We describe a geometric (or gravitational) analog of the Laughlin quasiholes in fractional quantum Hall states. Analogously to the quasiholes, these defects can be constructed by an insertion of an appropriate vertex operator into the conformal block representation of a trial wave function; however, unlike the quasiholes these defects are extrinsic and do not correspond to true excitations of the quantum fluid. We construct a wave function in the presence of such defects and explain how to assign an electric charge and a spin to each defect and calculate the adiabatic, non-Abelian statistics of the defects. The defects turn out to be equivalent to the genons in that their adiabatic exchange statistics can be described in terms of representations of the mapping class group of an appropriate higher genus Riemann surface. We present a general construction that, in principle, makes it possible to calculate the statistics of ${\mathbb{Z}}_n$ genons for any “parent” topological phase. We illustrate the construction on the example of the Laughlin state and perform an explicit calculation of the braiding matrices. In addition to non-Abelian statistics, geometric defects possess a universal Abelian overall phase, determined by the gravitational anomaly.

When two Landau levels are brought to a close coincidence between them and with the chemical potential in the integer quantum Hall regime, the two Landau levels can just cross or collapse while the external or pseudospin field that induces the alignment changes. In this work, all possible crossings are analyzed theoretically for the particular case of semiconductor trilayer systems, using a variational Hartree-Fock approximation. The model includes tunneling between neighboring layers, bias, intralayer, and interlayer Coulomb interaction among the electrons. We have found that the general pseudospin anisotropy classification scheme used in bilayers applies also to the trilayer situation, with the simple crossing corresponding to an easy-axis ferromagnetic anisotropy analogy, and the collapse case corresponding to an easy-plane ferromagnetic analogy. An isotropic case is also possible, with the levels just crossing or collapsing depending on the filling factor and the quantum numbers of the two nearby levels. While our results are valid for any integer filling factor $\nu$ $\left(=1,2,3,...\right)$, we have analyzed in detail the crossings at $\nu =3$ and 4, and we have given clear predictions that will help in their experimental search. In particular, the present calculations suggest that by increasing the bias, the trilayer system at these two filling factors can be driven from an easy-plane anisotropy regime to an easy-axis regime, and then can be driven back to the easy-plane regime. This kind of reentrant behavior is a unique feature of the trilayers, compared with the bilayers.

Point defects in the binary group-IV monochalcogenide monolayers of SnS, SnSe, GeS, and GeSe are investigated using density functional theory calculations. Several stable configurations are found for oxygen defects, however, we give evidence that these materials are less prone to oxidation than phosphorene, with which monochalcogenides are isoelectronic and share the same orthorhombic structure. Concurrent oxygen defects are expected to be vacancies and substitutional oxygen. We show that it is energetically favorable for oxygen to be incorporated into the layers substituting for a chalcogen (${\mathrm{O}}_{\mathrm{S}/\mathrm{Se}}$ defects), and different from most of the other defects investigated, this defect preserves the electronic structure of the material. Thus, we suggest that annealing treatments can be useful for the treatment of functional materials where loss mechanisms due to the presence of defects are undesirable.

We investigate the role of interatomic forces beyond the nearest neighbors on the thermal transport through an atomic junction with a heavy isotope impurity and in a silicon-germanium-like alloy with atomistic calculations. The thermal conductance of the junction incorporating second-nearest-neighbors forces reaches its minimum when the longitudinal optical phonon resonances in the phonon transmission are minimized. We relate the weakening of the optical phonon resonance with the flattening of the longitudinal optical phonon band of the infinite diatomic lattice with second-nearest-neighbors forces, which is the limit of an extended junction. We emphasize that the bypass of the heavy-atom components in the diatomic lattice by long-range interatomic bonds is crucial for the realization of the minimum in bulk thermal conductivity. We highlight the connection between the minimal thermal conductivity of a SiGe-like alloy with the flattening of the longitudinal optical phonon band of the diatomic lattice due to the second-nearest-neighbors forces, in combination with enhanced anharmonic phonon processes and phonon localizations.

