Session P14: 2D Materials: Stack and Twist Theory

First-Principles Electronic Structure Investigation of 2D Twisted Bilayers

Since the recent experimental observation of unconventional superconductivity in Twisted Bilayer Graphene (TBG) has brought 2D twisted materials to the front lines of research, there is a need to cover the underlying physics accurately and efficiently. We utilize the first-principles method to calculate both band structures and density of states (DOS) for various sized 2D twisted bilayers of Graphene, BN and MoS₂. Our results reveal that introducing a twist opens a band gap, and Van Hove Singularities are seen symmetric to the dirac point in the DOS. The introduction of a twist angle in graphene also creates a parabolic band dispersion of the dirac cones, normally seen only in Bernal stacked graphene on account of strong stability and interlayer correlation. We evaluate the contribution of cell size to band structure by enlarging the unit cell from 2×2 to 12×12. The electronic properties of the smaller cell remains constant as the cell size increases. Furthermore, we treat a non-periodic 2D twisted bilayer by introducing a vacuum, from which we can draw parallels between the electronic structures and reveal the deep underlying physics.   

A multi-scale numerical approach to model two-dimensional layered materials

Since the discovery of single-layer graphene crystal, more different types of two-dimensional layered materials are exfoliated or synthesized. The theoretical modeling would guide the further design and understanding with these materials. We develop a multi-scale numerical approach to model these layers and their heterostructures. The microscopic modeling is based on the density functional theory (DFT) calculations followed by Wannier transformation to derive localized orbitals. These allow us to capture the effects from coupling with adjacent layers and the deformation within each layer from crystal relaxations. The faithful representation of the wavefunction characters also enables the computation of Berry curvatures and responses to external electric and magnetic fields.   

Gate-Tunable Topological Flat Bands in Trilayer Graphene-Boron Nitride Moiré Superlattices

We investigate the electronic structure of the flat bands induced by moiré superlattices and electric fields in nearly aligned ABC trilayer graphene-boron nitride interfaces where Coulomb effects can lead to correlated gapped phases. Our calculations indicate that valley-spin resolved isolated superlattice flat bands that carry a finite Chern number C = 3 proportional to layer number can appear near charge neutrality for appropriate perpendicular electric fields and twist angles. When the degeneracy of the bands is lifted by Coulomb interactions these topological bands can lead to anomalous quantum Hall phases that embody orbital and spin magnetism. Narrow bandwidths of ∼10 meV achievable for a continuous range of twist angles θ ≤ 0.6° with moderate interlayer potential differences of ∼50 meV make the TLG/BN systems a promising platform for the study of electric-field tunable Coulomb interaction driven spontaneous Hall phases.

Reference: arXiv:1806.00462   

Composition and Stacking Dependent Topology in Bilayers from the Graphene Family

We investigate from first-principles the electronic and structural properties of silicene, germanene, and stanene bilayers. Due to the staggering of the individual layers, several stacking patterns are possible, most of which are not available to the bilayer graphene. Our results reveal the appearance of distinct band features, including orbital hybridization and band inversion, and they are attributed to the combined effects of the composition, stacking, and to the presence of the spin-orbit coupling. It is found that particular arrangements give rise to topological features in the Hall response, offering new directions for exploring Dirac features in 2D systems.
  

Ultraflat bands and shear solitons in Moiré patterns of twisted bilayer transition metal dichalcogenides

Ultraflat bands in twisted bilayers of two-dimensional materials have potential to host strong correlations, including the Mott-insulating phase at half-filling of the band. Using first-principles density functional theory calculations, we show the emergence of ultraflat bands at the valence band edge in twisted bilayer MoS₂, a prototypical transition metal dichalcogenide. The computed band widths are comparable to that of twisted bilayer graphene near 'magic' angles. Large structural transformations in the Moiré patterns lead to the formation of shear solitons at stacking boundaries and strongly influence the electronic structure. We extend our analysis for twisted bilayer MoS₂ to show that flat bands can occur at the valence band edge of twisted bilayer WS₂, MoSe₂ and WSe₂ as well.   

