Time-dependent photoexcitation and optical spectroscopy of pi-conjugated molecules is described using a new method for the simulation of excited state molecular dynamics in extended molecular systems with sizes up to hundreds of atoms. Applications are made to poly(p-phenylene vinylene) oligomers. Our analysis shows self-trapping of excitations on about six repeat units in the course of photoexcitation relaxation, identifies specific slow (torsion) and fast (bond-stretch) nuclear motions strongly coupled to the electronic degrees of freedom, and predicts spectroscopic signatures of molecular conformations.

A numerical implementation of self-consistent mean-field theory for the structural phase behavior of block copolymers is proposed. Our scheme does not require a priori assumptions of the underlying mesoscopic symmetries. The method potentially enables us to characterize, with high accuracy, the structural phase diagram of block copolymers with significant architectural complexity. We illustrate the method by applying it to a triblock copolymer system.

Recently spin textures called skyrmions have been discovered in certain chiral magnetic materials without spatial inversion symmetry, and have attracted enormous attention due to their promising application in spintronics since only a low applied current is necessary to drive their motion. When a conduction electron moves around the skyrmion, its spin is fully polarized by the spin texture and acquires a quantized phase; thus, the skyrmion yields an emergent electrodynamics that in turn determines skyrmion motion and gives rise to a finite Hall angle. As topological excitations, skyrmions behave as particles. In this work we derive the equation of motion for skyrmions as rigid point particles from a microscopic continuum model and obtain the short-range interaction between skyrmions, and the interaction between skyrmions and defects. Skyrmions also experience a Magnus force perpendicular to their velocity due to the underlying emergent electromagnetic field. We validate the equation of motion by studying the depinning transition using both the particle and the continuum models. By using the particle description, we explain the recent experimental observations of the rotation of a skyrmion lattice in the presence of a temperature gradient. We also predict quantum and thermal creep motion of skyrmions in the pinning potential.

Single-walled carbon nanotubes (SWNTs) are π-conjugated, quasi-one-dimensional structures consisting of rolled-up graphene sheets that, depending on their chirality, behave as semiconductors or metals 1 ; owing to their unique properties, they enable groundbreaking applications in mechanics, nanoelectronics and photonics 2,3 . In semiconducting SWNTs, medium-sized excitons (3-5 nm) with large binding energy and oscillator strength are the fundamental excitations 4-8 ; exciton wavefunction localization and one-dimensionality give rise to a strong electron-phonon coupling 9-11 , the study of which is crucial for the understanding of their electronic and optical properties. Here we report on the use of resonant sub-10-fs visible pulses 12 to generate and detect, in the time domain, coherent phonons in SWNT ensembles. We observe vibrational wavepackets for the radial breathing mode (RBM) and the G mode, and in particular their anharmonic coupling, resulting in a frequency modulation of the G mode by the RBM. Quantumchemical modelling 13 shows that this effect is due to a corrugation of the SWNT surface on photoexcitation, leading to a coupling between longitudinal and radial vibrations.Electron-phonon coupling in SWNTs is usually studied using Raman spectroscopy; this technique is useful for investigating ground-state vibrations 14 , whereas photoexcited-state vibrational dynamics remain largely unknown because, in the frequency domain, phonon replicas are hardly detectable in the presence of substantial inhomogeneous broadening. Time-domain observation of phonon dynamics has much lower sensitivity with respect to conventional Raman, but it enables direct measurement of excitedstate dynamics, vibrational dephasing and mode coupling in a distinct way 15,16 . Coherent phonon detection allows resolution in time of wavepacket dynamics that is otherwise averaged-out in standard Raman scattering.To detect coherent phonons in SWNTs, we use a standard pump-probe configuration, in which the observed quantity is the modulation depth in the differential transmission 17 ( T /T); details of the experimental setup are provided in the Methods section. Figure 1a shows T /T dynamics of SWNTs grown by the high-pressure carbon monoxide procedure dispersed in polymethylmethacrylate films following excitation with a sub-10-fs visible pulse (1.8-2.4 eV bandwidth), probed at an energy of 2.1 eV. The signal exhibits an initial photobleaching, which quickly turns into photoinduced absorption (PA). The fast photobleaching decay is ascribed to relaxation of the higher-lying exciton (second in an increasing energy scale) to the lower one, taking place with a 40-fs time constant 18 . The PA signal is generated by this lower exciton 4,5 and decays on the ps timescale, in agreement with previous results [19][20][21] . As shown in Fig. 1a, there is a clear oscillation in the T /T amplitude. The Fourier transform (FT) of the oscillatory component (Fig. 2a) shows a strong peak at 252 cm −1 (132-fs period). This frequency can be recognized as the RBM...