The anharmonic phonon properties of SnSe in the $Pnma$ phase were investigated with a combination of experiments and first-principles simulations. Using inelastic neutron scattering (INS) and nuclear resonant inelastic X-ray scattering (NRIXS), we have measured the phonon dispersions and density of states (DOS) and their temperature dependence, which revealed a strong, inhomogeneous shift and broadening of the spectrum on warming. First-principles simulations were performed to rationalize these measurements, and to explain the previously reported anisotropic thermal expansion, in particular the negative thermal expansion within the Sn-Se bilayers. Including the anisotropic strain dependence of the phonon free energy, in addition to the electronic ground state energy, is essential to reproduce the negative thermal expansion. From the phonon DOS obtained with INS and additional calorimetry measurements, we quantify the harmonic, dilational, and anharmonic components of the phonon entropy, heat capacity, and free energy. The origin of the anharmonic phonon thermodynamics is linked to the electronic structure.

We investigate the spin wave modes in asymmetric trilayer $[\mathrm{N}{\mathrm{i}}_{80}\mathrm{F}{\mathrm{e}}_{20}\left(10\mathrm{nm}\right)/\mathrm{Cu}\left(t_{\mathrm{Cu}}\right)/\mathrm{N}{\mathrm{i}}_{80}\mathrm{F}{\mathrm{e}}_{20}\left(30\mathrm{nm}\right)]$ nanowire structures as a function of the Cu thickness $\left(t_{\mathrm{Cu}}\right)$ in the range from 0 to 20 nm using perpendicular ferromagnetic resonance (pFMR) spectroscopy. For $t_{\mathrm{Cu}}=0\mathrm{nm}$, corresponding to the 40 nm thick single layer $\mathrm{N}{\mathrm{i}}_{80}\mathrm{F}{\mathrm{e}}_{20}$ nanowires, both the fundamental and first order modes are observed in the saturation region. However, for the trilayer structures, two additional modes, which are the fundamental and first order optical modes, are observed. We also found that the resonance fields of these modes are markedly sensitive to the Cu thickness due to the competing effects of interlayer exchange coupling and magnetostatic dipolar coupling. When the $t_{\mathrm{Cu}}\ge 10\mathrm{nm}$, the fundamental optical mode is more pronounced. Our experimental results are in quantitative agreement with the dynamic micromagnetic simulations.

We measure the magnetocaloric effect of the manganite series ${\mathrm{La}}_{0.67}{\mathrm{Ca}}_{0.33-x}{\mathrm{Sr}}_x{\mathrm{MnO}}_3$ by determining the isothermal entropy change upon magnetization, using variable-field calorimetry. The results demonstrate that the field dependence of the magnetocaloric effect close to the critical temperature is not given uniquely by the critical exponents of the ferromagnetic-paramagnetic phase transition, i.e., the scaling is nonuniversal. A theoretical description based on the Bean-Rodbell model and taking into account compositional inhomogeneities is shown to be able to account for the observed field dependence. In this way the determination of the nonuniversal field dependence of the magnetocaloric effect close to a phase transition can be used as a method to gain insight into the strength of the spin-lattice interactions of magnetic materials. The approach is shown also to be applicable to first-order transitions.

Coherent conversion of photons to magnons, and back, provides a natural mechanism for rapid control of interactions between stationary spins with long coherence times and high-speed photons. Despite the large frequency difference between optical photons and magnons, coherent conversion can be achieved through a three-particle interaction between one magnon and two photons whose frequency difference is resonant with the magnon frequency, as in optomechanics with two photons and a phonon. The large spin density of a transparent ferromagnetic insulator (such as the ferrite yttrium iron garnet) in an optical cavity provides an intrinsic photon-magnon coupling strength that we calculate to exceed reported optomechanical couplings. A large cavity photon number and properly selected cavity detuning produce a predicted effective coupling strength sufficient for observing electromagnetically induced transparency and the Purcell effect, and even to reach the ultrastrong coupling regime.

