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We investigate twisted double bilayer graphene (TDBG), a four-layer system composed of two AB-stacked graphene bilayers rotated with respect to each other by a small angle. Our ab initio band structure calculations reveal a considerable energy gap at the charge point neutrality that we assign to the intrinsic symmetric polarization (ISP). We then introduce the ISP effect into the tight-binding parameterization and perform calculations on TDBG models that include lattice relaxation effects down to very small twist angles. We identify a narrow region around the magic angle $\theta^\circ = 1.3^{\circ}$ characterized by a manifold of remarkably flat bands gapped out from other states even without external electric fields. To understand the fundamental origin of the magic angle in TDBG, we construct a continuum model that points to a hidden mathematical link to the twisted bilayer graphene (TBG) model, thus indicating that the band flattening is a fundamental feature of TDBG, and is not a result of external fields., Comment: 5+ pages, 4 figures

When two monolayers of graphene are stacked with a small relative twist angle, the resulting band structure exhibits a remarkably flat pair of bands at a sequence of 'magic angles' where correlation effects can induce a host of exotic phases. Here, we study a class of related models of $n$-layered graphene with alternating relative twist angle $\pm \theta$ which exhibit magic angle flat bands coexisting with several Dirac dispersing bands at the Moir\'e K point. Remarkably, we find that the Hamiltonian for the multilayer system can be mapped exactly to a set of decoupled bilayers at {\it different} angles, revealing a remarkable hierarchy mathematically relating all these magic angles to the TBG case. For the trilayer case ($n = 3$), we show that the sequence of magic angle is obtained by multiplying the bilayer magic angles by $\sqrt{2}$, whereas the quadrilayer case ($n = 4$) has two sequences of magic angles obtained by multiplying the bilayer magic angles by the golden ratio $\varphi = (\sqrt{5} + 1)/2 \approx 1.62$ and its inverse. We also show that for larger $n$, we can tune the angle to obtain several narrow (almost flat) bands simultaneously and that for $n \rightarrow \infty$, there is a continuum of magic angles for $\theta \lesssim 2^o$. Furthermore, we show that tuning several perfectly flat bands for a small number of layers is possible if the coupling between different layers is different. The setup proposed here can be readily achieved by repeatedly applying the "tear and stack" method without the need of any extra tuning of the twist angle and has the advantage that the first magic angle is always larger than the bilayer case., Comment: 5.5 pages, 6 figures; published version

Twisted Bilayer graphene (TBG) is known to feature isolated and relatively flat bands near charge neutrality, when tuned to special magic angles. However, different criteria for the magic angle such as the vanishing of Dirac speed, minimal bandwidth or maximal band gap to higher bands typically give different results. Here we study a modified continuum model for TBG which has an infinite sequence of magic angles $\theta$ at which, we simultaneously find that (i) the Dirac speed vanishes (ii) absolutely flat bands appear at neutrality and (iii) bandgaps to the excited bands are maximized. When parameterized in terms of $\alpha\sim 1/\theta, $ they recur with the simple periodicity of $\Delta \alpha \simeq 3/2$, which, beyond the first magic angle, differs from earlier calculations. Further, in this model we prove that the vanishing of the Dirac velocity ensures the exact flatness of the band and show that the flat band wave functions are related to doubly-periodic functions composed of ratios of theta functions. Also, using perturbation theory up to $\alpha^8$ we capture important features of the first magic angle $\theta\approx1.09^{\circ}$ ($\alpha \approx 0.586$), which precisely explains the numerical results. Finally, based on our model we discuss the prospects for observing the second magic angle in TBG., Comment: 7 pages, 4 figures

Due to their topological protection and nanometric size, magnetic skyrmions are anticipated to form components of new high-density memory technologies. In metallic systems skyrmion manipulation is achieved easily under a low density electric current flow, although the inevitable thermal dissipation ultimately limits the energy efficacy of potential applications. On the other hand, a near dissipation-free skyrmion and skyrmion phase manipulation is expected by using electric \emph{fields}, thus meeting better the demands of an energy-conscious society. In this work on an insulating chiral magnet Cu$_{2}$OSeO$_{3}$ with magnetoelectric coupling, we use neutron scattering to demonstrate directly i) the creation of metastable skyrmion states over an extended range in magnetic field and temperature, and ii) the in-situ electric field-driven switching between topologically distinct phases; the skyrmion phase and a competing non-topological cone phase. For our accessible electric field range, the phase switching is achieved in a high temperature regime, and the remnant (E=0) metastable skyrmion state is thermally volatile with an exponential lifetime on hour timescales. Nevertheless, by taking advantage of the demonstrably longer-lived metastable skyrmion states at lower temperatures, a truly non-volatile and near dissipation-free topological phase change memory function is promised in magnetoelectric chiral magnets.

We demonstrate that light-induced heat pulses of different duration and energy can write skyrmions in a broad range of temperatures and magnetic field in FeGe. Using a combination of camera-rate and pump-probe cryo-Lorentz Transmission Electron Microscopy, we directly resolve the spatio-temporal evolution of the magnetization ensuing optical excitation. The skyrmion lattice was found to maintain its structural properties during the laser-induced demagnetization, and its recovery to the initial state happened in the sub-{\mu}s to {\mu}s range, depending on the cooling rate of the system.

Magnetic skyrmions are topologically protected spin-whirl quasiparticles currently considered as promising components for ultra-dense memory devices. In the bulk they form lattices that are stable over just a few Kelvin below the ordering temperature. This narrow stability range presents a key challenge for applications, and finding ways to tune the SkL stability over a wider phase space is a pressing issue. Here we show experimentally that the skyrmion phase in the magnetoelectric insulator ${\text{Cu}_2 \text{O} \text{Se} \text{O}_3}$ can either expand or shrink substantially depending on the polarity of a moderate applied electric field. The data are well-described by an expanded mean-field model with fluctuations that show how the electric field provides a direct control of the free energy difference between the skyrmion and the surrounding conical phase. Our finding of the direct electric field control of the skyrmion phase stability offers enormous potential for skyrmionic applications based on a magnetoelectric coupling., Comment: 7 pages, 3 figures

This paper studies the influence of electric fields on the skyrmion lattice (SkL) in insulating skyrmion compounds with weak magnetoelectric (ME) coupling. The ME coupling mechanism is an interaction between the external electric field $E$ and local magnetization in the sample. Physically, the $E$-field perturbs the spin modulation wave vectors resulting in the distortion of the SkL and the $E$-field induced shift in energy. Due to the relativistic smallness of ME coupling, the important physics is captured already in the elastic ($\propto$$E$) and inelastic ($\propto$$E^2$) responses. In this spirit, the effect of the fourth-order cubic anisotropy responsible for stabilization of the skyrmion phase is taken into account perturbatively. The shift in energy can be either positive or negative, -- depending on the direction of electric field, -- thus stabilizing or destabilizing the SkL phase. Understanding the $E$-field energetics is important from the viewpoint of creation (writing) and destruction (erasing) of skyrmion arrays over the bulk, which is paramount for developing skyrmion-based logical elements and data storage., Comment: 10 pages, 7 figures

This paper introduces a quasiequilibrium one-dimensional Bose-Einstein condensation of photons trapped in a microtube. Light modes with a cut-off frequency (a photon's "mass") interact through different processes of absorption, emission, and scattering on molecules and atoms. In this paper, we study the conditions for the one-dimensional condensation of light and the role of photon-photon interactions in the system. The technique in use is the Matsubara's Green's functions formalism modified for the quasiequilibrium system under study., Comment: 14 pages, 4 figures