Bulletin of the American Physical Society
APS March Meeting 2016
Volume 61, Number 2
Monday–Friday, March 14–18, 2016; Baltimore, Maryland
Session K17: Many-body Interactions in Graphene |
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Sponsoring Units: DCMP DMP Chair: Vikram Deshpande, University of utah Room: 316 |
Wednesday, March 16, 2016 8:00AM - 8:12AM |
K17.00001: Gate-tunable electron focusing across graphene p-n junction Shaowen Chen, Zheng Han, Lei Wang, Cory Dean, James Hone Electrons moving across a ballistic semiconductor junction experience a change in trajectory described by an electronic version of Snell's law. In the case of a barrier separating regions of $n$ and $p $type carriers, negative refraction is expected, which theoretically leads to a Veselago type of electron focusing. Being a ballistic bipolar 2D system, hexagonal Boron Nitride-encapsulated graphene is expected to be a model a system to realize this effect, however, robust demonstration of veselago lensing has remained limited. We describe novel methods to fabricate high quality graphene p-n junctions with atomically sharp boundaries. Using a magnetic focusing measurement scheme, we demonstrate unambiguous signatures of negative refraction in these devices. Our observations are in good agreement with simulations and shed light on future application for electronic optics in ballistic graphene. [Preview Abstract] |
Wednesday, March 16, 2016 8:12AM - 8:24AM |
K17.00002: Dynamical polarizability of the 2D pseudospin-1 dice lattice John Malcolm, Elisabeth Nicol The two-dimensional dice lattice is composed of three triangular sublattices whose low-energy excitation spectrum consists of Dirac-Weyl fermions with pseudospin-1. The energy dispersion has two Dirac cones, like the pseudospin-1/2 two-triangular-sublattice graphene, with an additional third band exactly at zero energy. We present theoretical results for the electronic dynamical polarization function in the material. This is a fundamental entity in many-body physics, renormalizing the Coulomb interaction through the dielectric function. From the polarization function we also obtain the Lindhard function, the plasmon branch, and can discuss other screening effects. These are constrasted with those of graphene. [Preview Abstract] |
Wednesday, March 16, 2016 8:24AM - 8:36AM |
K17.00003: Dynamical Energy Gap Engineering in Graphene via Oscillating Out-of-Plane Deformations Nancy Sandler, Dawei Zhai The close relation between electronic properties and mechanical deformations in graphene has been the topic of active research in recent years. Interestingly, the effect of deformations on electronic properties can be understood in terms of pseudo-magnetic fields, whose spatial distribution and intensity are controllable via the deformation geometry. Previous results showed that electromagnetic fields (light) have the potential to induce dynamical gaps in graphene’s energy bands, transforming graphene from a semimetal to a semiconductor [1, 2]. However, laser frequencies required to achieve these regimes are in the THz regime, which imposes challenges for practical purposes. In this talk we report a novel method to create dynamical gaps using oscillating mechanical deformations, i.e., via time-dependent pseudo-magnetic fields. Using the Floquet formalism we show the existence of a dynamical gap in the band structure at energies set by the frequency of the oscillation, and with a magnitude tuned by the geometry of the deformation. This dynamical-mechanical manipulation strategy appears as a promising venue to engineer electronic properties of suspended graphene devices. [1] Syzranov et al. Phys. Rev. B 78, 045407 (2008). [2] Oka et al. Phys. Rev. B 79, 081406(R) (2009). [Preview Abstract] |
Wednesday, March 16, 2016 8:36AM - 8:48AM |
K17.00004: Hyperfine interaction in hydrogenated graphene Noel Garcia, Manuel Melle, Joaquin Fernandez-Rossier We study the hyperfine interaction of Hydrogen chemisorbed in graphene nanostructures with a gap in their spectrum, such as islands and ribbons. Chemisorption of Hydrogen on graphene results in a bound in-gap state that hosts a single electron localized around the adatom. Using both density functional theory and a four-orbital tight-binding model we study the hyperfine interaction between the hydrogen nuclear spin and the conduction electrons in graphene. We find that the strength of the hyperfine interaction decreases for larger nanostructures for which the energy gap is smaller. We then compare the results of the hyperfine interaction for large nanostructures with those of graphene 2D crystal with a periodic arrangement of chemisorbed Hydrogen atoms, obtaining very similar results. The magnitude of the hyperfine interaction is about 150 MHz, in line with that of Si:P. We acknowledge financial support by Marie-Curie-ITN 607904-SPINOGRAPH. [Preview Abstract] |
