Session P11: Focus Session: Graphene Structure, Stacking, Interactions: Strain and Stacking

Non-Abelian gauge potentials in graphene bilayers

We discuss the effect of spatial modulations in the interlayer hopping of graphene bilayers, such as those that arise upon shearing or twisting. We show that their single-particle physics, characterized by charge localization and recurrent formation of zero-energy bands as the pattern period L increases, is governed by a non-Abelian gauge potential arising in the low-energy electronic theory due to the coupling between layers. We find that such gauge-type couplings give rise to a confining potential that, for certain discrete values of L, localizes states at zero energy in particular regions of the Moire patterns. We also draw the connection between the recurrence of the flat zero-energy bands and the non-Abelian character of the potential.   

Electronic Topological Transition in Sliding Bilayer Graphene

We demonstrate theoretically that the topology of energy bands and Fermi surface in bilayer graphene undergoes a very sensitive transition when an extremely tiny lateral interlayer shift occurs in arbitrary directions. The phenomenon originates from a generation of an effective non-Abelian vector potential in the Dirac Hamiltonian by the sliding motions. The characteristics of the transition such as pair annihilations of massless Dirac fermions are dictated by the sliding direction owing to a unique interplay between the effective non-Abelian gauge fields and Berry's phases associated with massless electrons. The transition manifests itself in various measurable quantities such as anomalous density of states, minimal conductivity, and distinct Landau level spectrum.   

Fictitious gauge fields in bilayer graphene

We discuss the effect of elastic deformations on the electronic properties of bilayer graphene membranes. Distortions of the lattice translate into fictitious gauge fields in the electronic Dirac Hamiltonian which are explicitly derived for arbitrary elastic deformations. We include gauge fields associated to intra- as well as inter-layer hopping terms and discuss their effects on the strain-induced Lifshitz transition and on the electron-phonon resistivity. Of special interest is the appearance of a linear coupling for flexural modes which is shown to dominate the temperature-dependent resistivity in suspended samples with low tension.   

Effective theory of rotationally faulted multilayer graphene

The crystal structure of graphene multilayers with an interlayer twist is characterized by Moir\'{e} patterns with various commensurabilities. Also the electronic structure of the material, which grows for instance epitaxially on SiC, is remarkably rich. In this talk an effective low-energy description of such multilayers will be discussed. In certain limits the theory reduces to a (single-layer) Dirac model with space-dependent potentials and mass term. The consequences of this theory will be explored and comparison with experiment will be made. The discussion of experimental consequences will focus on the Landau quantization in a magnetic field, where much experimental data is available. For instance, a spatially modulated splitting of the zeroth Landau level in the material has been observed through scanning tunneling spectroscopy [1]. That splitting finds a natural explanation in the space-dependent mass term of the presented theory [2]. Also a large low-field splitting of higher Landau levels recently observed in graphene multilayers [3] will be shown to follow from that theory. Finally, a theoretically expected [4] amplitude modulation of the Landau level wavefunctions on the top layer of the material will be discussed. \\[4pt] [1] D. L. Miller, K. D. Kubista, G. M. Rutter, M. Ruan, W. A. de Heer, M. Kindermann, P. N. First, and J. A. Stroscio, Nature Physics \textbf{6}, 811 (2010). \\[0pt] [2] M. Kindermann and P. N. First, Phys. Rev. B \textbf{83}, 045425 (2010). \\[0pt] [3] Y. J. Song, A. F. Otte, Y. Kuk, Y. Hu, D. B. Torrance, P. N. First, W. A. de Heer, H. Min, S. Adam, M. D. Stiles, A. H. MacDonald, and J. A. Stroscio, Nature \textbf{467}, 185 (2010). \\[0pt] [4] M. Kindermann and E. G. Mele, Phys. Rev. B \textbf{84}, 161406(R) (2011).   

High-temperature topological insulator states in strained graphene

Recently, it was realized that the electronic properties of graphene can be manipulated via mechanical deformations, which opens prospects for both studying the Dirac fermions in new regimes and for device applications. More specifically, non-uniform strains give rise to pseudomagnetic fields that are opposite in the two valleys of Dirac fermions. Certain natural configurations of strain generate large nearly uniform pseudo-magnetic field, leading to flat spin- and valley-degenerate Landau levels (LL). Here we consider the effect of the Coulomb interactions in strained graphene with nearly uniform pseudo-magnetic field. We show that the spin/valley degeneracies of the LL get lifted, giving rise to topological insulator-like states. We find that both anomalous quantized Hall states and quantum spin Hall states can be realized. These many-body states are characterized by quantized conductance and persist to high temperature scale set by the Coulomb interactions. This work provides a new route to designing robust topological insulator states in mesoscopic graphene and other 2D Dirac materials. \\[4pt] [1] D. A. Abanin, D. A. Pesin, submitted.   

Theory of topological phases in multilayer Graphene

We present microscopic theories of possible topological phases (i.e. quantum anomalous Hall effect, quantum valley Hall effect , and two-dimensional topological insulators) in bilayer graphene systems. We show the phase diagrams as well as the resulting nontrivial edge states in these systems. We further generalize our findings to trilayer graphene systems, where similar topological states may exist. Finally, we give low energy effective models to reveal the underlying physics of these topological states.   

