Spin ice, a peculiar thermal state of a frustrated ferromagnet on the pyrochlore lattice, has a finite entropy density and excitations carrying magnetic charge. By combining analytical arguments and Monte Carlo simulations, we show that spin ice on the two-dimensional kagome lattice orders in two stages. The intermediate phase has ordered magnetic charges and is separated from the paramagnetic phase by an Ising transition. The transition to the low-temperature phase is of the three-state Potts or Kosterlitz-Thouless type, depending on the presence of defects in charge order. where D = (µ 0 /4π)µ 2 /r 3 nn is a characteristic strength of dipolar coupling, r i are spin locations,r ij = (r i − r j )/|r i − r j |, and r nn is the distance between nearest neighbors. In the absence of dipolar interactions, D = 0, and for ferromagnetic exchange, J > 0, the system is strongly frustrated because it is impossible to minimize the energy of every bond ij . In a ground state, two spins point into every tetrahedron and two point out, which is reminiscent of proton positions in water ice, where every oxygen has two protons nearby and two farther away. This ice rule is satisfied by a macroscopically large number of microstates, so that both protons in water ice and magnetic moments in spin ice can remain disordered even at low temperatures [6].Large magnetic moments (µ = 10µ B in Ho 2 Ti 2 O 7 ) make magnetic dipolar interactions between nearest neighbors comparable to exchange [7]. Together with the long-distance nature of dipolar interactions, the substantial value of D casts doubt on the usefulness of the shortrange (D = 0) model of spin ice. Yet numerical simulations show that, even after the inclusion of dipolar interactions, energy differences between states obeying the ice rule remain numerically small-so small that magnetic order induced by the dipolar interactions is expected to occur only at a rather low temperature, T ≈ 0.13D [8][9][10]. The persistent near-degeneracy of ice ground states in the presence of dipolar interactions was clarified by Castelnovo et al. [3], who introduced a "dumbbell" version of spin ice, in which magnetic dipoles are stretched into bar magnets of length a such that their poles meet at the centers of tetrahedra. The energy of the resulting model can be represented as a Coulomb interaction of magnetic charges of the dumbbells, q i = ±µ/a [3]:In this expression, Q α = i∈α q i is the sum of magnetic charges at the center of tetrahedron α. In a spin-ice state of the dumbbell model, every tetrahedron has two north and two south poles with a total magnetic charge Q α = 0, minimizing the first term in Eq. (2). As a result, no magnetic field will be generated and the magnetic dipolar energy is strictly zero. A partial cancellation occurs in the original model (1), making the Coulomb energy (2) a very good approximation. The charge of tetrahedron α, expressed in units of µ/a, iswith the plus sign for one sublattice of tetrahedra and minus for the other. Residual interactions, responsible for the fo...

Nanofibers are microstructured materials that span a broad range of applications from tissue engineering scaffolds to polymer transistors. An efficient method of nanofiber production is Rotary Jet-Spinning (RJS), consisting of a perforated reservoir rotating at high speeds along its axis of symmetry, which propels a liquid, polymeric jet out of the reservoir orifice that stretches, dries and eventually solidifies to form nanoscale fibers. We report a minimal scaling framework complemented by a semi-analytic and numerical approach to characterize the regimes of nanofiber production, leading to a theoretical model for the fiber radius consistent with experimental observations. In addition to providing a mechanism for the formation of nanofibers, our study yields a phase diagram for the design of continuous nanofibers as a function of process parameters with implications for the morphological quality of fibers.The combination of high surface area (10 3 m 2 /g), 1 mechanical flexibility, and directional strength make nanofibers an ideal platform for a diverse range of applications. [1][2][3] While nanofibers are most commonly produced using electrospinning, 4,5 we have recently demonstrated that Rotary Jet-Spinning (RJS) can be used as an alternative technique to fabricate sub-micron fibers using rotational inertial forces to extrude viscous polymer jets. 6,7,8 Our apparatus consists of a perforated reservoir containing polymer solutions attached to a motor (Fig. 1(a)). When the reservoir is spun about its axis of symmetry at a rate larger than a threshold determined by the balance between capillary and centrifugal forces, a viscous jet is ejected from a small orifice (Fig. 1(b)). This jet is thrown outwards along a spiral trajectory as solvent evaporates, owing to its relatively high surface area (Fig. 1(c-f)). While moving, it is extended by centrifugal forces (Fig. 1(g-j)) and solvent evaporates at a rate J, dependent on the diffusion coefficient D of solvent through the polymer (Fig. 1(k)). The jet travels until it reaches the walls of the stationary

Artificial spin ice has been recently implemented in two-dimensional arrays of mesoscopic magnetic wires. We propose a theoretical model of magnetization dynamics in artificial spin ice under the action of an applied magnetic field. Magnetization reversal is mediated by domain walls carrying two units of magnetic charge. They are emitted by lattice junctions when the local field exceeds a critical value Hc required to pull apart magnetic charges of opposite sign. Positive feedback from Coulomb interactions between magnetic charges induces avalanches in magnetization reversal.