Wednesday, March 16, 2016 8:48AM - 9:00AM |
K17.00005: Two-particle vortices in graphene Mikhail Portnoi, Charles Downing We show that a pair of two-dimensional massless Dirac-Weyl fermions can form a bound state independently on the sign of the inter-particle interaction potential, as long as this potential decays at large distances faster than Kepler's inverse distance law. The coupling occurs only at the Dirac point, when the charge carriers lose their chirality. These bipartite states must have a non-zero internal angular momentum, meaning that they only exist as stationary vortices. This leads to the emergence of a new type of energetically-favorable quasiparticles: double-charged zero-energy vortices. Their bosonic nature allows condensation and gives rise to Majorana physics without invoking a superconductor. The presence of dark-matter-like silent immobile vortices explains a range of poorly understood experiments in gated graphene structures at low doping. [Preview Abstract] |
Wednesday, March 16, 2016 9:00AM - 9:12AM |
K17.00006: Local density of states in bilayer graphene with 1D potential well Akihiro Okamoto, Takehito Yokoyama, Shuichi Murakami Monolayer graphene shows anomalous behaviors at the scattering by a 1D potential well due to the massless Dirac fermions, and it is called Klein paradox. In contrast, bilayer graphene shows different behaviors at the scattering by the potential well, and is attributed to the massive chiral fermions with a parabolic dispersion. We then expect that bound states at the 1D potential well for the two cases are different, due to the different effective models and the K and K' points. In the present work, we calculate bound states induced by a 1D potential well, and compare them with the properties of 1D edge states. In particular, in the bilayer graphene, there are two types of bound states, both of which have a parabolic dispersion near K and K' points, and we describe how the dispersion changes by the change of the potential strength. We then calculate the local density of states at various positions, contributed by the scattering states and the bound states by the 1D potential well, and discuss how they depend on the potential strength. [Preview Abstract] |
Wednesday, March 16, 2016 9:12AM - 9:24AM |
K17.00007: Non-perturbative renormalization group calculation of the quasi-particle velocity and the dielectric function of graphene. Anand Sharma, Carsten Bauer, Andreas Rueckriegel, Peter Kopietz We use a nonperturbative functional renormalization group approach to calculate the renormalized quasiparticle velocity $v (k)$ and the static dielectric function $\epsilon(k)$ of suspended graphene as function of an external momentum $k$. We fit our numerical result for $v(k)$ to $v(k)/v_F = A + B \ln(\Lambda_0/k)$, where $v_F$ is the bare Fermi velocity, $\Lambda_0$ is an ultraviolet cutoff, and $A = 1.37$, $B =0.51$ for the physically relevant value ($e^2/v_F =2.2$) of the coupling constant. In $\textit{stark}$ contrast to calculations based on the static random-phase approximation, we find that $\epsilon(k)$ approaches unity for $k\rightarrow 0$. Our result for $v(k)$ agrees very well with a recent measurement by Elias $\textit{et al.}$ [Nat. Phys. $\textbf{7}$, 701 (2011)]. With in the same approximation, we also explore an alternative scheme in order to understand the true nature of the low energy (momentum) behavior in graphene. [Preview Abstract] |
Wednesday, March 16, 2016 9:24AM - 9:36AM |
K17.00008: Majorana Zero Modes in Graphene Pablo San-Jose, Jose L. Lado, Ramón Aguado, Francisco Guinea, Joaquín Fernández-Rossier A clear demonstration of topological superconductivity (TS) and Majorana zero modes remains one of the major pending goal in the field of topological materials. One common strategy to generate TS is through the coupling of an s-wave superconductor to a helical half-metallic system. Numerous proposals for the latter have been put forward in the literature, most of them based on semiconductors or topological insulators with strong spin-orbit coupling. Here we demonstrate an alternative approach for the creation of TS in graphene/superconductor junctions without the need of spin-orbit coupling. Our prediction stems from the helicity of graphene's zero Landau level edge states in the presence of interactions, and on the possibility, experimentally demonstrated, to tune their magnetic properties with in-plane magnetic fields. We show how canted antiferromagnetic ordering in the graphene bulk close to neutrality induces TS along the junction, and gives rise to isolated, topologically protected Majorana bound states at either end. We also discuss possible strategies to detect their presence. Remarkable progress has recently been reported in the fabrication of the proposed type of junctions, which offers a promising outlook for Majorana physics in graphene systems. [Preview Abstract] |
