Non-Abelian Gauge Potentials in Graphene Bilayers

Charge carriers in bilayer graphene are widely believed to be massive Dirac fermions 1-3 that have a bandgap tunable by a transverse electric field 3,4 . However, a full transport gap, despite its importance for device applications, has not been clearly observed in gated bilayer graphene 5-7 , a longstanding puzzle. Moreover, the low-energy electronic structure of bilayer graphene is widely held to be unstable towards symmetry breaking either by structural distortions, such as twist 8-10 , strain 11,12 , or electronic interactions 7,13,14 that can lead to various ground states. Which effect dominates the physics at low energies is hotly debated. Here we show both by direct band-structure measurements and by calculations that a native imperfection of bilayer graphene, a distribution of twists whose size is as small as ∼0.1 • , is sufficient to generate a completely new electronic spectrum consisting of massive and massless Dirac fermions. The massless spectrum is robust against strong electric fields, and has a unusual topology in momentum space consisting of closed arcs having an exotic chiral pseudospin texture, which can be tuned by varying the charge density. The discovery of this unusual Dirac spectrum not only complements the framework of massive Dirac fermions, widely relevant to charge transport in bilayer graphene, but also supports the possibility of valley Hall transport 15 .

Nano Letters, 2010

We study the electronic structure of two Dirac electron gazes coupled by a periodic Hamiltonian such as it appears in rotated graphene bilayers. Ab initio and tight-binding approaches are combined and show that the spatially periodic coupling between the two Dirac electron gazes can renormalize strongly their velocity. We investigate in particular small angles of rotation and show that the velocity tends to zero in this limit. The localization is confirmed by an analysis of the eigenstates which are localized essentially in the AA zones of the Moiré patterns.

2019

We analyze a description of twisted graphene bilayers, that incorporates deformation of the layers due to the nature modern interlayer potentials, and a modification of the hopping parameters between layers in the light of the classic Slonczewski-Weiss-McClure parametrisation. We shall show that flat bands result in all cases, but that their nature can be rather different. We will show how to construct a more general reduction to a continuum model, and show that even though such a model can be constructed, its complexity increases, requiring more coupling parameters to be included, and the full in-layer dispersion to be taken into account. We conclude that the combination of all these effects will have a large impact on the wave functions of the flat bands, and that changes in the detail of the underlying models can lead to significant changes. A robust conclusion is that the natural strength of the interlayer couplings is higher than usually assumed, which causes additional Dirac p...

Physical Review B, 2007

Advanced Materials

Tuning interactions between Dirac states in graphene has attracted enormous interest because it can modify the electronic spectrum of the 2D material, enhance electron correlations, and give rise to novel condensed‐matter phases such as superconductors, Mott insulators, Wigner crystals, and quantum anomalous Hall insulators. Previous works predominantly focus on the flat band dispersion of coupled Dirac states from different twisted graphene layers. In this work, a new route to realizing flat band physics in monolayer graphene under a periodic modulation from substrates is proposed. Graphene/SiC heterostructure is taken as a prototypical example and it is demonstrated experimentally that the substrate modulation leads to Dirac fermion cloning and, consequently, the proximity of the two Dirac cones of monolayer graphene in momentum space. Theoretical modeling captures the cloning mechanism of the Dirac states and indicates that moiré flat bands can emerge at certain magic lattice con...

Physical Review B, 2009

We study how the electronic structure of the bilayer graphene (BLG) is changed by electric field and strain from ab initio density-functional calculations using the LMTO and the LAPW methods. Both hexagonal and Bernal stacked structures are considered. The BLG is a zero-gap semiconductor like the isolated layer of graphene. We find that while strain alone does not produce a gap in the BLG, an electric field does so in the Bernal structure but not in the hexagonal structure. The topology of the bands leads to Dirac circles with linear dispersion in the case of the hexagonally stacked BLG due to the interpenetration of the Dirac cones, while for the Bernal stacking, the dispersion is quadratic. The size of the Dirac circle increases with the applied electric field, leading to an interesting way of controlling the Fermi surface. The external electric field is screened due to polarization charges between the layers, leading to a reduced size of the band gap and the Dirac circle. The screening is substantial in both cases and diverges for the Bernal structure for small fields as has been noted by earlier authors. As a biproduct of this work, we present the tight-binding parameters for the free-standing single layer graphene as obtained by fitting to the density-functional bands, both with and without the slope constraint for the Dirac cone.

Physical Review B, 2015

Theory predicts that graphene under uniaxial compressive strain in an armchair direction should undergo a topological phase transition from a semimetal into an insulator. Due to the change of the hopping integrals under compression, both Dirac points shift away from the corners of the Brillouin zone towards each other. For sufficiently large strain, the Dirac points merge and an energy gap appears. However, such a topological phase transition has not yet been observed in normal graphene (due to its large stiffness) neither in any other electronic system. We show numerically and analytically that such a merging of the Dirac points can be observed in electronic artificial graphene created from a two-dimensional electron gas by application of a triangular lattice of repulsive antidots. Here, the effect of strain is modeled by tuning the distance between the repulsive potentials along the armchair direction. Our results show that the merging of the Dirac points should be observable in a recent experiment with molecular graphene.

