Transition-metal (TM) substituted SrTiO3 has attracted much attention
because its magnetism and/or ferroelectricity can be tuned via cation
substitution, point defects, strain and/or oxygen deficiency. For
example, Goto et al. [Phys. Rev. Applied, 7, 024006 (2017)] reported
the magnetization of SrTi1−xFexO3−δ (STF) grown under different oxygen
pressures and on various substrates. Here, we use hybrid density
functional theory to calculate the effects of different oxygen vacancy
(VO) states in STF on the magnetization for a variety of Fe cation
arrangements. The magnetic states of the cations associated with the
VO ground-states for x = {0.125, 0.25} are used within a Monte Carlo
model for collinear magnetism to simulate the spontaneous
magnetization. Our model captures several experimental features of
STF, i.e., an increase in magnetization for small δ up to a maximum of
∼0.35μB per formula unit at an intermediate number of vacancies, with
a slower decrease in magnetization with an increasing number of
vacancies. Our approach gives insight into the relation between
vacancy concentration and the oxygen pressure required to maximize the
magnetization.

We report the existence of moiré patterns and magic angle physics in all families of chiral collapsed carbon nanotubes. A detailed study of the electronic structure of all types of chiral nanotubes, previously collapsed via molecular dynamics, has been performed. We find that each family possesses a unique geometry and moiré disposition, as well as a characteristic number of flat bands. Remarkably, all kinds of nanotubes behave the same with respect to magic angle tuning, showing a monotonic behavior that gives rise to magic angles in full agreement with those of twisted bilayer graphene. Therefore, magic angle behavior is universally found in chiral collapsed nanotubes with a small chiral angle, giving rise to moiré patterns. Our approach comprises first-principles and semi-empirical calculations of the band structure, density of states and spatial distribution of the localized states signaled by flat bands.

From monolayers composed of different atoms, we can build structures with spontaneous vertical polarization by conveniently stacking multiple layers. We have studied, using first-principles methods and based on modern polarization theory, a system composed of three layers of hexagonal Boron-Nitride(h-BN) in all possible stackings. We obtain for each of the configurations how charge transfers between the layers and how it impacts on the polarization of the system. In addition, we studied a system of three layers, one of them rotated, and we found that not only did the magnitude of the polarization increase comparing with the bilayer but also, depending on the initial stacking and the rotated layer, we can create a variety of mosaic-like polarization arrangements, which are composed of regions with either triangular or hexagonal symmetry.

We study the microscopical origin of anisotropic ferromagnetism in the van der Waals magnet  CrI3. We conclude that the nearest-neighbor exchange is well described by the Heisenberg-Kitaev-Γ

(HKΓ) model and we also find a nonzero Dzyaloshinskii-Moriya interaction (DMI) on next-nearest neighbors. Both Kitaev and DMI are known to generate a nontrivial topology of the magnons in the honeycomb lattice and have been used separately to describe the low-energy regime of this material. We discuss how including one or the other leads to different signs of the Chern number. Furthermore, the topological gap at the K point seems to be mainly produced by the DMI, despite its being one order of magnitude smaller than Kitaev. Finally, we show that, by applying an external

Transition metal dichalcogenides (TMDs) are an exciting family of 2D materials; a member of this family, MoS2, became the first studied monolayer semiconductor. In this paper, a generalized phenomenological continuum approach for the optical vibrations of the monolayer TMDs valid in the long-wavelength limit is developed. The equation of motions for nonpolar and polar oscillations include the phonon dispersion up to a quadratic approximation in the phonon wave vector. On the other hand, the polar modes satisfy coupled equations for the displacement vector and the inner electric field. The two-dimensional phonon dispersion curves for in-plane and out-of-plane oscillations are thoroughly analyzed. The model parameters are fitted from density functional perturbation theory calculations. The current formalism provides an effective tool to describe the phonon dispersion curves around the Γ point of the Brillouin zone for a large group of members of the TMD monolayers. A detailed evaluation of the intravalley Pekar-Fröhlich and the A1-homopolar mode deformation potential coupling mechanisms is performed. The effects of metal ions and chalcogen atoms on polaron mass and binding energy are studied. It is argued that both

We present electronic structure calculations of twisted double bilayer graphene (TDBG): a tetralayer graphene structure composed of two AB-stacked graphene bilayers with a relative rotation angle between them. Using first-principles calculations, we find that TDBG is semiconducting with a band gap that depends on the twist angle, that can be tuned by an external electric field. The gap is consistent with TDBG symmetry and its magnitude is related to surface effects, driving electron transfer from outer to inner layers. The surface effect competes with an energy upshift of localized states at inner layers, giving rise to the peculiar angle dependence of the band gap, which reduces at low angles. For these low twist angles, the TDBG develops flat bands, in which electrons in the inner layers are localized at the AA regions, as in twisted bilayer graphene.

