Charge-transfer insulation in twisted bilayer graphene

We studied the real space structure of states in twisted bilayer graphene at the `magic angle' $\theta = 1.08^\circ$. The flat bands close to charge neutrality are composed of a mix of `ring' and `center' orbitals around the AA stacking region. An effective model with localized orbitals is constructed, which necessarily includes more than just the four flat bands. Long-range Coulomb interaction causes a charge-transfer at half-filling of the flat bands from the `center' to the `ring' orbitals. Consequently, the Mott phase is a featureless spin-singlet paramagnet. We estimate the effective Heisenberg coupling that favors the singlet coupling to be $J = 3.3$ K, consistent with experimental values. The superconducting state depends on the nature of the dopants: hole-doping yields $p+ip$-wave whereas electron-doping yields $d+id$-wave pairing symmetry.Comment: 8 pages, 6 figures. This second version contains more detailed computations on the Coulomb energy from the unequal charge distributio

Unpaired Majorana modes on dislocations and string defects in Kitaev's honeycomb model

We study the gapped phase of Kitaev's honeycomb model (a $Z_2$ spin liquid) on a lattice with topological defects. We find that some dislocations and string defects carry unpaired Majorana fermions. Physical excitations associated with these defects are (complex) fermion modes made out of two (real) Majorana fermions connected by a $Z_2$ gauge string. The quantum state of these modes is robust against local noise and can be changed by winding a $Z_2$ vortex around one of the dislocations. The exact solution respects gauge invariance and reveals a crucial role of the gauge field in the physics of Majorana modes. To facilitate these theoretical developments, we recast the degenerate perturbation theory for spins in the language of Majorana fermions.Comment: 15 pages, 7 figures; added a brief history of twists, references, and clarified the count of the topological degeneracy of the ground stat

Projective symmetry of partons in Kitaev's honeycomb model

Low-energy states of quantum spin liquids are thought to involve partons living in a gauge-field background. We study the spectrum of Majorana fermions of Kitaev's honeycomb model on spherical clusters. The gauge field endows the partons with half-integer orbital angular momenta. As a consequence, the multiplicities reflect not the point-group symmetries of the cluster, but rather its projective symmetries, operations combining physical and gauge transformations. The projective symmetry group of the ground state is the double cover of the point group.Comment: 5 pages, 3 figure

Spin model for the Honeycomb NiPS3\rm NiPS_3

In the Van der Waal material $\rm NiPS_3$, Ni atoms have spin S=1 and realize a honeycomb lattice. Six sulfur atoms surround each Ni and split their d manifold into three filled and two unfilled bands. Aimed to determine the spin Hamiltonian of $\rm NiPS_3$, we study its exchange mechanisms using a two-band half-filled Hubbard model. Hopping between d orbitals is mediated by p orbitals of sulfur and gives rise to bilinear and biquadratic spin couplings in the limit of strong electronic correlations. The microscopic model exposed a ferromagnetic biquadratic spin interaction $\rm K_1$ allowing the completion of a minimal $\rm J_1-J_3-K_1$ spin Hamiltonian for $\rm NiPS_3$. In bulk, a ferromagnetic first nearest neighbor $\rm J_1$ and a more significant antiferromagnetic third nearest neighbor spin coupling $\rm J_3$ agreed with the literature, while in monolayer $\rm J_1$ is positive and very small in comparison. Using a variational scheme we found that a zig-zag antiferromagnetic order is the ground state of bulk samples. The zig-zag pattern is adjacent to commensurate and incommensurate spin spirals, which could hint at the puzzling results reported in $\rm NiPS_3$ monolayers.Comment: 6 pages, 3 figures, 2 table

Photoinduced Floquet topological magnons in Kitaev magnets

We study periodically driven pure Kitaev model and ferromagnetic phase of the Kitaev-Heisenberg model on the honeycomb lattice by off-resonant linearly and circularly-polarized lights at zero magnetic field. Using a combination of linear spin wave and Floquet theories, we show that the effective time-independent Hamiltonians in the off-resonant regime map onto the corresponding anisotropic static spin model, plus a tunable photoinduced magnetic field along the $[111]$ direction, which precipitates Floquet topological magnons and chiral magnon edge modes. They are tunable by the light amplitude and polarization. Similarly, we show that the thermal Hall effect induced by the Berry curvature of the Floquet topological magnons can also be tuned by the laser field. Our results pave the way for ultrafast manipulation of topological magnons in irradiated Kitaev magnets, and could play a pivotal role in the investigation of ultrafast magnon spin current generation in Kitaev materials.Comment: 7 pages, 5 figures + Supplemental Materia

Mechanical response of a self avoiding membrane: fold collisions and the birth of conical singularities

An elastic membrane that is forced to reside in a container smaller than its natural size will deform and, upon further volume reduction, eventually crumple. The crumpled state is characterized by the localization of energy in a complex network of highly deformed crescent-like regions joined by line ridges. Previous studies have focused on the onset of the crumpled state by analyzing the mechanical response and stability of a conical dislocation, while others have simulated the highly packed regime neglecting the importance of the connectivity of the membrane. Here we show, through a combination of experiments, numerical simulations, and analytic approach, that the emergence of new regions of high stretching is a generic outcome when a self avoiding membrane is subject to a severe geometrical constraint. We demonstrate that, at moderate packing fraction, interlayer interactions produce a response equivalent to the one of a thicker membrane that has the shape of the deformed one. Evidence is found that friction plays a key role stabilizing the folded structures.Comment: 10 page