Recent experiments on twisted bilayer graphene show an anomalous quantum Hall (AQH) effect at filling of $3$ electrons per moirè unit cell. The AQH effect arises in an insulating state with both valley- and ferromagnetic order. We argue, that weak doping of such a system leads to the formation of a novel topological spin texture, a `double-tetarton lattice'. The building block of this lattice, the `double-tetarton', is a spin configuration which covers $1/4$ of the unit-sphere twice. In contrast to skyrmion lattices, the net magnetization of this magnetic texture vanishes. Only at large magnetic fields more conventional skyrmion lattices are recovered. But even for large fields the addition of a single charge to the ferromagnetic AQH state flips hundreds of spins. Our analysis is based on the investigation of an effective non-linear sigma model which includes the effects of long-ranged Coulomb interactions.
We theoretically study a stabilization mechanism of the skyrmion crystal in centrosymmetric magnets with a bilayer structure. We show that the interplay between a layer-dependent staggered Dzyaloshinskii-Moriya interaction that arises from the absence of local inversion symmetry and the interlayer exchange interaction gives rise to a plethora of multiple-$Q$ states including the skyrmion crystal with a quantized topological number. By performing the simulated annealing for the bilayer triangular-lattice model under an external magnetic field, we demonstrate that the skyrmion forms the triangul…
Motivated by recent low-temperature magnetoresistance measurements in twisted bilayer graphene aligned with hexagonal Boron Nitride substrate, we perform a systematic study of possible symmetry breaking orders in this device at a filling of two electrons per Moiré unit cell. We find that the surprising non-monotonic dependence of the resistance on an out-of-plane magnetic field is difficult to reconcile with particle-hole charge carriers from the low-energy bands in symmetry broken phases. We invoke the non-zero Chern numbers of the twisted bilayer graphene flat bands to argue that skyrmion te…
We theoretically propose a new stabilization mechanism of a skyrmion crystal (SkX) in a bilayer triangular lattice system consisting of the ferromagnetic and the antiferromagnetic layers. By performing variational calculations and Monte Carlo simulations in a complementary way, we find that a magnetic frustration between the ferromagnetic and antiferromagnetic layers is a source of a finite-Q spiral state and the SkX in the strong interlayer coupling regime. We also show that the degree of frustration is related to the interlayer exchange interaction. The stronger interlayer coupling tends to …
We analyze bilayer quantum Hall ferromagnets, whose underlying symmetry group is SU(4). Spin-pseudospin coherence develops spontaneously when the total electron density is low enough. Quasiparticles are CP^3 skyrmions. One skyrmion induces charge modulations on both of the two layers. At the filling factor$ν=2/m$ one elementary excitation consists of a pair of skyrmions and its charge is $2e/m$. Recent experimental data due to Sawada et al. [Phys. Rev. Lett. {\bf 80}, 4534 (1998)] support this conclusion.
Quantum Hall states that result from interaction induced lifting of the eight-fold degeneracy of the zeroth Landau level in bilayer graphene are considered. We show that at even filling factors electric charge is injected into the system in the form of charge $2e$ skyrmions. This is a rare example of binding of charges in a system with purely repulsive interactions. We calculate the skyrmion energy and size as a function of the Zeeman interaction, and discuss signatures of the charge $2e$ skyrmions in the scanning tunneling microscopy experiments.