A monolayer of CrI3 is a two-dimensional crystal in its equilibrium configuration is a ferromagnetic semiconductor. In contrast, two coupled layers can be ferromagnetic, or antiferromagnetic depending on the stacking. We study the magnetic phase diagram upon the strain of the antiferromagnetically coupled bilayer with C2/m symmetry. We found that strain can be an efficient tool to tune the magnetic phase of the structure. A tensile strain stabilizes the antiferromagnetic phase, while a compressive strain turns the system ferromagnetic. We associate that behavior to the relative displacement between layers induced by the strain. We also study the evolution of the magnetic anisotropy, the magnetic exchange coupling, and how the Curie temperature is affected by the strain.

In this work we propose a two-dimensional carbon-nitrogen allotrope composed of pentagons and octagons in a structure of carbon chains bound by nitrogen dimers. Our first-principles calculations show the system behaves as a small-gap semiconductor which is thermodynamically stable at room temperature confirmed by molecular dynamic simulations. By cutting the sheet along different crystallographic directions, a variety of metallic or semiconductor one-dimensional ribbons can be obtained. We explore the topological properties of these nanoribbons finding that for a particular boundary geometry nontrivial topological phases can be obtained, depending on the ribbon termination. We investigate the emergence of symmetry protected interface topological states in heterojunctions and topological-induced edge states in finite ribbons.

We have studied how a generic bilayer kagome lattice behaves upon layer rotation. We employed a tight-binding model with one orbital per site and found: (i) for low rotational angles and at low energies, the same flat bands structure, such as in twisted bilayer graphene; although, for a larger value of the magic angle. Moreover, (ii) at high energies due to the superstructure symmetry regions, we found the characteristic three-band dispersion of the kagome lattice. In the latter, its bandwidth decreases for lower angles confining them within a few meV. Therefore, we found, in the twisted kagome lattice, the coexistence of two sets of flat bands in different energies and lying in different spatial regions of the bilayer system.

We demonstrate that one-dimensional moiré patterns, analogous to those found in twisted bilayer graphene, can arise in collapsed chiral carbon nanotubes. Resorting to a combination of approaches, namely, molecular dynamics to obtain the relaxed geometries and tight-binding calculations validated against ab initio modeling, we find that magic angle physics occur in collapsed carbon nanotubes. Velocity reduction, flat bands, and localization in AA regions with diminishing moiré angle are revealed, showing a magic angle close to 1°. From the spatial extension of the AA regions and the width of the flat bands, we estimate that many-body interactions in these systems are stronger than in twisted bilayer graphene. Chiral collapsed carbon nanotubes stand out as promising candidates to explore many-body effects and superconductivity in low dimensions, emerging as the one-dimensional analogues of twisted bilayer graphene.

Recently intrinsic ferromagnetism in two-dimensional(2D) van der Waals materials was discovered (Huang et al 2017 Nature 546 270–3; Gong et al 2017 Nature 546 265–9; O’Hara et al 2018 Nano Lett. 18 3125–31). A monolayer of Chromiun triiodide(CrI3) is ferromagnetic while a bilayer structure was reported to be anti-ferromagnetic, moreover an external electric field changes its magnetic phase (Jiang et al 2018 Nat. Mater. 17 406–10). We have studied the two found in nature stackings of CrI3 bilayers and found that indeed the magnetic phase of one of them can be tuned by an external electric field while the other remains ferromagnetic. We simulate those results with ab initio calculations and explain them with a simple model based on a rigid shift of the bands associated with different spins. The model can be applied to similar van der Waal stacked insulating bilayer anti-ferromagnets.

