3-hexylthiophene):[6,6]-phenyl-${\mathrm{C}}_{61}$-butyric acid methyl ester blends with results showing that an external electric field can in fact increase recombination. Monte Carlo simulations suggest that this contradiction to conventional wisdom relates to electron-hole pairs that are separated at donor-acceptor interfaces where the electric field acts in synergy with their Coulomb attraction. For this behavior to occur a critical initial separation of $\sim 5\mathrm{nm}$ between the carriers is required.

We theoretically investigate the multipolar effects on the dipole-forbidden transitions of a semiconductor quantum dot. An approximated expression for the decay rate of these transitions is derived. Unlike the general theory of the spontaneous emission beyond the dipole approximation, the distinct roles of the emitter and the vacuum electric field in the transition rate are here clearly recognizable and can be separately optimized. We illustrate the potential of this formalism by calculating the spontaneous emission decay rate of an InAs/GaAs quantum dot embedded into two realistic nanostructures—an L3 photonic crystal cavity and a plasmonic dimer antenna. The obtained results show that, although the two structures provide an enhancement of the same order of magnitude, the plasmonic antenna constitutes a more promising candidate for the experimental observation of the dipole-forbidden transitions of a quantum dot.

Interatomic potentials have been widely used in atomistic simulations such as molecular dynamics. Recently, frameworks to construct accurate interatomic potentials that combine a set of density functional theory (DFT) calculations with machine learning techniques have been proposed. One of these methods is to use compressed sensing to derive a sparse representation for the interatomic potential. This facilitates the control of the accuracy of interatomic potentials. In this study, we demonstrate the applicability of compressed sensing to deriving the interatomic potential of ten elemental metals, namely, Ag, Al, Au, Ca, Cu, Ga, In, K, Li, and Zn. For each elemental metal, the interatomic potential is obtained from DFT calculations using elastic net regression. The interatomic potentials are found to have prediction errors of less than 3.5 meV/atom, 0.03 eV/Å, and 0.15 GPa for the energy, force, and the stress tensor, respectively, which enable the accurate prediction of physical properties such as lattice constants and the phonon dispersion relationship.

We develop the anisotropic Eliashberg framework for superconductivity in the presence of an applied magnetic field. Using as input the ab initio calculated electron and phonon band structures and electron-phonon coupling, we solve self-consistently the anisotropic Eliashberg equations for the archetypal superconductor ${\mathrm{MgB}}_2$. We find two self-consistent solutions, time-even two-band superconductivity, as well as unconventional time-odd $s$-wave spin triplet two-band superconductivity emerging with applied field. We provide the full momentum, frequency, and spin-resolved dependence and magnetic field-temperature phase diagrams of the time-even and time-odd superconducting pair amplitudes and predict fingerprints of this novel odd-frequency state in tunneling experiments.

Neutron diffraction and small angle scattering experiments have been carried out on the double-isotopic polycrystalline sample $\left({}^7\mathrm{L}{\mathrm{i}}_{0.82}\mathrm{F}{\mathrm{e}}_{0.18}\mathrm{OD}\right)\mathrm{FeSe}$. Profile refinements of the diffraction data establish the composition and reveal an essentially single phase material with lattice parameters of $a=3.7827\AA$ and $c=9.1277\AA$ at 4 K, in the ferromagnetic-superconductor regime, with a bulk superconducting transition of $T_C=18\mathrm{K}$. Small angle neutron scattering measurements in zero applied field reveal the onset of ferromagnetic order below $T_F\approx 12.5K$, with a wave vector and temperature dependence consistent with an inhomogeneous ferromagnet of spontaneous vortices or domains in a mixed state. No oscillatory long range ordered magnetic state is observed. Field-dependent measurements establish a separate component of magnetic scattering from the vortex lattice, which occurs at the expected wave vector. The temperature dependence of the vortex scattering does not indicate any contribution from the ferromagnetism, consistent with diffraction data that indicate that the ordered ferromagnetic moment is quite small.

We report on a class of dark solitons and vortices existing in the exciton-polariton condensates and having discontinuity in their excitonic component. These solutions exist due to an intrinsic bistability of the exciton density in the given optical field and for nonzero detuning between the cavity and excitonic resonances. We specify a well defined energy boundary where they transform into previously known polaritonic dark solitons and vortices.

We propose to realize a two-dimensional chiral topological superconducting (TSC) state from the quantum anomalous Hall plateau transition in a magnetic topological insulator thin film through the proximity effect to a conventional $s$-wave superconductor. This state has a full pairing gap in the bulk and a single chiral Majorana mode at the edge. The optimal condition for realizing such chiral TSC is to have inequivalent superconducting pairing amplitudes on top and bottom surfaces of the doped magnetic topological insulator. We further propose several transport experiments to detect the chiral TSC. One unique signature is that the conductance will be quantized into a half-integer plateau at the coercive field in this hybrid system. In particular, with the point contact formed by a superconducting junction, the conductance oscillates between $e^2/2h$ and $e^2/h$ with the frequency determined by the voltage across the junction. We close by discussing the feasibility of these experimental proposals.

We investigate the quantum electrodynamics of a device based on a topological superconducting circuit embedded in a microwave resonator. The device stores its quantum information in coherent superpositions of fermion parity states originating from Majorana fermion hybridization. This generates a highly isolated qubit whose coherence time could be greatly enhanced. We extend the conventional semiclassical method and obtain analytical derivations for strong transmon-photon coupling. Using this formalism, we develop protocols to initialize, control, and measure the parity states. We show that, remarkably, the parity eigenvalue can be detected via dispersive shifts of the optical cavity in the strong-coupling regime and its state can be coherently manipulated via a second-order sideband transition.