Wednesday, March 16, 2016 9:36AM - 9:48AM |
K17.00009: Electron interactions in graphene through an effective Coulomb potential Joao N. B. Rodrigues, Shaffique Adam A recent numerical work [H.-K. Tang {\it et al}, PRL 115, 186602 (2015)] considering graphene's $\pi$-electrons interacting through an effective Coulomb potential that is finite at short-distances, stressed the importance of the $sp^{2}$-electrons in determining the semimetal to Mott insulator phase transition in graphene. Some years ago, I. F. Herbut [PRL 97, 146401 (2006)] studied such a transition by mapping graphene's $\pi$-electrons into a Gross-Neveu model. From a different perspective, D. T. Son [PRB 75, 235423 (2007)] put the emphasis on the long-range interactions by modelling graphene as Dirac fermions interacting through a bare Coulomb potential. Here we build on these works and explore the phase diagram of Dirac fermions interacting through an effective Coulomb-like potential screened at short-distances. The interaction potential used allows for analytic results that controllably switch between the two perspectives above. [Preview Abstract] |
Wednesday, March 16, 2016 9:48AM - 10:00AM |
K17.00010: Quasiparticle weight and renormalized Fermi velocity of graphene with long-range Coulomb interactions Ho-Kin Tang, Jia Ning Leaw, J. N. B. Rodrigues, P. Sengupta, F. F. Assaad, S. Adam In this work, we study the effects of realistic Coulomb interactions in graphene using a projective quantum Monte Carlo simulation of electrons at half-filing on a honeycomb lattice. We compute the quasiparticle residue, the renormalized Fermi velocity and the antiferromagnetic order parameter as a function of both the long-range and short-range components of the Coulomb potential. We find that the Mott insulator transition is determined mostly by the short-range interaction and is consistent with the Gross-Neveu-Yukawa critical theory. Far from the critical point and in the semi-metallic regime, we find that the Fermi-velocity and quasiparticle residue are influenced by the long-range tail of the Coulomb potential, and for very small interaction strength are consistent with predictions of first order perturbation theory. For experimentally relevant and stronger values of the long-range interaction, our numerical data contradicts prediction from both perturbation theory and the renormalization group approaches. [Preview Abstract] |
Wednesday, March 16, 2016 10:00AM - 10:12AM |
K17.00011: Snake states and their symmetries in graphene Rakesh Tiwari, Yang Liu, Matej Brada, C. Bruder, F. V. Kusmartsev, E. J. Mele Snake states are open trajectories for charged particles moving in two dimensions under the influence of a spatially varying perpendicular magnetic field. They can also occur in a constant perpendicular magnetic field when the particle density is made nonuniform as realized at a pn junction in a semiconductor, or in graphene. We examine the correspondence of such trajectories in monolayer graphene in the quantum limit for two families of domain walls: (a) a uniform doped carrier density in an antisymmetric perpendicular magnetic field and (b) antisymmetric carrier density distribution in a uniform perpendicular magnetic field. Although, these families support different internal symmetries, the pattern of the boundary and interface currents is the same in both cases. We demonstrate that these two physically different situations are gauge equivalent when rewritten in a Nambu doubled formulation of the two limiting problems. Using gauge transformations in particle-hole space to connect these two problems, we map the protected interfacial modes to the Bogoliubov quasiparticles of an interfacial one-dimensional p-wave paired state. [Preview Abstract] |
Wednesday, March 16, 2016 10:12AM - 10:24AM |
