Evidence of Orbital Ferromagnetism in Twisted Bilayer Graphene Aligned to Hexagonal Boron Nitride

Orbital Hall conductivity in a Graphene Haldane and Haldane Haldane bilayers

We investigate the orbital Hall conductivity in bilayer graphene (G/G) by modifying one or both the layers as Haldane type ([Formula: see text] : Graphene/Haldane and [Formula: see text] : Haldane/Haldane) with the inclusion of next nearest neighbour (NNN) hopping strength ([Formula: see text]) and flux (ϕ). It is observed that the low energy bands of [Formula: see text] and [Formula: see text] are isolated with a gap at charge neutrality with the next nearest neighbour (NNN) hopping term [Formula: see text]. The time reversal (TR) symmetry breaking with [Formula: see text] induces a large orbital magnetic moment ([Formula: see text]) for the [Formula: see text] band in [Formula: see text] and [Formula: see text] bilayers. This TR symmetry breaking, modulated by the [Formula: see text] strength, leads to the emergence of Orbital Ferromagnetism and Valley Orbital Magnetism within the BZ for the Haldane single layer as well for both [Formula: see text] and [Formula: see text]. We show that for the applied longitudinal electric fields, the intrinsic angular momentum ([Formula: see text]) gives the orbital current ([Formula: see text]) along a transverse direction and generates the orbital Hall conductivity (OHC). We further show that the orbital magnetic polarity leads the Haldane single layer to Orbital Chern Insulator. Interestingly, the orbital Hall conductivities are finite and exhibit a large plateau in the gap over the occupied bands. Moreover, the accumulation of orbital magnetic moment of the bands in Haldane graphene bilayer shows Orbital Hall Insulator and Orbital Chern Insulators with large plateaus. Similarly, we show that in the hetero-bilayers, one of the layers of the Haldane type generates the orbital magnetism and induces the OHC. We conclude that the isolated bands in Haldane graphene bilayers with external stimuli are of an orbital nature and have various orbital Hall phases.

Nematic versus Kekulé Phases in Twisted Bilayer Graphene under Hydrostatic Pressure

We address the precise determination of the phase diagram of magic angle twisted bilayer graphene under hydrostatic pressure within a self-consistent Hartree-Fock method in real space, including all the remote bands of the system. We further present a novel algorithm that maps the full real-space density matrix to a 4×4 density matrix based on a SU(4) symmetry of sublattice and valley degrees of freedom. We find a quantum critical point between a nematic and a Kekulé phase, and show also that our microscopic approach displays a strong particle-hole asymmetry in the weak coupling regime. We arrive then at the prediction that the superconductivity should be Ising-like in the hole-doped nematic regime, with spin-valley locking, and spin-triplet in the electron-doped regime.

Quasiperiodic Moiré Reconstruction and Modulation of Electronic Properties in Twisted Bilayer Graphene Aligned with Hexagonal Boron Nitride

Twisted van der Waals systems have emerged as intriguing arenas for exploring exotic strongly correlated and topological physics, with structural reconstruction and strain playing essential roles in determining their electronic properties. In twisted bilayer graphene aligned with hexagonal boron nitride (TBG/h-BN), the interplay between the two sets of moiré patterns from graphene-graphene (G-G) and graphene-h-BN (G-h-BN) interfaces can trigger notable moiré pattern reconstruction (MPR). Here, we present the quasiperiodic MPR in the TBG/h-BN with two similar moiré wavelengths, wherein the MPR results from the incommensurate mismatch between the wavelengths of the G-G and G-h-BN moiré patterns. The short-range, nearly ordered moiré super-superstructures deviate from moiré quasicrystal and are accompanied by inhomogeneous strain, thereby inducing spatially variable energy separations between the Van Hove singularities (VHs) in the band structures of the TBG near the magic angle. By tuning the carrier densities in our sample, correlated gaps at specific AA sites are observed, uncovering the quantum-dot-like behavior and incoherent characteristics of the AA sites in the TBG. Our findings would give new hints on the microscopic mechanisms underlying the abundant novel quantum phases in the TBG/h-BN.

