We complete a classification of topological phases and their topological defects in crystalline insulators and superconductors. We consider topological phases and defects described by noninteracting Bloch and Bogoliubov–de Gennes Hamiltonians that support additional order-two spatial symmetry, besides any of 10 classes of symmetries defined by time-reversal symmetry and particle-hole symmetry. The additional order-two spatial symmetry we consider is general and it includes ${\mathit{Z}}_2$ global symmetry, mirror reflection, twofold rotation, inversion, and their magnetic point group symmetries. We find that the topological periodic table shows a periodicity in the number of flipped coordinates under the order-two spatial symmetry, in addition to the Bott periodicity in the space dimensions. Various symmetry-protected topological phases and gapless modes will be identified and discussed in a unified framework. We also present topological classification of symmetry-protected Fermi points. The bulk classification and the surface Fermi point classification provide a realization of the bulk-boundary correspondence in terms of the $K$ theory.

The strain dependence of electric and magnetic properties has been widely investigated, both from a fundamental science perspective and an applications point of view. Electromechanical coupling through field-induced polarization rotation (PRO) and polarization reorientation (PRE) in piezoelectric single crystals can provide an effective strain in film/substrate epitaxial heterostructures. However, the specific pathway of PRO and PRE is a complex thermodynamic process, depending on chemical composition, temperature, electric field, and mechanical load. Here, systematic studies of the temperature-dependent field-induced phase transitions in ${\mathrm{Pb}(\mathrm{Mg},\mathrm{Nb})\mathrm{O}}_3\text{−}{\mathrm{PbTiO}}_3$ single crystals with different initial phase and orientation configurations have been performed. Different types of strains, volatile/nonvolatile and biaxial/uniaxial, have been measured by both macroscopic and in situ x-ray diffraction techniques. In addition, the strain state of epitaxial Mn-doped ${\mathrm{CoFe}}_2{\mathrm{O}}_4$ thin films was examined by magnetic anisotropy measurements, where a giant magnetoelectric coupling has been demonstrated.

The quasi-one-dimensional transport of Abelian and non-Abelian anyons is studied in the presence of a random topological background. In particular, we consider the quantum walk of an anyon that braids around islands of randomly filled static anyons of the same type. Two distinct behaviors are identified. We analytically demonstrate that all types of Abelian anyons localize purely due to the statistical phases induced by their random anyonic environment. In contrast, we numerically show that non-Abelian Ising anyons do not localize. This is due to their entanglement with the anyonic environment, which effectively induces dephasing. Our study demonstrates that localization properties strongly depend on nonlocal topological interactions, and it provides a clear distinction in the transport properties of Abelian and non-Abelian anyons.

We have carried out an extensive phonon study on multiferroic ${\mathrm{GaFeO}}_3$ to elucidate its dynamical behavior. Inelastic neutron scattering measurements are performed over a wide temperature range, 150 to 1198 K. First principles lattice dynamical calculations are done for the sake of the analysis and interpretation of the observations. The comparison of the phonon spectra from magnetic and nonmagnetic calculations highlights pronounced differences. The energy range of the vibrational atomistic contributions of the Fe and O ions are found to differ significantly in the two calculation types. Therefore, magnetism induced by the active spin degrees of freedom of Fe cations plays a key role in stabilizing the structure and dynamics of ${\mathrm{GaFeO}}_3$. Moreover, the computed enthalpy in various phases of ${\mathrm{GaFeO}}_3$ is used to gain deeper insights into the high-pressure phase stability of this material. Further, the volume dependence of the phonon spectra is used to determine its thermal expansion behavior.

We use a first-principles based approach to theoretically investigate the room-temperature phase diagram of $\left({\mathrm{BiFeO}}_3\right){}_x\left({\mathrm{BaTiO}}_3\right){}_{1-x}$ solid solutions. Using a modified effective Hamiltonian scheme, we show that random fields originating from off-valent substitutions decrease the ferroelectric transition temperature leading to a paraelectric ground state in the intermediate range of concentrations $x$. The predicted critical concentrations at which lattice distortions inherited from the ferroelectric phases of parent compounds vanish fall within the range of the experimental values. Furthermore, the obtained results give the necessary microscopical insight into the mechanism driving the pseudocubic phase formation.

The magnetic order, spin dynamics, and crystal structure of the multiferroic ${\mathrm{Sr}}_{0.56}{\mathrm{Ba}}_{0.44}{\mathrm{MnO}}_3$ have been investigated using neutron and x-ray scattering. Ferroelectricity develops at $T_C=305$ K with a polarization of 4.2 $\mu {\mathrm{C}/\mathrm{cm}}^2$ associated with the displacements of the Mn ions, while the ${\mathrm{Mn}}^{4+}$ spins order below $T_N\approx 200$ K into a simple $G$-type commensurate magnetic structure. Below $T_N$ the ferroelectric order decreases dramatically, demonstrating that the two order parameters are strongly coupled. The ground state spin dynamics is characterized by a spin gap of 4.6(5) meV and the magnon density of states peaking at 43 meV. Detailed spin wave simulations with a gap and isotropic exchange of $J=4.8\left(2\right)$ meV describe the excitation spectrum well. Above $T_N$ strong spin correlations coexist with robust ferroelectric order.

