Related papers: Topological Electrostatics
An integrable two-dimensional system related to certain fermion-soliton systems is studied. The self-consistent solutions of a static version of the system are obtained by using the tau function approach. The self-consistent solutions…
The discovery of zero-field fractional Chern insulators (FCIs) in moir\'e materials has attracted intense interest in the interplay between topology and correlations. Here, we demonstrate that fractionalized topological order can emerge…
We introduce a model to study magnon scattering in skyrmion crystals, sandwiched between ferromagnets which act as the source of magnons. Skyrmions are topological objects while skyrmion crystals break internal and translational symmetries,…
An electromagnetic response of a single graphene layer to a uniform, arbitrarily strong electric field $E(t)$ is calculated by solving the kinetic Boltzmann equation within the relaxation-time approximation. The theory is valid at low…
We derive effective-mass electron Hamiltonian for a N\'eel antiferromagnet in the presence of a smooth texture of the staggered magnetization. For certain locations of electron band extrema, the texture produces a peculiar and anomalously…
Topological textures in magnetically ordered materials are important case studies for fundamental research with promising applications in data science. They can also serve as photonic elements to mold electromagnetic fields endowing them…
Topological flat bands (FBs) offer an ideal platform for realizing exotic topological phases, such as fractional Chern insulators, yet their realization with both exact flatness and stable topology in local lattice models has been long…
Topological phases of matter are usually realized in deconfined phases of gauge theories. In this context, confined phases with strongly fluctuating gauge fields seem to be irrelevant to the physics of topological phases. For example, the…
Semi-metals are characterized by nodal band structures that give rise to exotic electronic properties. The stability of Dirac semi-metals, such as graphene in two spatial dimensions (2D), requires the presence of lattice symmetries, while…
Topological orbital moments can arise in non-coplanar spin structures even in the absence of spin-orbit coupling and a net topological orbital magnetization occurs for the triple-Q state and for isolated skyrmions. For atomic-scale skyrmion…
We adapt Gromov's notion of ideal-valued measures to symplectic topology, and use it for proving new results on symplectic rigidity and symplectic intersections. Furthermore, it enables us to discuss three "big fiber theorems", the…
We consider quantum error-correcting subsystem codes whose gauge generators realize a translation-invariant, free-fermion-solvable spin model. In this setting, errors are suppressed by a Hamiltonian whose terms are the gauge generators of…
In this paper, we study five-dimensional Dirac fermions of which extra-dimension is compactified on quantum graphs. We find that there is a non-trivial correspondence between matrices specifying boundary conditions at the vertex of the…
Motivated by recent results on the index of the Dirac operator D={\gamma}^{{\mu}}D_{{\mu}} of QCD on lattice and also by results on topological features of electrons and holes of 2-dimensional graphene, we compute in this paper the Index of…
We study ferromagnetism and its stability in twisted bilayer graphene. We work with a Hubbard-like interaction that corresponds to the screened Coulomb interaction in a well-defined limit where the Thomas-Fermi screening length…
In recent experiments bosonic [Atala et al., Nat. Phys. 10, 588 (2014), B. K. Stuhl et al., Science 349, 1514 (2015)] as well as fermionic ladders [M. Mancini et al., Science 349, 1510 (2015)] with a uniform flux were studied and different…
In the fermionic liquids, the Fermi surface is topologically stable,\cite{Volovik2003} which is at the origin of the applicability of the Landau theory of Fermi liquid (LFL). The LFL exists under special condition, when the Green's function…
We report on analytic and numerical studies of spin textures in quantum Hall systems using a long-wavelength effective action for the magnetic degrees of freedom derived previously. The majority of our results concern skyrmions or solitons…
In this work, we propose a new and simple model that supports Chern semimetals. These new gapless topological phases share several properties with the Chern insulators like a well-defined Chern number associated to each band, topologically…
Rhombohedral stacked multilayer graphene is an ideal platform to search for correlated electron phenomena, due to its pair of flat bands touching at zero energy and further tunability by an electric field. Furthermore, its valley-dependent…