Arising from emergent electromagnetic field of magnetic skyrmions due to their nontrivial topology, the skyrmion Hall effect might be a roadblock for practical applications since any longitudinal motions of skyrmions in nanotrack is accompanied by a transverse motion. A direct consequence of such an effect is easy destruction of skyrmions at the nanotrack edges during their fast motions along the nanotrack, despite their topological protection. Here we propose an entirely novel solution of completely inhibiting such skyrmion Hall effect without affecting its topological properties based on a a…
By tilting the samples in the magnetic field, we measured and compared the Skyrmion excitations in the bilayer quantum Hall (QH) state at the Landau-level filling factor $ν=2$ and in the monolayer QH state at $ν=1$. The observed number of flipped spins is $N_s=14$ in the bilayer system with a large tunneling gap, and $N_s=7$ in the bilayer system with a small tunneling gap, while it is $N_s=7$ in the monolayer system. The difference is interpreted due to the interlayer exchange interaction. Moreover, we have observed seemingly preferred numbers $N_s=14,7,1$ for the flipped spins by tilting bil…
We investigate the dynamics of two skyrmions lying in distinct layers of an antiferromagnetic bilayer system, consisting of nanostripes with the shape of racetracks. The top and bottom nanostripes are separated by a height offset and they are coupled through a ferromagnetic exchange, allowing the interaction between the skyrmions from both layers. Depending on the distance between the skyrmions they attract each other sufficiently to achieve a bound state. We also analyze their dynamics when an electric current is applied in a unique layer and we determine how the bound-state nucleation depend…
We present a comprehensive theory of the magnetic phases in twisted bilayer Cr-trihalides through a combination of first-principles calculations and atomistic simulations. We show that the stacking-dependent interlayer exchange leads to an effective moiré field that is mostly ferromagnetic with antiferromagnetic patches. A wide range of noncollinear magnetic phases can be stabilized as a function of the twist angle and Dzyaloshinskii-Moriya interaction as a result of the competing interlayer antiferromagnetic coupling and the energy cost for forming domain walls. In particular, we demonstrate …
We show that the electric charge of the Skyrmion in the vector order parameters that characterize the quantum anomalous spin Hall state and the layer-antiferromagnet in a graphene bilayer is four and zero, respectively. The result is based on the demonstration that a vortex configuration in two broken symmetry states in bilayer graphene with the quadratic band crossing has the number of zero modes doubled relative to the single layer. The doubling can be understood as a result of Kramers' theorem implied by the "pseudo time reversal" symmetry of the vortex Hamiltonian. Disordering the quantum …
The advent of Moiré materials has galvanized interest in the nature of charge carriers in topological bands. In contrast to conventional materials where charge carriers are electron-like quasiparticles, topological bands allow for more exotic possibilities where charge is carried by nontrivial topological textures, such as skyrmions. However, the real space description of skyrmions is ill-suited to address the limit of small or `baby' skyrmions which consist of an electron and a few spin flips. Here, we study the formation of the smallest skyrmions -- spin polarons, formed as bound states of a…
We determined the magnetic B-T phase diagram of PdFe bilayer on Ir(111) surface by performing Monte Carlo and spin dynamics simulations based on an effective classical spin model. The parameters of the spin model were determined by ab initio methods. At low temperatures we found three types of ordered phases, while at higher temperatures, below the completely disordered paramagnetic phase, a large region of the phase diagram is associated with a fluctuation-disordered phase. Within the applied model, this state is characterized by the presence of skyrmions with finite lifetime. According to th…
We investigate quasiparticles in bilayer quantum Hall systems around total filling factor nu =1 by current-pumped and resistively detected NMR. The measured Knight shift reveals that the spin component in the quasiparticle increases continuously with $Δ_{SAS}$. Combined with results for the pseudospin component obtained by activation gap measurements, this demonstrates that both spin and pseudospin are contained in a quasiparticle at intermediate $Δ_{SAS}$, providing evidence for the existence of the spin-pseudospin intermixed SU(4) skyrmion. Nuclear spin relaxation measurements show that the …
Single-layer and Bilayer of graphene are new classes of two-dimensional electron systems with unconventional band structures and valley degrees of freedom. The ground states and excitations in the integer and fractional quantum Hall regimes are investigated on torus and spherical geometries with the use of the density matrix renormalization group (DMRG) method. At nonzero Landau level indices, the ground states at effective filling factors 1, 1/3, 2/3 and 2/5 are valley polarized both in single-layer and bilayer graphenes. We examine the elementary charge excitations which could couple with th…
Synthetic quantum Hall bilayer (SQHB), realized by optically driven monolayer graphene in the quantum Hall regime, provides a flexible platform for engineering quantum Hall phases as discussed in [Phys. Rev. Lett. 119, 247403]. The coherent driving which couples two Landau levels mimicks an effective tunneling between synthetic layers. The tunneling strength, the effective Zeeman coupling, and two-body interaction matrix elements are tunable by varying the driving frequency and the driving strength. Using infinite density matrix renormalization group (iDMRG) techniques combined with exact diag…