We explore the Floquet band structure and electronic transport in laser-illuminated bilayer graphene ribbons. By using a bias voltage perpendicular to the graphene bilayer we show how to get one-way charge and valley transport among two unbiased leads. In contrast to quantum pumping, our proposal uses a different mechanism based on generating a nonreciprocal band structure with a built-in directionality. The Floquet states at one edge of a graphene layer become hybridized with the continuum on the other layer, so the resulting band structure allows for one-way transport as in an isolator. Our proof of concept may serve as a building block for devices exploiting one-way states

Twisted bilayer graphene is a chiral system which has been recently shown to present circular dichroism. In this work we show that the origin of this optical activity is the rotation of the Dirac fermions’ helicities in the top and bottom layer. Starting from the Kubo formula, we obtain a compact expression for the Hall conductivity that takes into account the dephasing of the electromagnetic field between the top and bottom layers and gathers all the symmetries of the system. Our results are based in both a continuum and a tight-binding model, and they can be generalized to any two-dimensional Dirac material with a chiral stacking between layers.

We explore the electronic structure and transport properties of a metal on top of a (weakly coupled) two-dimensional topological insulator. Unlike the widely studied junctions between topological nontrivial materials, the systems studied here allow for a unique band structure and transport steering. First, states on the topological insulator layer may coexist with the gapless bulk and, second, the edge states on one edge can be selectively switched off, thereby leading to nearly perfect directional transport of charge and spin even in the zero bias limit. We illustrate these phenomena for Bernal stacked bilayer graphene with Haldane or intrinsic spin-orbit terms and a perpendicular bias voltage. This opens a path for realizing directed transport in materials such as van der Waals heterostructures, monolayer, and ultrathin topological insulators.

We report that two rotated layers of blue phosphorene behave as a direct band gap semiconductor. The optical spectrum shows absorption peaks in the visible region of the spectrum and in addition the energy of these peaks can be tuned with the rotational angle. These findings makes twisted bilayer blue phosphorene a strong candidate as a solar cell or photodetection device. Our results are based on ab initio calculations of several rotated blue phosphorene layers.

Graphene has established itself as a promising optoelectronic material. Many details of the photoresponse (PR) mechanisms in graphene in the THz-to-visible range have been revealed, however, new intricacies continue to emerge. Interface junctions, formed at the boundaries between parts of graphene with different number of layers or different stacking orders, and making connection between electrical contacts, provide another peculiar setup to establish PR. Here, we experimentally demonstrate an enhanced polarization sensitive photoelectric PR in graphene sheets containing interface junctions as compared to homogenous graphene sheets in the visible, infrared, and THz spectral regions. Our numerical simulations show that highly localized electronic states are created at the interface junctions, and these states exhibit a unique energy spectrum and enhanced probabilities for optical transitions. The interaction of electrons from interface junction states with electromagnetic fields generates a polarization-sensitive PR that is maximal for the polarization direction perpendicular to the junction interface.

We have performed an ab initio investigation of transition metals (TMs=Mo, Ru, Co, and Pt)
embedded in twisted bilayer graphene (tBG) layers. Our total energy results reveal that, triggered by the misalignment between the graphene layers, Mo and Ru atoms may form a quasiperiodic (triangular) array of intercalated atoms. In contrast, the formation of those structures is not expected for the other TMs, the Co and Pt atoms. The net magnetic moment (m) of Mo and Ru atoms may be quenched upon intercalation, depending on the stacking region (AA or AB). For instance, we find a magnetic moment of 0.3μB(1.8μB) for Ru atoms intercalated between the AA (AB) regions of the stacked twisted layers. Through simulated scanning tunneling microscopy (STM) images, we verify that the presence of intercalated TMs can be identified by the formation of bright (hexagonal) spots lying on the graphene surface.

We study the transport properties of a twisted bilayer graphene flake contacted by two monolayer nanoribbons which act as leads. We analyze the conductance in terms of the spectra of the bilayer nanoribbon and the monolayer contacts. The low-energy transport properties are governed by the edge states with AB stacking. Remarkably, the electronic conductance in this energy region does not depend much on the relative position of the leads, in contrast with that of bilayer flakes with more symmetric stackings. We attribute this feature to the localization of these low-energy states in the AB edge regions of the flake, having a much smaller weight at the junctions between the flake and the nanoribbon leads.