Prediction of metal-free Stoner and Mott-Hubbard magnetism in triangulene-based two-dimensional polymers

Ferromagnetism and antiferromagnetism require robust long-range magnetic ordering, which typically involves strongly interacting spins localized at transition metal atoms. However, in metal-free systems, the spin orbitals are largely delocalized, and weak coupling between the spins in the lattice hampers long-range ordering. Metal-free magnetism is of fundamental interest to physical sciences, unlocking unprecedented dimensions for strongly correlated materials and biocompatible magnets. Here, we present a strategy to achieve strong coupling between spin centers of planar radical monomers in π-conjugated two-dimensional (2D) polymers and rationally control the orderings. If the π-states in these triangulene-based 2D polymers are half-occupied, then we predict that they are antiferromagnetic Mott-Hubbard insulators. Incorporating a boron or nitrogen heteroatom per monomer results in Stoner ferromagnetism and half-metallicity, with the Fermi level located at spin-polarized Dirac points. An unprecedented antiferromagnetic half-semiconductor is observed in a binary boron-nitrogen-centered 2D polymer. Our findings pioneer Stoner and Mott-Hubbard magnetism emerging in the electronic π-system of crystalline-conjugated 2D polymers.

Emergent phases in graphene flat bands

Electronic correlations in two-dimensional materials play a crucial role in stabilising emergent phases of matter. The realisation of correlation-driven phenomena in graphene has remained a longstanding goal, primarily due to the absence of strong electron-electron interactions within its low-energy bands. In this context, magic-angle twisted bilayer graphene has recently emerged as a novel platform featuring correlated phases favoured by the low-energy flat bands of the underlying moiré superlattice. Notably, the observation of correlated insulators and superconductivity, and the interplay between these phases have garnered significant attention. A wealth of correlated phases with unprecedented tunability was discovered subsequently, including orbital ferromagnetism, Chern insulators, strange metallicity, density waves, and nematicity. However, a comprehensive understanding of these closely competing phases remains elusive. The ability to controllably twist and stack multiple graphene layers has enabled the creation of a whole new family of moiré superlattices with myriad properties. Here, we review the progress and development achieved so far, encompassing the rich phase diagrams offered by these graphene-based moiré systems. Additionally, we discuss multiple phases recently observed in non-moiré multilayer graphene systems. Finally, we outline future opportunities and challenges for the exploration of hidden phases in this new generation of moiré materials.

Spin Polarization and Flat Bands in Eu-Doped Nanoporous and Twisted Bilayer Graphenes

Advanced two-dimensional spin-polarized heterostructures based on twisted (TBG) and nanoporous (NPBG) bilayer graphenes doped with Eu ions were theoretically proposed and studied using Periodic Boundary Conditions Density Functional theory electronic structure calculations. The significant polarization of the electronic states at the Fermi level was discovered for both Eu/NPBG(AA) and Eu/TBG lattices. Eu ions' chemi- and physisorption to both graphenes may lead to structural deformations, drop of symmetry of low-dimensional lattices, interlayer fusion, and mutual slides of TBG graphene fragments. The frontier bands in the valence region at the vicinity of the Fermi level of both spin-polarized 2D Eu/NPBG(AA) and Eu/TBG lattices clearly demonstrate flat dispersion laws caused by localized electronic states formed by TBG Moiré patterns, which could lead to strong electron correlations and the formation of exotic quantum phases.

Sensitivity enhanced tunable plasmonic biosensor using two-dimensional twisted bilayer graphene superlattice

This study theoretically demonstrated an insight for designing a novel tunable plasmonic biosensor, which was created by simply stacking a twisted bilayer graphene (TBG) superlattice onto a plasmonic gold thin film. To achieve ultrasensitive biosensing, the plasmonic biosensor was modulated by Goos-Hänchen (GH) shift. Interestingly, our proposed biosensor exhibited tunable biosensing ability, largely depending on the twisted angle. When the relative twisted angle was optimized to be 55.3°, such a configuration: 44 nm Au film/1-TBG superlattice could produce an ultralow reflectivity of 2.2038 × 10-9 and ultra-large GH shift of 4.4785 × 104 µm. For a small refractive index (RI) increment of 0.0012 RIU (refractive index unit) in sensing interface, the optimal configuration could offer an ultra-high GH shift detection sensitivity of 3.9570 × 107 µm/RIU. More importantly, the optimal plasmonic configuration demonstrated a theoretical possibility of quantitatively monitoring severe acute respiratory syndrome coronavirus (SARS-CoV-2) and human hemoglobin. Considering an extremely small RI change as little as 3 × 10-7 RIU, a good linear response between detection concentration of SARS-CoV-2 and changes in differential GH shift was studied. For SARS-CoV-2, a linear detection interval was obtained from 0 to 2 nM. For human hemoglobin, a linear detection range was achieved from 0 to 0.002 g/L. Our work will be important to develop novel TBG-enhanced biosensors for quantitatively detecting microorganisms and biomolecules in biomedical application.