The correct solution for strain-induced pseudo vector potentials in graphene

Prior calculations of the strain-induced pseudo vector potential considered only the change in the nearest neighbor hopping energy in their derivations [1,2]. Here we show that including lattice deformations introduces new terms of the same order in strain. These terms are different at each K point, causing each population of electrons to feel different strain induced pseudo magnetic fields. We use isotropic strain, a situation where lattice deformations solely determine the pseudo vector potential, to illustrate the conceptual importance of these new terms. Finally, we exhibit how the additional terms force us to rethink the strain geometries that were previously thought to generate particular pseudo magnetic fields. [1] A.H. Castro Neto, et al. \textit{Rev. Mod. Phys.} \textbf{81}, 109 (2009). [2] M.A.H. Vozmediano, M.I. Katsnelson, and F. Guinea, Phys. Rep. \textbf{496}, 109 (2010).   

Two-Dimensional Topological Insulator State and Topological Phase Transition in Bilayer Graphene

In this talk, we show that gated AB-stacking bilayer graphene can host a quantum phase transition from a quantum valley Hall (QVH) insulator to a two-dimensional strong topological insulator (TI) as a function of Rashba spin-orbit (SO) coupling. Different from a conventional TI phase, the edge modes of our strong TI phase exhibit both spin and valley filtering, and thus share the properties of both TI and QVH insulators. The strong TI phase remains robust in the presence of weak intrinsic SO coupling.   

Disorder-induced inhomogeneity in bilayer graphene

We describe the effect of charge density inhomgeneity (electron and hole puddles) and a spatially fluctuating band gap caused by charged impurity disorder in bilayer graphene. We derive a phenomenological averaging technique to calculate $\frac{d\mu}{dn}$ in the presence of this disorder and apply it recent experimental measurements in suspended bilayer graphene. This work was done in collaboration with S. Das Sarma, E. Hwang, and H. Min.   

Raman spectra of strained bilayer graphene

In the Raman spectra of strained single layer graphene, modified electron and phonon dispersions result in the splitting of the double resonance 2D Raman band. It originates from significant changes in the resonant conditions owing to both the distorted Dirac cones and anisotropic modifications of the phonon dispersion under uniaxial strains [D. Yoon et al., Phys. Rev. Lett. \textbf{106}, 155502 (2011)]. In unstrained bilayer graphene, the Raman 2D band consists of 4 Lorentzian peaks corresponding to the double resonance Raman scattering processes between the two conduction bands and the two valance bands. Under uniaxial strain, each of the four peaks in the Raman 2D band. We examined the polarization behaviors of the split 2D band and analyzed using a model similar to the one used for single layer graphene.   

Field Effects on the Optical Vibrations in Bilayer Graphene

A first-principles study of the optical phonon modes in bilayer graphene (BLG) under a perpendicular electric field is presented. It is found that the electric field breaks the inversion symmetry of BLG and mixes the eigenvectors of the in-phase and out-of-phase optical modes. Detailed analysis shows that the mixing effect is more evident on the out-of-plane optical modes than on the in-plane modes. The field effects on the electron-phonon coupling in BLG will also be discussed.   

Six-band nearest-neighbor tight-binding model for the $\pi $-bands of bulk graphene and graphene nanoribbons

The commonly used single-p$_{z}$ orbital first nearest-neighbor tight-binding model faces two main problems: (i) it fails to reproduce asymmetries in the bulk graphene bands; (ii) it cannot provide a realistic model for hydrogen passivation of the edge atoms. As a result, some armchair graphene nanoribbons (AGNRs) are incorrectly predicted as metallic. A new nearest-neighbor, three orbital per atom p/d tight-binding model [1] is built to address these issues. The parameters of the model are fit to bandstructures obtained from first-principles density-functional theory and many-body perturbation theory within the GW approximation, giving excellent agreement with the ab initio AGNR bands. This model is employed to calculate the current-voltage characteristics of an AGNR MOSFET and the conductance of rough-edge AGNRs, finding significant differences versus the single-p$_{z}$ model. Taken together these results demonstrate the importance of an accurate and computational efficient band structure model for predicting the performance of graphene-based nanodevices. [1] T. B. Boykin, M. Luisier, G. Klimeck, X. Jiang, N. Kharche, Y. Zhou and S. Nayak, J. Appl. Phys. 109, 104304 (2011)   

Electronic structures of geometrically restricted nanocarbons

We use large scale ab-initio calculations to explore the electronic structures of graphene, graphene nanoribbons, and carbon nanotubes periodically perforated with nanopores. We disclose common features in electronic structures of these porous nanocarbons (PNCs) with nanopores of different size, shapes, and localization. We develop a unified picture that permits to analytically predict and systematically characterize metal-semiconductor transitions in PNCs, allowing mapping of their electronic structures on those in pristine nanocarbons [1]. In contrast to other studies, we show that porous graphene can be metallic for certain arrangements of the pores. When we replace pores by defects (such as SW 55-77), we observe similar features in the electronic structures of the formed nanocarbons. We also study magnetic ordering in these nanocarbons and show that the position of pores/defects can influence the ordering of localized electronic spin states. These periodically modified nanocarbons with highly tunable band structures have great potential applications in electronics and optics. [1] A.I. Baskin and P. Kral, Sci. Rep.1, 36 (2011).