A model is discussed for magnetoelectric (ME) interactions originating from the motion of magnetic domain walls (DWs) in a multiferroic composite of orthoferrites $R{\mathrm{FeO}}_3$ $(R\text{FO}$) with magnetic stripe domains and a piezoelectric such as lead magnesium niobate-lead titanate (PMN-PT). The DWs in $R\text{FO}$ can be set in motion with an ac magnetic field up to a critical speed of 20 km/s, the highest for any magnetic system, leading to the excitation of bulk and shear magnetoacoustic waves. Thus, the ME coupling will arise from flexural deformation associated with DW motion (rather than the Joule magnetostriction mediated coupling under a static or quasistatic condition). A $c$ plane orthoferrite with a single Néel-type DW in the $bc$ plane and an ac magnetic field $H$ along the $c$ axis is assumed. The deflection in the bilayer due to DW motion is obtained when the DW velocity is a linear function $H$ and the resulting induced voltage across PMN-PT is estimated. It is shown that a combination of spatial and time harmonics of the bending deformation leads to (i) a linear ME coefficient defined by ${\alpha }_E=E/H$ and (ii) a quadratic ME coefficient ${\alpha }_{\mathrm{EQ}}=E/H^2$. The model is applied to yttrium orthoferrites (YFO) and a PMN-PT bilayer since YFO has one of the highest DW mobility amongst the orthoferrites. The coefficient ${\alpha }_E$ is dependent on the DW position, and it is maximum when the DW equilibrium position is at the center of the sample. In YFO/PMN-PT the estimated low-frequency ${\alpha }_E$ ∼ 30 mV/cm Oe and resonance value is 1.5 V/(cm Oe). Since orthoferrites (and PMN-PT) are transparent in the visible region and have a large Faraday rotation, the DW dynamics and the ME coupling could be studied simultaneously. The theory discussed here is of interest for studies on ME coupling and for applications such as magnetically controlled electro-optic devices.

We apply the method of compressed sensing (CS) quantum process tomography (QPT) to characterize quantum gates based on superconducting Xmon and phase qubits. Using experimental data for a two-qubit controlled-Z gate, we obtain an estimate for the process matrix $\chi$ with reasonably high fidelity compared to full QPT, but using a significantly reduced set of initial states and measurement configurations. We show that the CS method still works when the amount of used data is so small that the standard QPT would have an underdetermined system of equations. We also apply the CS method to the analysis of the three-qubit Toffoli gate with numerically added noise, and similarly show that the method works well for a substantially reduced set of data. For the CS calculations, we use two different bases in which the process matrix $\chi$ is approximately sparse, and show that the resulting estimates of the process matrices match each other with reasonably high fidelity. For both two-qubit and three-qubit gates, we characterize the quantum process by not only its process matrix and fidelity, but also by the corresponding standard deviation, defined via variation of the state fidelity for different initial states.

We investigate the real-time dynamics of photoexcited electronic instabilities in a charge-transfer system model, using the time-dependent density matrix renormalization group method. The model of choice was the quarter-filled one-dimensional extended Peierls-Hubbard Hamiltonian interacting with classical few-cycle electromagnetic radiation. The results show that only one electronic instability drives the main features of the photogenerated time-dependent behavior. Indeed, the photoresponse of the system shows a large enhancement of the $4k_F$ (bond and charge) instability whereas the $2k_F$ state remains largely unaffected. This conclusion holds regardless of the nature of the optical excitations and whether the system is perturbed resonantly or not. Our results suggest potential applications of charge-transfer systems with slow phononic dynamics as optoelectronic switching devices.

We study the electronic properties of $AA$-stacked bilayer graphene in a transverse electric field. The strong on-site Coulomb repulsion stabilizes the antiferromagnetic order in such a system. The antiferromagnetic order is suppressed by the transverse bias voltage, at least partially. The interplane Coulomb repulsion and nonzero voltage stabilize an exciton order parameter. The exciton order parameter coexists with the antiferromagnetism and can be as large as several tens of meV for realistic values of the bias voltage and interaction constants. The application of a transverse bias voltage can be used to control the transport properties of the bilayer.

We present here an investigation of the magnetic ordering in the Mott insulating oxyselenide materials $L{n}_2{\mathrm{O}}_2{\mathrm{Fe}}_2{\mathrm{OSe}}_2$ $(Ln=\text{Ce}$, Nd). Neutron powder diffraction data are consistent with a noncollinear multi-$k$ ordering on the iron sublattice structure and analysis indicates a reduced magnetic correlation length perpendicular to the $[{\mathrm{Fe}}_2\mathrm{O}{\mathrm{]}}^{2+}$ layers. The magnetic role of the $L{n}^{3+}$ cations is investigated and ${\mathrm{Ce}}^{3+}$ moments are found to order at $T\le 16$ K.