We studied the real space structure of states in twisted bilayer graphene at the 'magic angle' θ = 1.08 • . 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 + ipwave whereas electron-doping yields d + id-wave pairing symmetry.

Doping twisted bilayer graphene away from charge neutrality leads to an enormous buildup of charge inhomogeneities within each Moiré unit cell. Here we show, using unbiased real-space selfconsistent Hartree calculations on a relaxed lattice, that Coulomb interactions smoothen this charge imbalance by changing the occupation of earlier identified 'ring' orbitals in the AB/BA region and 'center' orbitals at the AA region. For hole doping, this implies an increase of the energy of the states at the Γ point, leading to a further flattening of the flat bands and a pinning of the Van Hove singularity at the Fermi level. The charge smoothening will affect the subtle competition between different possible correlated phases.Studies of twisted bilayer graphene have revealed a number of striking electronic properties, 1-11 and recently culminated in the discovery of a correlated insulator and superconducting phase. 12,13 Several new experiments performed since then 14-20 have revealed new correlated and topological states, and even more theoretical works have appeared 21-61 . However, there is no consensus yet on the correct low-energy effective band-structure, let alone the relevant many-body interactions.It is well known that at fillings away from charge neutrality the electronic charge piles up in the AA regions of the Moiré unit cell. [1][2][3][4]28,48,50 The Coulomb interaction will counterbalance the formation of such large charge inhomogeneities, and is expected to significantly modify the non-interacting band dispersion. Here we study the effect of the electronic interactions on AA localization via an unbiased, self-consistent Hartree calculation.Starting from a microscopic tight-binding model on a relaxed twisted bilayer at the magic angle θ = 1.08 • at fillings at and below charge neutrality, we show that the Hartree corrections indeed cause the redistribution of charges within the unit cell. The resulting charge distribution is much smoother than that found with noninteracting theories. The smoothening itself is made possible by increasing the energy of the states at the Γ point in the Brillouin zone, which causes a further substantial flattening of the (already nearly) flat bands. Our results are qualitatively similar to earlier results based on a continuum model. 48,49 Given the tight competition between different possible correlated phases, 21,24,43 the charge transfer reported here will almost certainly affect this subtle competition.In the remainder of this paper, we first introduce our model of twisted bilayer graphene and the details of our calculation. We then present and compare the charge inhomogeneities before and after the Hartree corrections. Finally, we discuss the ramifications of our result for future theoretical modelling.The model -Our starting point is a tight-binding model of twisted bilayer graphene, 28 which builds on earlier continuum models. 6 We construct twisted bilayer graphene by starting with an AB stacked bilayer and rotating the top layer around an AB site. For a commensurate twist ...

Electric charge screening is a fundamental principle governing the behaviour in a variety of systems in nature. Through reconfiguration of the local environment, the Coulomb attraction between electric charges is decreased, leading, for example, to the creation of polaron states in solids or hydration shells around proteins in water. Here, we directly visualize the real-time creation and decay of screened magnetic charge configurations in a two-dimensional artificial spin ice system, the dipolar dice lattice. By comparing the temperature dependent occurrence of screened and unscreened emergent magnetic charge defects, we determine that screened magnetic charges are indeed a result of local energy reduction and appear as a transient minimum energy state before the system relaxes towards the predicted ground state. These results highlight the important role of emergent magnetic charges in artificial spin ice, giving rise to screened charge excitations and the emergence of exotic low-temperature configurations.

Although geometrical frustration transcends scale, it has primarily been evoked in the micro- and mesoscopic realm to characterize such phases as spin ice, liquids, and glasses and to explain the behavior of such materials as multiferroics, high-temperature superconductors, colloids, and copolymers. Here we introduce a system of macroscopic ferromagnetic rotors arranged in a planar lattice capable of out-of-plane movement that exhibit the characteristic honeycomb spin ice rules studied and seen so far only in its mesoscopic manifestation. We find that a polarized initial state of this system settles into the honeycomb spin ice phase with relaxation on multiple time scales. We explain this relaxation process using a minimal classical mechanical model that includes Coulombic interactions between magnetic charges located at the ends of the magnets and viscous dissipation at the hinges. Our study shows how macroscopic frustration arises in a purely classical setting that is amenable to experiment, easy manipulation, theory, and computation, and shows phenomena that are not visible in their microscopic counterparts.

We study the gapped phase of Kitaev's honeycomb model (a Z2 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 Z2 gauge string. The quantum state of these modes is robust against local noise and can be changed by winding a Z2 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.