We address the origin of beadlike edge states observed by scanning tunneling microscopy (STM) in moiré patterns of graphite. Low-bias STM measurements indicate these edge states are centered around AB stacking sites, contrary to the common assumption of them being at AA sites. This shift in the beads intensity with respect to the bulk moiré pattern has been corroborated by a tight-binding calculation of the edge states in bilayer flakes. Our results are valid not only for graphite, but also for few-layer graphene where these states have also been recently observed.

We study the band structure, density of states, and spatial localization of edge states in twisted bilayer graphene nanoribbons. We devise these ribbons by cutting a stripe of commensurate twisted bilayer graphene along a direction with a maximum number of zigzag edge atoms. Due to the spatially inhomogeneous interlayer coupling, edge states stemming from regions with AB stacking are closer to the energy of the Dirac point, whereas those arising from AA-stacked edge states are split in energy due to the stronger interlayer coupling. As opposed to bulk bilayer graphene, for which states near the Dirac point are localized in AA-stacked regions, the interplay of edge and moiré localization produces a distinct spatial distribution of low-energy states in these ribbons.

Using ab initio calculations we have studied the optical linear response of different configurations of twisted trilayer graphene systems. We have found that when one of the outer layers is rotated the system shows an angle-dependent optical spectrum as its twisted bilayer counterpart; however, in this case there are two absorption peaks located in the visible range of the spectrum and one more in the intermediate infrared range for large relative rotation angles. When two layers are rotated the spectrum exhibits only two absorption peaks in the visible range revealing information about the two relative rotation angles between the layers in the structure. All these absorption peaks in the visible range shift to the intermediate infrared range for small angles.

We study the electronic properties of a twisted trilayer graphene, where two of the layers have Bernal stacking and the third one has a relative rotation with respect to the AB-stacked layers. Near the Dirac point, the AB-twisted trilayer graphene spectrum shows two parabolic Bernal-like bands and a twistedlike Dirac cone. For small twist angles, the parabolic bands present a gap that increases for decreasing rotation angle. There is also a shift in the twistedlike Dirac cone with a similar angle dependence. We correlate the gap in the trilayer with the shift of the Dirac cone in an isolated twisted bilayer, which is due to the loss of electron-hole symmetry caused by sublattice mixing in the rotated geometry. Using a tight-binding and a continuum model, we derive an effective Hamiltonian which accounts for the relevant low-energy properties of this system

We report on the effects of laser illumination on the electronic properties of bilayer graphene. By using Floquet theory combined with Green’s functions, we unveil the appearance of laser-induced gaps not only at integer multiples of ℏΩ/2 but also at the Dirac point with features which are shown to depend strongly on the laser polarization. Trigonal warping corrections are shown to lead to important corrections for radiation in the terahertz range, reducing the size of the dynamical gaps. Furthermore, our analysis of the topological properties at low energies reveals that, when irradiated with linearly polarized light, ideal bilayer graphene behaves as a trivial insulator, whereas circular polarization leads to a nontrivial insulator per valley.

We investigate the electronic density redistribution of rotated bilayer graphene under a perpendicular electric field, showing that the layers are actually coupled even for large angles. This layer-layer coupling is evidenced by the charge transfer on these structures as a function of the external voltage. We find an inhomogeneous excess charge distribution that is related to the moiré patterns for small angles, but that persists for larger angles where the carriers’ velocity is equal to that of single layer graphene. Our results show that rotated bilayer systems are coupled for all rotation angles.

In this work, we show that the trigonal warping of the electronic bands in bilayer graphene dramatically modifies the behavior of the topologically confined one-dimensional modes due to an inhomogeneous bias that changes sign across a channel. Up to four zero modes are present, depending on the orientation of the channel, these zero modes are related to a fractionalization of the topological charge due to the trigonal warping.

The presence of flat bands near Fermi level has been proposed as an explanation for high transition temperature superconductors. The bands of graphite are extremely sensitive to topological defects which modify the electronic structure. In this Rapid Communication, we found nondispersive flat bands no farther than 10 meV of the Fermi energy in slightly twisted bilayer graphene as a signature of a transition from a parabolic dispersion of bilayer graphene to the characteristic linear dispersion of graphene. This transition occurs for relative rotation angles of layers around 1.5° and is related to a process of layer decoupling. We have performed ab initio calculations to develop a tight-binding model with an interaction Hamiltonian between layers that include the π  orbitals of all atoms and takes into account interactions up to third nearest neighbors within a layer.