We present a method to determine the impurity Green's function of the interacting resonant level model (IRLM) using numerical simulation techniques based on the expansion of a resolvent expression in terms of Chebyshev polynomials. The iterative determination of the contributions to the expansion is based on a density matrix renormalization group algorithm. The spectral function has Lorentzian shape, where we can show that the width grows monotonically with the interaction on the contact link. Moreover, for values of the interaction comparable to the bandwidth, there are additional peaks showing up for energies located outside the conduction band.

The recent discovery of a polaron-associated zero phonon line in the band-edge photoluminescence of high optical quality EuTe crystals opens up the prospect of answering long-standing questions about the polaron internal structure, thermal stability, and generation efficiency. Here, a Schrödinger equation for the polaron was formulated and resolved by using both variational and self-consistent methods. The theory is in good agreement with measurements of the zero phonon line as a function of magnetic field and temperature, and it could be applied to other polaronic systems. It is deduced that, in EuTe, at $0\mathrm{K}$, a polaron carries a magnetic moment of $610{\mu }_B$, and its binding energy is 27 meV. However, this binding energy does not carry the usual meaning of thermal stability, because it decreases drastically when the sample is warmed up. For instance, at $T=100\mathrm{K}$, the binding energy is already reduced to only 6 meV. The thermal destruction of a polaron is brought about by thermal fluctuations of the spin lattice that suppress the electron's self-energy. Photoluminescence excitation spectra of EuTe demonstrate that the photogeneration of polarons becomes increasingly inefficient when the energy of the pumping photon is increased above the band gap.

The opening of the energy gap at the Dirac point when the helical edge states of two-dimensional topological insulators are hybridized in narrow channels is investigated. While the energy gap widens exponentially as the width is reduced within the block-diagonal effective four-band model, the dependence is no longer monotonic when off-diagonal terms representing spin-orbit coupling are taken into account. The energy gap vanishes periodically as the width is varied with the period being almost inversely proportional to the strength of the spin-orbit coupling. Both the bulk inversion asymmetry and Rashba terms cause the cancellation of the confinement effect. The disappearance of the hybridization takes place when the overlap integral becomes zero in the presence of the spin-orbit coupling due to the oscillatory decay of the transverse wave function.

Most commonly known hard transition-metal nitrides crystallize in rocksalt structure (B1). The discovery of ultraincompressible pyrite-type ${\mathrm{PtN}}_2$ 10 years ago has raised a question about the cause of its exceptional mechanical properties. We answer this question by a systematic computational analysis of the pyrite-type ${\mathrm{PtN}}_2$ and other transition-metal pernitrides ($M{\mathrm{N}}_2$) with density functional theory. Apart from ${\mathrm{PtN}}_2$, the three hardest phases are found among them in the $3d$ transition-metal period. They are ${\mathrm{MnN}}_2$, ${\mathrm{CoN}}_2$, and ${\mathrm{NiN}}_2$, with computed Vickers hardness ($H_{\mathrm{V}}$) values of 19.9 GPa, 16.5 GPa, and 15.7 GPa, respectively. Harder than all of these is ${\mathrm{PtN}}_2$, with a $H_{\mathrm{V}}$ of 23.5 GPa. We found the following trends and correlations that explain the origin of hardness in these pernitrides. (a) Charge transfer from $M$ to N controls the length of the N-N bond, resulting in a correlation with bulk modulus, dominantly by providing Coulomb repulsion between the pairing N atoms. (b) Elastic constant $C{}_{44}$, an indicator of mechanical stability and hardness is correlated with total density of states at $E$, an indicator of metallicity. (c) Often cited monotonic variation of $H_{\mathrm{V}}$ and Pugh's ratio with valence electron concentration found in rocksalt-type early transition-metal nitrides is not evident in this structure. (d) The change in $M-M$ bond strength under a shearing strain indicated by crystal orbital Hamilton population is predictive of hardness. This is a direct connection between a specific bond and shear related mechanical properties. This panoptic view involving ionicity, metallicity, and covalency is essential to obtain a clear microscopic understanding of hardness.

We report spatially resolved, time-dependent, magnetization reversal measurements of an ${\mathrm{Fe}}_8$ single molecular magnet using a microscopic Hall bar array. We found that a deflagration process, where molecules reverse their spin direction along a moving front, can be ignited quantum mechanically $\left(T\to 0\right)$ at a resonance field, with no phonon pulse. The avalanche front velocity is of the order of $1\mathrm{m}/\mathrm{s}$ and is sensitive to field gradients and sweep rates. We also measured the thermal diffusivity $\kappa$ in ${\mathrm{Fe}}_8$. This allows us to estimate the “flame” temperature.