Topological phases and twisting of graphene on a dichalcogenide monolayer

Graphene placed in proximity to a transition metal dichalcogenide semiconductor monolayer has been shown to exhibit interesting modifications of its electronic properties. The role of incommensurability and a possible relative twist between layers require implementing a continuum model approach to fully investigate this multilayered system. Results of this model are in agreement with simplified approaches, such as the tight-binding model, that assumes commensurate supercells. We show that the misaligned system can also exhibit multiple different topological phases depending on the relative twist angle and applied gate voltages between the layers[1]. An interesting topological phase exhibits inverted bands which is robust to incommensurate structure effects.
Using an effective Hamiltonian to fully describe the continuum model of graphene-TMD heterostructure reveals that a staggered potential and effective SOC are induced onto the graphene, which controls the appearance of the non-trivial topological phase. Our estimates suggest that the intrinsic SOC induced onto graphene deposited on typical TMDs is somewhat weak and must be enhanced by additional means, such as heavy metal intercalation, to achieve a tunable quantum spin Hall phase.
[1]A. Alsharari, et.al, arXiv:1808.06662, (2018)   

Band nesting and valley exciton in monolayer MoS2

We report the effect of band nesting on single valley excitons in monolayer MoS_{2 .} We start with ab-initio based electronic structure obtained within tight binding model of MoS₂ [1]. We next turn on electron-electron interactions, form a Hartree-Fock ground state and construct electron-hole excitations. We compute e.-e. interactions, self-energy in the screened exchange and Coulomb hole approximation and direct and exchange electron-hole interaction. We solve Bethe-Salpeter equation to obtain exciton states and absorption spectrum. We disentangle effects of electron-hole dispersion, details of band structure on Coulomb intra/inter - valley interactions, topology, screening and dielectric environment. In particular, we discuss the effect of Q-points and band nesting on ground and excited states of excitons in MoS₂ .

[1] M. Bieniek, M. Korkusinski, L. Szulakowska, P. Potasz, I. Ozfidan, and P. Hawrylak, PRB 97, 085153 (2018).

  

A metal-insulator transition by hole doping in boron triangular Kagome lattice

A flat band is the hallmark of a variety of exotic phases because electrons are confined in a narrow energy widnow with a very high density of states. Recently, much attention has been paid to magic-angle twisted bilayer graphene which possesses a flat band feature and exhibits strongly correlated and unconventional superconducting phases. This experiment indicates that partially-filled flat bands are the birthpalce of many intersesting phenomena and motivate further studies for the hidden physics of partially-filled flat bands in other systems. In this work, through first-principles calculations, we investigate the electronic structure and structural stability of a paritally-filled flat band in boron triangular Kagome lattice which has been recently predicted. We find that a large Fermi surface nesting in the partially-filled flat band enhances electron-phonon intearctions and induces dynamical instability. For hole doping levels above a 2/3-filling of the spin-polarized flat band, a metal-insulator transition occurs. Our results suggest that the boron triangular Kagome lattice is a suitable material to study the effect of partially-filled flat bands on exotic phases.   

Landau levels in bilayer transition metal dichalcogenides

The quantum binary system at low temperature is not limited to only spin, but that of valley and layer degrees of freedom as well. A prime example is bilayer transition metal dichalcogenide (TMD). Here we examine the Landau level structure of bilayer TMD. We show how the interlayer electric field and the magnetic Zeeman field couple and control the layer and valley pseudospins, respectively, thereby tuning the Landau levels. To understand the underlaying mechanics, we develop an effective model accurate within the experimental range to model and analyze the results. Our work sheds a new light on the quantum Hall effects of atomically thin TMD's.   

Tunable spin-polarized edge currents in proximitized transition metal dichalcogenides

We explore proximity-induced ferromagnetism on transition metal dichalcogenide (TMD), focusing on molybdenum ditelluride (MoTe₂) ribbons with zigzag edges, deposited on ferromagnetic europium oxide (EuO). A three-orbital tight-binding model allows modeling MoTe₂ monolayer structures in real space, incorporating the exchange and Rashba fields induced by proximity to the EuO substrate. For in-gap Fermi levels, electronic modes in the nanoribbon are strongly spin-polarized and localized along the edges, acting as 1D conducting channels with tunable spin-polarized currents. We also study the effect of atomic defects on the 1D conducting channels and on the spin-polarized currents, finding a nonvanishing spin-polarized current even in the presence of either Te and/or Mo vacancies. Hybrid structures such as the MoTe₂/EuO configuration can serve as building blocks for spintronic devices and provide versatile platforms to further understand proximity effects in diverse materials systems.

[1] N. Cortes et al., arXiv:1807.05316 (2018).   

