Multiflavor Dirac fermions in Kekulé-distorted 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 .

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...

Nature, 2013

Lateral superlattices have attracted major interest as this may allow one to modify spectra of two dimensional (2D) electron systems and, ultimately, create materials with tailored electronic properties 1-8 . Previously, it proved difficult to realize superlattices with sufficiently short periodicity and weak disorder, and most of the observed features could be explained in terms of commensurate cyclotron orbits 1-4 . Evidence for the formation of superlattice minibands (so called Hofstadter's butterfly 9 ) has been limited to the observation of new low-field oscillations 5 and an internal structure within Landau levels 6-8 . Here we report transport properties of graphene placed on a boron nitride substrate and accurately aligned along its crystallographic directions. The substrate's moiré potential 10-12 leads to profound changes in graphene's electronic spectrum. Second-generation Dirac points 13-22 appear as pronounced peaks in resistivity accompanied by reversal of the Hall effect. The latter indicates that the sign of the effective mass changes within graphene's conduction and valence bands. Quantizing magnetic fields lead to Zak-type cloning 23 of the third generation of Dirac points that are observed as numerous neutrality points in fields where a unit fraction of the flux quantum pierces the superlattice unit cell. Graphene superlattices open a venue to study the rich physics expected for incommensurable quantum systems 7-9,22-24 and illustrate the possibility to controllably modify electronic spectra of 2D atomic crystals by using their crystallographic alignment within van der Waals heterostuctures 25 .

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2010

We review the energy spectrum and transport properties of several types of one-dimensional superlattices (SLs) on single-layer and bilayer graphene. In single-layer graphene, for certain SL parameters an electron beam incident on an SL is highly collimated. On the other hand, there are extra Dirac points generated for other SL parameters. Using rectangular barriers allows us to find analytical expressions for the location of new Dirac points in the spectrum and for the renormalization of the electron velocities. The influence of these extra Dirac points on the conductivity is investigated. In the limit of δ -function barriers, the transmission T through and conductance G of a finite number of barriers as well as the energy spectra of SLs are periodic functions of the dimensionless strength P of the barriers, , with v F the Fermi velocity. For a Kronig–Penney SL with alternating sign of the height of the barriers, the Dirac point becomes a Dirac line for P = π /2+ nπ with n an intege...

Physical Review B

Flat bands in the energy spectrum have attracted a lot of attention in recent years because of their unique properties and promising applications. Special arrangement of impurities on monolayer graphene are proposed to generate multiflat bands in the electronic band structure. In addition to the single midgap states in the spectrum of graphene with low hydrogen density, we found closely spaced bands around the Fermi level with increasing impurity density, which are similar to discrete lines in the spectrum of quantum dots, as well as the unusual Landau-level energy spectrum of graphene in the presence of a strong magnetic field. The presence of flat bands crucially depends on whether or not there are odd or even electrons of H(F) atoms bound to graphene. Interestingly, we found that a fully hydrogenated (fluoridated) of a hexagon of graphene sheet with six hydrogen (fluorine) atoms sitting on top and bottom in consecutive order exhibits Dirac cones in the electronic band structure with a 20% smaller Fermi velocity as compared to the pristine graphene. Functionalizing graphene introduces various CC bond lengths resulting in nonuniform strains. Such a nonuniform strain may induce a giant pseudomagnetic field in the system, resulting in quantum Hall effect.

arXiv (Cornell University), 2024

Generating discernible valley contrasts and segregating valley-indexed fermions in real space within graphene poses considerable challenges due to the isotropic transport within the continuum energy range for degenerate valleys. This study unveils an interesting finding: introducing valley contrast through anisotropic chiral transport in isotropic Dirac systems like graphene, achieved by implementing a tilted PN junction. The tilted junction shifts the angular spectrum to larger angles in accordance with the tilt angle. This modifies the pseudospin-conserved modes across the junction, resulting in valley-resolved chiral transport. This approach not only induces valley splitting within the real space but also preserves the remarkable mobility of fermions, offering distinct advantages over alternative strategies. The comprehensive analysis includes optimizing the experimental setup, scrutinizing factors such as the sequence of the doped region, and examining critical parameters like the tilt angle (δ) and transition width (d) across the junction. Surprisingly, an increased transition width enhances transmission, attributed to specular edge scattering. Importantly, the system remains resilient to Anderson's short-range edge disorder. The broader implication lies in the transformative potential of inducing analogous anisotropic chiral transport behaviors in isotropic Dirac systems, resembling the characteristics of tilted Dirac-Weyl semimetals, by incorporating a tilted PNJ.