Spontaneous time-reversal symmetry breaking in twisted double bilayer graphene

Twisted double bilayer graphene (tDBG) comprises two Bernal-stacked bilayer graphene sheets with a twist between them. Gate voltages applied to top and back gates of a tDBG device tune both the flatness and topology of the electronic bands, enabling an unusual level of experimental control. Metallic states with broken spin and valley symmetries have been observed in tDBG devices with twist angles in the range 1.2–1.3°, but the topologies and order parameters of these states have remained unclear. We report the observation of an anomalous Hall effect in the correlated metal state of tDBG, with hysteresis loops spanning hundreds of mT in out-of-plane magnetic field (B_⊥) that demonstrate spontaneously broken time-reversal symmetry. The B_⊥ hysteresis persists for in-plane fields up to several Tesla, suggesting valley (orbital) ferromagnetism. At the same time, the resistivity is strongly affected by even mT-scale values of in-plane magnetic field, pointing to spin-valley coupling or to a direct orbital coupling between in-plane field and the valley degree of freedom.

Twisted double bilayer graphene (tDBG) comprises two Bernal-stacked bilayer graphene sheets with a twist between them. Here, the authors report a strong anomalous Hall effect in the correlated-metal regime of tDBG, indicating time reversal symmetry breaking from orbital ferromagnetism, likely associated with valley polarization.

Spin-orbit-driven ferromagnetism at half moiré filling in magic-angle twisted bilayer graphene

Strong electron correlation and spin-orbit coupling (SOC) can have a profound influence on the electronic properties of materials. We examined their combined influence on a two-dimensional electronic system at the atomic interface between magic-angle twisted bilayer graphene and a tungsten diselenide crystal. We found that strong electron correlation within the moiré flatband stabilizes correlated insulating states at both quarter and half filling, and that SOC transforms these Mott-like insulators into ferromagnets, as evidenced by a robust anomalous Hall effect with hysteretic switching behavior. The coupling between spin and valley degrees of freedom could be demonstrated through control of the magnetic order with an in-plane magnetic field or a perpendicular electric field. Our findings establish an experimental knob to engineer topological properties of moiré bands in twisted bilayer graphene and related systems.

Tunable Orbital Ferromagnetism at Noninteger Filling of a Moiré Superlattice

The flat bands resulting from moiré superlattices exhibit fascinating correlated electron phenomena such as correlated insulators, ( Nature 2018, 556 (7699), 80-84), ( Nature Physics 2019, 15 (3), 237) superconductivity, ( Nature 2018, 556 (7699), 43-50), ( Nature 2019, 572 (7768), 215-219) and orbital magnetism. ( Science 2019, 365 (6453), 605-608), ( Nature 2020, 579 (7797), 56-61), ( Science 2020, 367 (6480), 900-903) Such magnetism has been observed only at particular integer multiples of n₀, the density corresponding to one electron per moiré superlattice unit cell. Here, we report the experimental observation of ferromagnetism at noninteger filling (NIF) of a flat Chern band in a ABC-TLG/hBN moiré superlattice. This state exhibits prominent ferromagnetic hysteresis behavior with large anomalous Hall resistivity in a broad region of densities centered in the valence miniband at n = -2.3n₀. We observe that, not only the magnitude of the anomalous Hall signal, but also the sign of the hysteretic ferromagnetic response can be modulated by tuning the carrier density and displacement field. Rotating the sample in a fixed magnetic field demonstrates that the ferromagnetism is highly anisotropic and likely purely orbital in character.