We study the dynamics of skyrmions in Dzyaloshinskii-Moriya materials with easy-axis anisotropy. An important link between topology and dynamics is established through the construction of unambiguous conservation laws obtained earlier in connection w
ith magnetic bubbles and vortices. In particular, we study the motion of a topological skyrmion with skyrmion number $Q=1$ and a non-topological skyrmionium with $Q=0$ under the influence of an external field gradient. The $Q=1$ skyrmion undergoes Hall motion perpendicular to the direction of the field gradient with a drift velocity proportional to the gradient. In contrast, the non-topological $Q=0$ skyrmionium is accelerated in the direction of the field gradient, thus exhibiting ordinary Newtonian motion. When the external field is switched off the $Q=1$ skyrmion is spontaneously pinned around a fixed guiding center, whereas the $Q=0$ skyrmionium moves with constant velocity $v$. We give a systematic calculation of a skyrmionium traveling with any constant velocity $v$ that is smaller than a critical velocity $v_c$.
Photons and excitons in a semiconductor microcavity interact to form exciton-polariton condensates. These are governed by a nonlinear quantum-mechanical system involving exciton and photon wavefunctions. We calculate all non-traveling harmonic solito
n solutions for the one-dimensional lossless system. There are two frequency bands of bright solitons when the inter-exciton interactions produce an attractive nonlinearity and two frequency bands of dark solitons when the nonlinearity is repulsive. In addition, there are two frequency bands for which the exciton wavefunction is discontinuous at its symmetry point, where it undergoes a phase jump of pi. A band of continuous dark solitons merges with a band of discontinuous dark solitons, forming a larger band over which the soliton far-field amplitude varies from zero to infinity; the discontinuity is initiated when the operating frequency exceeds the free exciton frequency. The far fields of the solitons in the lowest and highest frequency bands (one discontinuous and one continuous dark) are linearly unstable, whereas the other four bands have linearly stable far fields, including the merged band of dark solitons.
Bose-Einstein condensates of exciton-polaritons are described by a Schrodinger system of two equations. Nonlinearity due to exciton interactions gives rise to a frequency band of dark soliton solutions, which are found analytically for the lossless z
ero-velocity case. The solitons far-field value varies from zero to infinity as the operating frequency varies across the band. For positive detuning (photon frequency higher than exciton frequency), the exciton wavefunction becomes discontinuous when the operating frequency exceeds the exciton frequency. This phenomenon lies outside the parameter regime of validity of the Gross-Pitaevskii (GP) model. Within its regime of validity, we give a derivation of a single-mode GP model from the initial Schrodinger system and compare the continuous polariton solitons and GP solitons using the healing length notion.
A vortex-antivortex dipole can be generated due to current with in-plane spin-polarization, flowing into a magnetic element, which then behaves as a spin transfer oscillator. Its dynamics is analyzed using the Landau-Lifshitz equation including a Slo
nczewski spin-torque term. We establish that the vortex dipole is set in steady state rotational motion due to the interaction between the vortices, while an external in-plane magnetic field can tune the frequency of rotation. The rotational motion is linked to the nonzero skyrmion number of the dipole. The spin-torque acts to stabilize the vortex dipole at a definite vortex-antivortex separation distance. In contrast to a free vortex dipole, the rotating pair under spin-polarized current is an attractor of the motion, therefore a stable state. Three types of vortex-antivortex pairs are obtained as we vary the external field and spin-torque strength. We give a guide for the frequency of rotation based on analytical relations.
The use of coherent optical dressing of atomic levels allows the coupling of ultracold atoms to effective gauge fields. These can be used to generate effective magnetic fields, and have the potential to generate non-Abelian gauge fields. We consider
a model of a gas of bosonic atoms coupled to a gauge field with U(2) symmetry, and with constant effective magnetic field. We include the effects of weak contact interactions by applying Gross-Pitaevskii mean-field theory. We study the effects of a U(2) non-Abelian gauge field on the vortex lattice phase induced by a uniform effective magnetic field, generated by an Abelian gauge field or, equivalently, by rotation of the gas. We show that, with increasing non-Abelian gauge field, the nature of the groundstate changes dramatically, with structural changes of the vortex lattice. We show that the effect of the non-Abelian gauge field is equivalent to the introduction of effective interactions with non-zero range. We also comment on the consequences of the non-Abelian gauge field for strongly correlated fractional quantum Hall states.
A vortex-antivortex (VA) dipole may be generated due to a spin-polarized current flowing through a nano-aperture in a magnetic element. We study the vortex dipole dynamics using the Landau-Lifshitz equation in the presence of an in-plane applied magn
etic field and a Slonczewski spin-torque term with in-plane polarization. We establish that the vortex dipole is set in steady state rotational motion. The frequency of rotation is due to two independent forces: the interaction between the two vortices and the external magnetic field. The nonzero skyrmion number of the dipole is responsible for both forces giving rise to rotational dynamics. The spin-torque acts to stabilize the vortex dipole motion at a definite vortex-antivortex separation distance. We give analytical and numerical results for the angular frequency of rotation and VA dipole features as functions of the parameters.