We discuss charged topological spin textures in quantum Hall ferromagnets in which the electrons carry a pseudospin as well as the usual spin degree of freedom, as is the case in bilayer GaAs or monolayer graphene samples. We develop a theory which treats spin and pseudospin on a manifestly equal footing, which may also be of help in visualizing the relevant spin textures. We in particular consider the entanglement of spin and pseudospin in the presence of realistic anisotropies. An entanglement operator is introduced which generates families of degenerate Skyrmions with differing entanglement…
Recent experiments on twisted bilayer graphene have shown a high-temperature parent state with massless Dirac fermions and broken electronic flavor symmetry; superconductivity and correlated insulators emerge from this parent state at lower temperatures. We propose that the superconducting and correlated insulating orders are connected by Wess-Zumino-Witten terms, so that defects of one order contain quanta of another order and skyrmion fluctuations of the correlated insulator are a "mechanism" for superconductivity. We present a comprehensive listing of plausible low-temperature orders, and t…
Electron transport coupled with magnetism has attracted attention over the years as exemplified in anomalous Hall effect due to a Berry phase in momentum space. Another type of unconventional Hall effect -- topological Hall effect, originating from the real-space Berry phase, has recently become of great importance in the context of magnetic skyrmions. We have observed topological Hall effect in bilayers consisting of ferromagnetic SrRuO$_3$ and paramagnetic SrIrO$_3$ over a wide region of both temperature and magnetic field. The topological term rapidly decreases with the thickness of SrRuO$_…
Tuning the magnetic properties of Kitaev materials via the antiferromagnetic proximity effect: Novel phases and application to an $α$-RuCl$_3$/MnPS$_3$ bilayer
When quantum flavor Hall insulator phases of itinerant fermions are disordered by strong quantum fluctuations, the condensation of skyrmion textures of order parameter fields can lead to superconductivity. In this work, we address the mechanism of skyrmion condensation by considering the scattering between (2+1)-dimensional, Weyl fermions and hedgehog type tunneling configurations of order parameters that violate the skyrmion-number conservation law. We show the quantized, flavor Hall conductivity ($σ^f_{xy}$) controls the degeneracy of topologically protected, fermion zero-modes, localized on…
We study in this paper effects of Dzyaloshinskii-Moriya (DM) magnetoelectric coupling between ferroelectric and magnetic layers in a superlattice formed by alternate magnetic and ferroelectric films.Magnetic films are films of simple cubic lattice with Heisenberg spins interacting with each other via an exchange $J$ and a DM interaction with the ferroelectric interface. Electrical polarizations of $\pm{1}$ are assigned at simple cubic lattice sites in the ferroelectric films.We determine the ground-state (GS) spin configuration in the magnetic film. In zero field, the GS is periodically non co…
The effects of spin-orbit coupling and symmetry breaking at the interface between a ferromagnet and heavy metal are particularly important for spin-based information storage and computation. Recent discoveries suggest they can create chiral spin structures (e.g. skyrmions), which have often been identified through the appearance of the bump/dip features of Hall signals, the so-called topological Hall effect (THE). In this work, however, we have present an unusual anomalous Hall effect (UAHE) in MnxGa/Pt bilayers and demonstrated that the features extremely similar to THE can be generated witho…
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 $l_\text{TF}$ is much larger than monolayer graphene's lattice spacing $l_g \ll l_\text{TF}$ and much smaller than the Moiré super lattice's spacing $ l_\text{TF} \ll l_{\text{Moiré}}$. We show that in the perfectly flat band "chiral" limit and at filling fractions $\pm 3/4$, the saturated ferromagnetic (spin and valley polarized) states are ideal ground states candidat…
Twisted double- and mono-bilayer graphene are graphene-based moiré materials hosting strongly correlated fermions in a gate-tunable conduction band with a topologically non-trivial character. Using unbiased exact diagonalization complemented by unrestricted Hartree-Fock calculations, we find that the strong electron-electron interactions lead to a non-coplanar magnetic state, which has the same symmetries as the tetrahedral antiferromagnet on the triangular lattice and can be thought of as a skyrmion lattice commensurate with the moiré scale, competing with a set of ferromagnetic, topological …
We develop a comprehensive theory of twisted bilayer magnetism. Starting from the first-principles calculations of two-dimensional honeycomb magnet CrI3, we construct the generic spin models that represent a broad class of twisted bilayer magnetic systems. Using Monte-Carlo method, we discover a variety of non-collinear magnetic orders and topological magnons that have been overlooked in the previous theoretical and experimental studies. As a function of the twist angle, the collinear magnetic order undergoes the phase transitions to the non-collinear order and the magnetic domain phase. In th…
The emergence of alternating twist multilayer graphene (ATMG) as a generalization of twisted bilayer graphene (TBG) raises the question - in what important ways do these systems differ? Here, we utilize ab-initio relaxation and single-particle theory, analytical strong coupling analysis, and Hartree-Fock to contrast ATMG with $n=3,4,5,\ldots$ layers and TBG. $\textbf{I}$: We show how external fields enter in the decomposition of ATMG into TBG and graphene subsystems. The parallel magnetic field has little effect for $n$ odd due to mirror symmetry, but surprisingly also for any $n > 2$ if we ar…
Superconductivity of Incoherent Electrons near the Relativistic Mott Transition in Twisted Dirac Materials
Institute for Theory of Condensed Matter, Karlsruhe Institute of Technology（凝聚态理论研究所，卡尔斯鲁厄理工学院）；Institute for Theoretical Physics III, University of Stuttgart（理论物理第三研究所，斯图加特大学）；Department of Physics and Astronomy, Louisiana State University（物理与天文系，路易斯安那州立大学）；Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology（量子材料与技术研究所，卡尔斯鲁厄理工学院）