K17.00012: A complete set of data to characterize loop braiding statistics in (3+1)-D topological phases Dominic Else, Chetan Nayak In (2+1)-D, topological phases of matter can be classified by the braiding statistics of their particle-like excitations. Similarly, in (3+1)-D one expects topological phases to be characterized by the braiding statistics of their excitations, which may be particle-like or loop-like. A ``braiding'' of loop-like excitations is any continuous deformation of some collection of (possibly linked) loops which eventually returns the loops to their original locations. Here, we identify a finite set of basic data which determines the amplitude for \emph{any} loop braiding in an abelian (3+1)-D topological phase. This includes the ``three-loop braiding'' recently considered by several authors, but also all other possible braidings. Our basic data are the natural generalization of the $F$ and $R$ symbols of (2+1)-D topological phases to (3+1)-D. From a mathematical point of view, we expect them to correspond to a ``ribbon 2-category''. [Preview Abstract] |
Wednesday, March 16, 2016 10:24AM - 10:36AM |
K17.00013: A Bosonic Analogue of a Topological Dirac Semi-Metal Matthew Lapa, Gil Young Cho, Taylor Hughes We construct a bosonic analogue of a two-dimensional topological Dirac Semi-Metal (DSM). The low-energy description of the most basic 2D DSM model consists of two Dirac cones at positions $\pm\mathbf{k}_0$ in momentum space. The local stability of the Dirac cones is guaranteed by a composite symmetry $Z_2^{\mathcal{TI}}$, where $\mathcal{T}$ is time-reversal and $\mathcal{I}$ is inversion. This model also exhibits interesting time-reversal and inversion symmetry breaking electromagnetic responses. In this work we construct a bosonic analogue of a DSM by replacing each Dirac cone with a copy of the $O(4)$ Nonlinear Sigma Model (NLSM) with topological theta term and theta angle $\theta=\pm \pi$. One copy of this NLSM also describes the gapless surface termination of the 3D Bosonic Topological Insulator (BTI). We compute the time-reversal and inversion symmetry breaking electromagnetic responses for our model and show that they are twice the value one gets in the DSM case. We also investigate the local stability of the individual $O(4)$ NLSM's in the BSM model. Along the way we clarify many aspects of the surface theory of the BTI including the electromagnetic response, the charges of vortex excitations, and the stability to symmetry-allowed perturbations. [Preview Abstract] |
Wednesday, March 16, 2016 10:36AM - 10:48AM |
K17.00014: Hydrodynamic & Transport Properties of Dirac Materials in the Quantum Limit Matthew Gochan, Kevin Bedell Dirac materials are a versatile class of materials in which an abundance of unique physical phenomena can be observed. Such materials are found in all dimensions, with the shared property that their low-energy fermionic excitations behave as massless Dirac fermions and are therefore governed by the Dirac equation. The most popular Dirac material, its two dimensional version in graphene, is the focus of this work. We seek a deeper understanding of the interactions in the quantum limit within graphene. Specifically, we derive hydrodynamic and transport properties, such as the conductivity, viscosity, and spin diffusion, in the low temperature regime where electron-electron scattering is dominant. To conclude, we look at the so-called universal lower bound conjectured by the anti-de Sitter/conformal field theory (AdS/CFT) correspondence for the ratio of shear viscosity to entropy density ratio. The lower bound, given by $\eta/s\geq\hbar/(4\pi k_B)$, is supposedly obeyed by all quantum fluids. This leads us to ask whether or not graphene can be considered a quantum fluid and perhaps a "nearly perfect fluid"(NPF); if this is the case, is it possible to find a violation of this bound at low temperatures. [Preview Abstract] |
Wednesday, March 16, 2016 10:48AM - 11:00AM |
K17.00015: Matrix Product State approach to quantum Hall quasielectrons Hans Hansson, Eddy Ardonne, Jonas Kjäll Matrix product state (MPS) techniques have been successfully used to study quasiholes in different quantum Hall states. In particular it has provided a numerically very efficient way to calculate statistical braiding phases. So far it has been hard to generalize these methods to also describe quasielectrons. Using recently developed techniques for constructing explicit wave functions for the abelian quantum Hall hierarchy, we suggest a new way to construct MPS wave functions for states containing quasielectrons, and also for Abelian hierarchy states. [Preview Abstract] |
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