Physical Review B, 2010

We investigate the emergence of extra Dirac points in the electronic structure of a periodically spaced barrier system, i.e., a superlattice, on single-layer graphene, using a Dirac-type Hamiltonian. Using square barriers allows us to find analytic expressions for the occurrence and location of these new Dirac points in k space and for the renormalization of the electron velocity near them in the low-energy range. In the general case of unequal barrier and well widths the new Dirac points move away from the Fermi level and for given heights of the potential barriers there is a minimum and maximum barrier width outside of which the new Dirac points disappear. The effect of these extra Dirac points on the density of states and on the conductivity is investigated.

Physical Review Letters, 2014

Bilayer graphene is a highly promising material for electronic and optoelectronic applications since it is supporting massive Dirac fermions with a tuneable band gap. However, no consistent picture of the gap's effect on the optical and transport behavior has emerged so far, and it has been proposed that the insulating nature of the gap could be compromised by unavoidable structural defects, by topological in-gap states, or that the electronic structure could be altogether changed by many-body effects. Here we directly follow the excited carriers in bilayer graphene on a femtosecond time scale, using ultrafast time-and angle-resolved photoemission. We find a behavior consistent with a single-particle band gap. Compared to monolayer graphene, the existence of this band gap leads to an increased carrier lifetime in the minimum of the lowest conduction band. This is in sharp contrast to the second sub-state of the conduction band, in which the excited electrons decay through fast, phonon-assisted inter-band transitions.

Physical review letters, 2016

We revisit the effect of local interactions on the quadratic band touching (QBT) of the Bernal honeycomb bilayer model using renormalization group (RG) arguments and quantum Monte Carlo (QMC) simulations. We present a RG argument which predicts, contrary to previous studies, that weak interactions do not flow to strong coupling even if the free dispersion has a QBT. Instead, they generate a linear term in the dispersion, which causes the interactions to flow back to weak coupling. Consistent with this RG scenario, in unbiased QMC simulations of the Hubbard model we find compelling evidence that antiferromagnetism turns on at a finite U/t despite the U=0 hopping problem having a QBT. The onset of antiferromagnetism takes place at a continuous transition which is consistent with (2+1)D Gross-Neveu criticality. We conclude that generically in models of bilayer graphene, even if the free dispersion has a QBT, small local interactions generate a Dirac phase with no symmetry breaking and ...

arXiv (Cornell University), 2016

We revisit the effect of local interactions on the quadratic band touching (QBT) of Bernal stacked bilayer graphene models using renormalization group (RG) arguments and quantum Monte Carlo simulations of the Hubbard model. We present an RG argument which predicts, contrary to previous studies, that weak interactions do not flow to strong coupling even if the free dispersion has a QBT. Instead they generate a linear term in the dispersion, which causes the interactions to flow back to weak coupling. Consistent with this RG scenario, in unbiased quantum Monte Carlo simulations of the Hubbard model we find compelling evidence that antiferromagnetism turns on at a finite U/t, despite the U = 0 hopping problem having a QBT. The onset of antiferromagnetism takes place at a continuous transition which is consistent with a dynamical critical exponent z = 1 as expected for 2+1 d Gross-Neveu criticality. We conclude that generically in models of bilayer graphene, even if the free dispersion has a QBT, small local interactions generate a Dirac phase with no symmetry breaking and that there is a finite-coupling transition out of this phase to a symmetry-broken state.