The strained Fe-Co alloy in body-centered tetragonal (bct) structure has raised considerable interest due to its giant uniaxial magnetocrystalline anisotropy energy. On the basis of the classical Heisenberg Hamiltonian with ab initio interatomic exchange interactions, we perform a theoretical study of fundamental finite temperature magnetic properties of ${\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x$ alloy films as a function of three variables: chemical composition $0.3\le x\le 0.8$, bct geometry $[a,c(a\left)\right]$ arising from in-plane strain and associated out-of-plane relaxation, and atomic long-range order (ALRO). The Curie temperatures $T_{\text{C}}(x,a)$ obtained from Monte Carlo simulations display a competition between a pronounced dependence on tetragonality, strong ferromagnetism in the Co-rich alloy, and the beginning instability of ferromagnetic order in the Fe-rich alloy when $c/a\to \sqrt{2}$. Atomic ordering enhances $T_{\text{C}}$ and arises mainly due to different distributions of atoms in neighboring coordination shells rather than altering exchange interactions significantly. We investigate the ordering effect on the shape of the adiabatic spin-wave spectrum for selected pairs $(x,a)$. Our results indicate that long-wavelength acoustic spin-wave excitations show dependencies on $x, a$, and ALRO similar to those of $T_{\text{C}}$. The directional anisotropy of the spin-wave stiffness $d(x,a)$ peaks in narrow ranges of composition and tetragonality. ALRO exhibits a strong effect on $d$ for near equiconcentration Fe-Co. We also discuss our findings in the context of employing Fe-Co as perpendicular magnetic recording medium.

${\text{Sr}}_2{\text{CuWO}}_6$ is a double perovskite proposed to be at the border between two- and three-dimensional magnetism, with a square lattice of $S=\frac{1}{2}{\mathrm{Cu}}^{2+}$ ions. We have used inelastic neutron scattering to investigate the spin wave excitations of the system, to find out how they evolve as a function of temperature, as well as to obtain information about the magnetic exchange interactions. We observed well defined dispersive spin wave modes at 6 K, which partially survive above the magnetic ordering temperature $T_N=24$ K. Linear spin wave theory is used to determine the exchange interactions revealing them to be highly two dimensional in nature. Density functional theory calculations are presented supporting this experimental finding, which is in contrast to a previous ab initio study of the magnetic interactions. Our analysis confirms that not the nearest neighbor, but the next nearest neighbor interactions in the tetragonal $ab$ plane are the strongest. Low incident energy measurements reveal the opening of a 0.6(1) meV gap below $T_N$, which suggests the presence of a very weak single ion anisotropy term in the form of an easy axis along $\widehat{\mathbf{a}}$.

Vortex cutting and reconnection is an intriguing and still-unsolved problem central to many areas of classical and quantum physics, including hydrodynamics, astrophysics, and superconductivity. Here, we describe a comprehensive investigation of the crossing of magnetic vortices in superconductors using time dependent Ginsburg-Landau modeling. Within a macroscopic volume, we simulate initial magnetization of an anisotropic high temperature superconductor followed by subsequent remagnetization with perpendicular magnetic fields, creating the crossing of the initial and newly generated vortices. The time resolved evolution of vortex lines as they approach each other, contort, locally conjoin, and detach, elucidates the fine details of the vortex-crossing scenario under practical situations with many interacting vortices in the presence of weak pinning. Our simulations also reveal left-handed helical vortex instabilities that accompany the remagnetization process and participate in the vortex crossing events.

We report investigations of molybdenum nitride (MoN) thin films with different thickness and disorder and with superconducting transition temperature $9.89\mathrm{K}\ge T_c\ge 2.78\mathrm{K}$. Using terahertz frequency-domain spectroscopy we explore the normal and superconducting charge carrier dynamics for frequencies covering the range from 3 to $38{\mathrm{cm}}^{-1}$ (0.1 to 1.1 THz). The superconducting energy scales, i.e., the critical temperature $T_c$, the pairing energy $\mathrm{\Delta }$, and the superfluid stiffness $J$, and the superfluid density $n_s$ can be well described within the Bardeen-Cooper-Schrieffer theory for conventional superconductors. At the same time, we find an anomalously large dissipative conductivity, which cannot be explained by thermally excited quasiparticles, but rather by a temperature-dependent normal-conducting fraction, persisting deep into the superconducting state. Our results on this disordered system constrain the regime, where discernible effects stemming from the disorder-induced superconductor-insulator transition possibly become relevant, to MoN films with a transition temperature lower than at least 2.78 K.