Tight-binding modeling of bilayer TMDCs with lithium intercalation

We present an ab-initio tight-binding modeling of bilayer TMDCs with lithium intercalation based on the wannier transformation of first-principles calculations. Specifically, we take MoS₂ as an example. As a starting point, we investigate the energetics of different intercalation sites for Li between layers of MoS₂. We find that the intercalation energetics is related to the local coordination type and the number of vertically aligned molybdenum atoms. In addition, we verify that Li intercalation tunes the Fermi level to the conduction bands and make the system metallic. Further, we use three variables to characterize the relative configuration between the sulfur pair and the Li and describe the interlayer sulfur-sulfur interactions. As expected, Li brings extra influence and dramatically tunes the interlayer interactions. Our results pave the way for further modeling of twisted bilayer TMDCs with Li intercalation.   

Properties of doubly-aligned graphene/boron nitride heterostructures

A long-wavelength superlattice moiré potential emerges in heterostructures of graphene and boron nitride (BN) with small interlayer twist. The bandstructure of graphene is substantially modified by this superlattice potential, with secondary Dirac cones emerging at finite energy and band gaps opening at both the original and secondary Dirac points. We investigate the behavior of BN-encapsulated graphene in which the bottom BN is aligned to the graphene and the top BN can be rotated freely. We observe a significant enhancement of the band gap at the Dirac point in the case where both the top and bottom BN layers are perfectly aligned to the graphene. Additionally, while rotations of 60° are equivalent in typical graphene on BN heterostructures, we observe symmetry under 120° rotations of the top BN in our doubly-aligned devices, owing to the inequivalence of the boron and nitrogen potentials in the BN unit cell. In particular, we find the resistance of the Dirac point at room temperature is enhanced with the top BN at 0° but suppressed at 60°.   

Modifying the Band Structure of Hexagonal Boron Nitride with Metal Electrodes

Tuning the large band gap of BN to make it functional in a given device configuration has been challenging. Theoretical attempts via an external electric field, strain, and changing the interlayer distance have produced promising results, however, at unrealistically high electric field and strain values. In this DFT-based study, we propose an alternate scheme for tuning the electronic states in BN. We investigate systems in which a few layers of BN are sandwiched between two metals with different work functions, such as Cu/BN/K, creating a large electric field through the BN slab. We find that the energy gap among the BN states can be significantly decreased in such configurations. We also report on the dependence of this effect on the different metals used and the number of BN layers, as well as the BN stacking order, as the controlled growth of an alternative (Bernal) stacking order was recently reported (S. M. Gilbert et al., arXiv:1810.04814) and thus became available for such applications.   

Exchange driven dimerization, band gap, and magnetism of diamond(111) surface from first principles

Strong electron-electron interaction in ultraflat edge states can be responsible for correlated phases of matter, such as magnetism, charge density wave or superconductivity. The diamond(111) surface, after Pandey reconstruction, presents zig-zag carbon chains, generating a very flat surface band. More than 100 years after Bragg determined the structure of bulk diamond, the structure of the (111) surface of diamond is still controversial. Full structural optimization using hybrid density functionals with exact exchange shows that a substantial dimerization occurs on the Pandey π-chains — that is the primary mechanism for the opening of an insulating gap. This effect is absent in standard functionals. The exchange interaction further stabilizes a ferrimagnetic order along the Pandey π-chains with magnetic moments of 0.27 μB, opening a direct band gap of ~1.4 eV, in agreement with experiments. Our work is relevant for systems with flat bands in general and wherever the interplay between structural and electronic degrees of freedom is crucial, as in twisted bilayer graphene, IVB atoms on IVB(111) surfaces such as Pb/Si(111) or molecular crystals.   

Nano-Makisu: Two-Dimensional Carbon derived from One-Dimensional Carbon

The synthesis of carbon nanotubes and the rediscovery of graphene has sparked experimental and theoretical studies on new allotropes of carbon. Herein, we report first-principles calculations on novel two-dimensional carbon allotropes that are formed from embedding single-walled carbon nanotubes (SWNTs) within graphene sheets. The SWNTs are joined to the sheet via hexagonal or tetragon-octagon rings. We call this predicted allotrope of carbon nano-makisu. Results of phonon and molecular dynamics calculations demonstrate that these new carbon allotropes are dynamically and thermally stable, and they are energetically more favorable than pure SWNTs. Electronic structure calculations indicate that these two-dimensional carbon allotropes are metallic. Moreover, anisotropic Dirac-cone like features are found in nano-makisu. Because of its intriguing electronic transport properties nano-makisu are potential materials for nanoelectronics.