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We derive underdamped evolution equations for the order-parameter (OP ) strains of a ferroelastic material undergoing a structural transition, using Lagrangian variations with Rayleigh dissipation, and a free energy as a polynomial expansion in the N = n + Nop symmetry-adapted strains. The Nop strain equations are structurally similar in form to the Lagrange-Rayleigh 1D strain dynamics of Bales and Gooding (BG), with 'strain accelerations' proportional to a Laplacian acting on a sum of the free energy strain derivative and frictional strain force. The tensorial St. Venant's elastic compatibility constraints that forbid defects, are used to determine the n non-order-parameter strains in terms of the OP strains, generating anisotropic and long-range OP contributions to the free energy, friction and noise. The same OP equations are obtained by either varying the displacement vector components, or by varying the N strains subject to the Nc compatibility constraints. A Fokker-Planck equation, based on the BG dynamics with noise terms, is set up. The BG dynamics corresponds to a set of nonidentical nonlinear (strain) oscillators labeled by wavevector k, with competing short-and long-range couplings. The oscillators have different 'strain-mass' densities ρ(k) ∼ 1/k 2 and dampings ∼ 1/ρ(k) ∼ k 2 , so the lighter large-k oscillators equilibrate first, corresponding to earlier formation of smaller-scale oriented textures. This produces a sequential-scale scenario for post-quench nucleation, elastic patterning, and hierarchical growth. Neglecting inertial effects yields a late-time dynamics for identifying extremal free energy states, that is of the time-dependent Ginzburg-Landau form, with nonlocal, anisotropic Onsager coefficients, that become constants for special parameter values. We consider in detail the two-dimensional (2D) unit-cell transitions from a triangular to a centered rectangular lattice (Nop = 2, n = 1, Nc = 1); and from a square to a rectangular lattice (Nop = 1, n = 2, Nc = 1) for which the OP compatibility kernel is retarded in time, or frequencydependent in Fourier space (in fact, acoustically resonant in ω/k). We present structural dynamics for all other 2D symmetry-allowed ferroelastic transitions: the procedure is also applicable to the 3D case. Simulations of the BG evolution equations confirm the inherent richness of the static and dynamic texturings, including strain oscillations, domain-wall propagation at near sound speeds, grain-boundary motion, and nonlocal 'elastic photocopying' of imposed local stress patterns.

We study the equilibrium phase diagram of ultrathin chiral magnets with easy-plane anisotropy A. The vast triangular skyrmion lattice phase that is stabilized by an external magnetic field evolves continuously as a function of increasing A into a regime in which nearest-neighbor skyrmions start overlapping with each other. This overlap leads to a continuous reduction of the skyrmion number from its quantized value Q = 1 and to the emergence of antivortices at the center of the triangles formed by nearest-neighbor skyrmions. The antivortices also carry a small "skyrmion number" Q A 1 that grows as a function of increasing A. The system undergoes a first order phase transition into a square vortex-antivortex lattice at a critical value of A. Finally, a canted ferromagnetic state becomes stable through another first order transition for a large enough anisotropy A. Interestingly enough, this first order transition is accompanied by metastable meron solutions.

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