Unconventional superconductivity often arises from Cooper pairing between neighboring atomic sites, stipulating a characteristic pairing symmetry in the reciprocal space. The twisted bilayer graphene (TBG) presents a new setting where superconductivity emerges on the flat bands whose Wannier wavefunctions spread over many graphene unit cells, forming the so-called Moiré pattern. To unravel how Wannier states form Cooper pairs, we study the interplay between electronic, structural, and pairing instabilities in TBG. For comparisons, we also study graphene on boron-nitride (GBN) possessing a different Moiré pattern, and single-layer graphene (SLG) without a Moiré pattern. For all cases, we compute the pairing eigenvalues and eigenfunctions by solving a linearized superconducting gap equation, where the spin-fluctuation mediated pairing potential is evaluated from materials specific tight-binding band structures. We find an extended s-wave as the leading pairing symmetry in TBG, in which the nearest-neighbor Wannier sites form Cooper pairs with same phase. In contrast, GBN assumes a p + ip-wave pairing between nearest-neighbor Wannier states with odd-parity phase, while SLG has the d + id-wave symmetry for inter-sublattice pairing with even-parity phase. Moreover, while p + ip, and d + id pairings are chiral, and nodeless, but the extended s-wave channel possesses accidental nodes. The nodal pairing symmetry makes it easily distinguishable via power-law dependencies in thermodynamical entities, in addition to their direct visualization via spectroscopies.

The growth was monitored by in-situ RHEED (reflection high energy electron diffraction). Fig. S1(a) shows the time dependence of intensity of specular reflection (0,0), recorded during the growth of NdNiO 3 (NNO) film on NdGaO 3 (NGO) substrate and layer-by-layer growth has been confirmed by the sharp drops during ablation and gradual recovery within next few seconds to the same level of intensity after the deposition of each unit cell. Inset of Fig. S1(b) shows RHEED pattern for the NNO film, recorded after cooling to room temperature. The streak patterns of specular and off-specular: (0 1), (0-1) reflections (in pseudo cubic (p.c.) notation) confirm the desired two-dimensional surface morphology. X-ray diffraction: Success of epitaxial growth along [0 0 1] p.c. has been further confirmed by 2θ-ω scan in X-ray diffraction (Fig. S1(b)). Each diffraction pattern consists of a sharp substrate peak, a broad film peak (indicated by solid triangle in Fig. S1(b)) and thickness fringes, arises due to the finite thickness of film. Out-of plane lattice constant (c p.c. of NNO films are found to be 3.75Å (STO), 3.78Å (NGO), 3.83Å (SPGO), 3.84Å (SLAO) and 3.86Å (YAO) and these follow the expected tetragonal distortion relation for the cube on cube growth.

We report a theoretical prediction of a new class of bulk and intrinsic quantum Anomalous Hall (QAH) insulators LaX (X=Br, Cl, and I) via relativistic first-principle calculations. We find that these systems are innate long-ranged ferromagnets which, with the help of intrinsic spin-orbit coupling, become QAH insulators. A low-energy multiband tight binding model is developed to understand the origin of the QAH effect. Finally integer Chern number is obtained via Berry phase computation for each two-dimensional plane. These materials have the added benefit of a sizable band gap of as large as ∼ 25 meV, with the flexibility of enhancing it to above 75 meV via strain engineering. The synthesis of LaX materials will provide the impurity-free single crystals and thin-film QAH insulators for versatile experiments and functionalities.

The relative twist angle in heterostructures of two-dimensional (2D) materials with similar lattice constants result in a dramatic alteration of the electronic properties. Here, we investigate the electrical and magnetotransport properties in bilayer graphene (BLG) encapsulated between two hexagonal boron nitride (hBN) crystals, where the top and bottom hBN are rotationally aligned with bilayer graphene with a twist angle θt ∼ 0 • and θ b < 1 • , respectively. This results in the formation of two moiré superlattices, with the appearance of satellite resistivity peaks at carrier densities ns1 and ns2, in both hole and electron doped regions, together with the resistivity peak at zero carrier density. Furthermore, we measure the temperature(T) dependence of the resistivity (ρ). The resistivity shows a linear increment with temperature within the range 10K to 50K for the density regime ns1 < n < ns2 with a large slope dρ/dT ∼ 8.5 Ω/K. The large slope of dρ/dT is attributed to the enhanced electron-phonon coupling arising due to the suppression of Fermi velocity in the reconstructed minibands, which was theoretically predicted, recently in doubly aligned graphene with top and bottom hBN. Our result establishes the uniqueness of doubly aligned moire system to tune the strength of electron-phonon coupling and to modify the electronic properties of multilayered heterostructures.

The recent discovery of two-dimensional (2D) van der Waals magnets is a crucial turning point in the quantum magnet research field, since quantum fluctuations and experimental difficulties often elude stable magnetic orders in two dimensions. This opens new doors to delve for novel quantum and topological spin configurations, which may or may not have direct analogs in bulk counterparts. Here we study a twisted bilayer geometry of 2D magnets in which long-range spin-spin interactions naturally commence along the interlayer Heisenberg (J ⊥ ) and dipole-dipole (J D ) channels. The J ⊥ -J D parameter space unveils a hierarchy of distinct skyrmion phases, including point-, rod-, and ring-shaped topological charge distributions. Furthermore, we predict a topological antiferroelectric phase, where oppositely charged antiskyrmion pairs are formed, and the corresponding topological dipole moments become ordered in a Néel-like state-hence dubbed the topological antiferroelectric state. The results indicate that the twisted magnetic layer provides a versatile setting to engineer and tune a plethora of skyrmion phases and their dynamics.