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Until the late 1980s, phases of matter were understood in terms of Landau's symmetry breaking theory. Following the discovery of the quantum Hall effect the introduction of a second class of phases, those with topological order, was…
The quantum anomalous Hall effect has been theoretically predicted and experimentally verified in magnetic topological insulators. In addition, the surface states of these materials exhibit a hedgehog-like "spin" texture in momentum space.…
We consider spin-polarized electrons in a single Landau level on a cylinder as the circumference of the cylinder goes to infinity. This gives a model of interacting electrons on a circle where the momenta of the particles are restricted and…
The flow of electric current through a two-dimensional material in a magnetic field gives rise to the family of Hall effects. The quantum versions of these effects accommodate robust electronic edge channels and fractional charges.…
Skyrmions with the topological number $Q$ equal an integer larger than 1 are called high-topological-number skyrmions or high-$Q$ skyrmions. In this work, we theoretically study the topological Hall effect in square-lattice high-$Q$…
Skyrmions in condensed matter physics appear as classical topological spin structures. This nontrivial state can be obtained solving the corresponding micromagnetic model, where the magnetization is treated as a continuous classical vector…
Since the 1950s Heisenberg and others have attempted to explain the appearance of countable particles in quantum field theory in terms of stable localized field configurations. As an exception Skyrme's model succeeded to describe nuclear…
The transition from the quantum to the classical regime of the nucleation of the closed Robertson-Walker Universe with spacially homogeneous matter fields is investigated with a perturbation expansion around the sphaleron configuration. A…
Topological order is important in many aspects of condensed matter physics, and has been extended to bosonic systems. In this Letter we report on the nontrivial topology of the magnon bands in two distinct quantum skyrmion crystals…
We have investigated the effect of weak disorder on the ground state of a two dimensional electron gas in the quantum Hall regime at filling factors slightly deviating from unity. The skyrmions and antiskyrmions are found to be present even…
Quantum Hall skyrmions are quantized solitons of a ferromagnetic O(3) sigma-model. The reference, classical, solutions depend upon the interaction between the electrons and exhibit completely different asymptotic profiles for the physical…
Skyrmions are topological magnetic textures that can arise in non-centrosymmetric ferromagnetic materials. In most systems experimentally investigated to date, skyrmions emerge as classical objects. However, the discovery of skyrmions with…
A quantum system can undergo a continuous phase transition at the absolute zero of temperature as some parameter entering its Hamiltonian is varied. These transitions are particularly interesting for, in contrast to their classical finite…
We study the structure and elastic energy of the ground states of crystalline caps conforming to a spherical surface. These ground states consist of positive disclination defects in structures spanning from flat and weakly curved crystals…
We derive the the long-wavelength elastic theory for the quantum Hall smectic state starting from the Hartree-Fock approximation. Dislocations in this state lead to an effective nematic model for $T>0$, which undergoes a disclination…
The skyrmion crystal is a periodic array of a swirling topological spin texture. Since it is regarded as an interference pattern by multiple helical spin density waves, the texture changes with the relative phases among the constituent…
Quantum skyrmionic phase is modelled in a 2D helical spin lattice. This topological skyrmionic phase retains its nature in a large parameter space before moving to a ferromagnetic phase. Next nearest-neighbour interaction improves the…
It is commonly assumed in the studies of the fractional quantum Hall effect that the physics of a fractional quantum Hall state, in particular the character of its excitations, is invariant under a continuous deformation of the Hamiltonian…
The natures of the ground state in a $\nu_{\rm T}=1$ bilayer quantum Hall system at a variety of layer spacing are investigated. At small layer separations the system exhibits spontaneous interlayer phase coherence. It is claimed that the…
Using both atomistic and particle-based simulations, we investigate the current-driven dynamics of skyrmions on two-dimensional periodic substrates when there are multiple skyrmions per substrate minimum. At zero drive, the system forms…