We study the interplay between population imbalance in a two-component fermionic system and nearest-neighbor interaction using the matrix product states method. Our analysis reveals a parameter regime for the existence of the Fulde-Ferrell-Larkin-Ovchinnikov phase. Furthermore, we find distinct evidence for the presence of hidden order in the system. We present an effective model to understand the emergent oscillations in the string correlations due to the imbalance and show how they can become an efficient tool to investigate systems with imbalance.

Intra-Landau-level thermal activation, from localized states in the tail to delocalized states above the mobility edge in the same Landau level, explains the $B_c\left(T\right)$ (half width of the dissipationless state) phase diagram for a number of different quantum Hall samples with widely ranging carrier density, mobility, and disorder. Good agreement is achieved over two to three orders of magnitude in temperature and magnetic field for a wide range of filling factors. The Landau-level width is found to be independent of magnetic field. The mobility edge moves in the case of changing Landau-level overlap to maintain a sample dependent critical density of states at that energy. An analysis of filling factor $\nu =2/3$ shows that the composite fermion Landau levels have exactly the same width as their electron counterparts. An important ingredient of the model is the Lorentzian broadening with long tails which provide localized states deep in the gap which are essential in order to reproduce the robust high-temperature $B_c\left(T\right)$ phase observed in experiment.

The nonlinear response of graphene to a THz laser pulse is studied by solving the time-dependent Dirac equation and the time-dependent Schrödinger equation within a tight-binding approximation applied to finite-sized structures. We compare predictions of these two approximations for the harmonic spectrum with the recent experiment by P. Bowlan et al. [Phys. Rev. B 89, 041408(R) (2014)]. We highlight the influence of short-range and long-range disorder which can be accounted for within the tight-binding description on a microscopic level. We find good agreement with the experiment. Most notably, the intensity of the second harmonic offers a quantitative indicator for the amount of short-range disorder.

We observe nuclear magnetic resonance (NMR) in the fractional quantum Hall regime at the Landau-level filling factor of $\nu =2/3$ from simultaneous measurement of longitudinal resistance and photoluminescence (PL). The dynamic nuclear-spin polarization is induced by applying a huge electronic current at the spin phase transition point of $\nu =2/3$. The NMR spectra obtained from changes in resistance and PL intensity are qualitatively the same; that is, the Knight-shift (spin-polarized region) and zero-shift (spin-unpolarized region) resonances are observed in both. The observed change in PL intensity is interpreted as a consequence of the trion scattering induced by polarized nuclear spins. We conclude that both detection methods probe almost the same local phenomena.

Ab initio calculations allow us to establish a close connection between the Ruddlesden-Popper layered nickelates and cuprates not only in terms of filling of $d$ levels (close to $d^9$) but also because they show ${\mathrm{Ni}}^{1+}(S=1/2)/{\mathrm{Ni}}^{2+}(S=0)$ stripe ordering. The insulating charge-ordered ground state is obtained from a combination of structural distortions and magnetic order. The ${\mathrm{Ni}}^{2+}$ ions are in a low-spin configuration $\left(S=0\right)$ yielding an antiferromagnetic arrangement of ${\mathrm{Ni}}^{1+} S=1/2$ ions like the long-sought spin-1/2 antiferromagnetic insulator analog of the cuprate parent materials. The analogy extends further with the main contribution to the bands near the Fermi energy coming from hybridized Ni $d_{x^2-y^2}$ and O $p$ states.

We propose a matrix quantum mechanics for a class of non-Abelian quantum Hall states. The model describes electrons which carry an internal $\text{SU}\left(p\right)$ spin. The ground states of the matrix model include spin-singlet generalizations of the Moore-Read and Read-Rezayi states and, in general, lie in a class previously introduced by Blok and Wen. The effective action for these states is a $\text{U}\left(p\right)$ Chern-Simons theory. We show how the matrix model can be derived from quantization of the vortices in this Chern-Simons theory and how the matrix model ground states can be reconstructed as correlation functions in the boundary WZW model.

We describe the extension of the density matrix embedding theory framework to coupled interacting fermion-boson systems. This provides a frequency-independent, entanglement embedding formalism to treat bulk fermion-boson problems. We illustrate the concepts within the context of the one-dimensional Hubbard-Holstein model, where the phonon bath states are obtained from the Schmidt decomposition of a self-consistently adjusted coherent state. We benchmark our results against accurate density matrix renormalization group calculations.