Physics Reports-Review Section of Physics Letters, 2010

The physics of graphene is acting as a bridge between quantum field theory and condensed matter physics due to the special quality of the graphene quasiparticles behaving as massless two dimensional Dirac fermions. Moreover, the particular structure of the 2D crystal lattice sets the arena to study and unify concepts from elasticity, topology and cosmology. In this paper we analyze these connections combining a pedagogical, intuitive approach with a more rigorous formalism when required.

Scientific Reports, 2016

Moiré superlattices in graphene supported on various substrates have opened a new avenue to engineer graphene's electronic properties. Yet, the exact crystallographic structure on which their band structure depends remains highly debated. In this scanning tunneling microscopy and density functional theory study, we have analysed graphene samples grown on multilayer graphene prepared onto SiC and on the close-packed surfaces of Re and Ir with ultra-high precision. We resolve small-angle twists and shears in graphene, and identify large unit cells comprising more than 1,000 carbon atoms and exhibiting nontrivial nanopatterns for moiré superlattices, which are commensurate to the graphene lattice. Finally, a general formalism applicable to any hexagonal moiré is presented to classify all reported structures. Graphene (gr) is a two-dimensional crystal with honeycomb structure, whose peculiar electronic properties have raised considerable interest in the past few years. Indeed, its electronic bands cross at the K and K′ corners of the Brillouin zone, giving rise to a linear energy dispersion of its quasiparticles close to the Fermi level 1. Moreover, the bipartite nature of graphene's lattice, with two triangular carbon sub-lattices (A and B), confers unique properties to these quasiparticles. By analogy to quantum electrodynamics 2 , a sublattice-related quantum number, so-called pseudo-spin, equivalent to the spin of Dirac fermions is defined 3. For these reasons, the conical electronic bands around the K and K′ points of the Brillouin zone are called Dirac cones. Such exotic electronic properties are predicted for pristine graphene, but are altered when graphene is supported by a substrate. Indeed, due to the structural mismatch between graphene and its support, graphene has periodically varying stacking configurations with its substrate 4-9. This effect modulates the graphene-substrate interaction and distance 10-14 , over a so-called moiré periodicity, which can range from ~1 to ~15 nm. Depending on the interaction between graphene and the substrate, the moiré can have a dramatic impact on graphene's properties. Some substrates impose only a weak interaction dominated by van der Waals forces, which is the case for graphene on hexagonal boron nitride 15 or multilayer graphene on the carbon face of SiC 16. In this case, the graphene-substrate distance is about 3.4 Å (refs 16,17), very close to the value 3.3539 Å of highly oriented pyrolytic graphite (HOPG) 18 , and graphene's electronic properties are mostly preserved 17,19. In these systems, the moiré acts as a smooth superpotential that varies slowly compared to the one associated to carbon atoms. The corresponding unit cell, which is larger than the one of pristine graphene, is associated with replica Dirac cones, reduced Fermi velocity 20-23 , with either superlattice Dirac cones 21,22,24,25 or mini-gaps 20,26 at the moiré Brillouin zone boundary. Such properties make this system an ideal playground to investigate quantum phases arising in periodic two-dimensional electron gases subjected to an external magnetic field 25-27. In bilayer graphene samples, Van Hove singularities and electron localization also emerge from the coexistence of the Dirac cones of each layer 28,29. Overall, in low-interaction systems, tuning moiré superlattices is a mean to tailor graphene's electronic properties. Other surfaces interact more strongly with graphene, and are prone to exchange electrons with it, establishing partially covalent bonds. Graphene-substrate bonding then implies both van der Waals forces (physisorption) and partial covalent bonding (chemisorption), and is modulated along the moiré periodicity 11,12,30-32. Graphene is thus nanorippled, the shortest graphene-substrate distances showing tendency to covalent bonding. Nanorippling amplitudes varying from 0.03 (on Pt(111) 33) to 1.6 Å (on Re(0001) 32) have been reported depending on the strength of the graphene-substrate interaction 8. Systems with strong nanorippling amplitudes usually

One of the fundamental properties of spin 1/2 particles is their interaction with magnetic fields. The exploration of this coupling can be quite elusive, for example in the case of neutrinos. Graphene has been shown to be a condensed matter platform for the study of such ultrarelativistic particles, with its neutrino-like charge carriers having a spin-like degree of freedom called pseudospin. Here we show that in analogy to the spin alignment of a fermion in a magnetic field, the pseudo-spin of graphene can be oriented by a strain induced pseudomagnetic field through the Zeeman term. We reveal this pseudo-spin polarization as a sublattice symmetry breaking by tunably straining graphene using the tip of a scanning tunnelling microscope. The observed pseudo-spin polarization scales with the lifting height of the strained deformation and therefore with the pseudo-magnetic field strength. Its magnitude is quantitatively reproduced by analytic and tight-binding models. This adds a key ingredient to the celebrated analogy of graphene's charge carriers to ultra-relativistic Dirac fermions. Furthermore, the deduced fields of about 1000 T could provide an effective THz valley filter, as a basic element of valleytronics.