Band topology and quantum spin Hall effect in bilayer graphene

We consider bilayer graphene in the presence of spin orbit coupling, to assess its behavior as a topological insulator. The first Chern number $n$ for the energy bands of single and bilayer graphene is computed and compared. It is shown that for a given valley and spin, $n$ in a bilayer is doubled with respect to the monolayer. This implies that bilayer graphene will have twice as many edge states as single layer graphene, which we confirm with numerical calculations and analytically in the case of an armchair terminated surface. Bilayer graphene is a weak topological insulator, whose surface spectrum is susceptible to gap opening under spin-mixing perturbations. We also assess the stability of the associated topological bulk state of bilayer graphene under various perturbations. Finally, we consider an intermediate situation in which only one of the two layers has spin orbit coupling, and find that although individual valleys have non-trivial Chern numbers, the spectrum as a whole is not gapped, so that the system is not a topological insulator.Comment: 9 pages. 9 figures include

Non-hermitian topology as a unifying framework for the Andreev versus Majorana states controversy

Zero-energy Andreev levels in hybrid semiconductor-superconductor nanowires mimic all expected Majorana phenomenology, including 2 e2∕ h conductance quantisation, even where band topology predicts trivial phases. This surprising fact has been used to challenge the interpretation of various transport experiments in terms of Majorana zero modes. Here we show that the Andreev versus Majorana controversy is clarified when framed in the language of non-Hermitian topology, the natural description for quantum systems open to the environment. This change of paradigm allows one to understand topological transitions and the emergence of zero modes in more general systems than can be described by band topology. This is achieved by studying exceptional point bifurcations in the complex spectrum of the system’s non-Hermitian Hamiltonian. Within this broader topological classification, Majoranas from both conventional band topology and a large subset of Andreev levels at zero energy are in fact topologically equivalent, which explains why they cannot be distinguishedWe thank J. Cayao for useful discussions in the early stages of this work. Research supported by the Spanish Ministry of Science, Innovation and Universities through Grants PGC2018-097018-B-I00, FIS2015-65706-P, FIS2015-64654-P, FIS2016-80434-P (AEI/FEDER, EU), the FPI programme BES-2016-078122, the Ramón y Cajal programme Grants RYC-2011-09345, RYC-2013-14645, the María de Maeztu Programme for Units of Excellence in R&D (MDM-2014-0377), and the European Union’s Horizon 2020 research and innovation programme under the FETOPEN Grant Agreement No. 828948. We also acknowledge support from CSIC Research Platform on Quantum Technologies PTI-00

Zero Landau level in folded graphene nanoribbons

Graphene nanoribbons can be folded into a double layer system keeping the two layers decoupled. In the Quantum Hall regime folds behave as a new type of Hall bar edge. We show that the symmetry properties of the zero Landau level in metallic nanoribbons dictate that the zero energy edge states traversing a fold are perfectly transmitted onto the opposite layer. This result is valid irrespective of fold geometry, magnetic field strength and crystallographic orientation of the nanoribbon. Backscattering suppression on the N=0 Hall plateau is ultimately due to the orthogonality of forward and backward channels, much like in the Klein paradox.Comment: Final published version, with supplementary material appendi

Strain-induced bound states in transition-metal dichalcogenide bubbles

This is an author-created, un-copyedited version of an article published in 2D Materials. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/2053-1583/ab0113We theoretically study the formation of single-particle bound states confined by strain at the center of bubbles in monolayers of transition-metal dichalcogenides (TMDs). Bubbles ubiquitously form in two-dimensional crystals on top of a substrate by the competition between van der Waals forces and the hydrostatic pressure exerted by trapped fluid. This leads to strong strain at the center of the bubble that reduces the bangap locally, creating potential wells for the electrons that confine states inside. We simulate the spectrum versus the bubble radius for the four semiconducting group VI TMDs, MoS2, WSe2, WS2 and MoSe2, and find an overall Fock-Darwin spectrum of bubble bound states, characterised by small deviations compatible with Berry curvature effects. We analyse the density of states, the state degeneracies, orbital structure and optical transition rules. Our results show that elastic bubbles in these materials are remarkably efficient at confining photocarriersWe acknowledge funding from the Graphene Flagship, contract CNECTICT-604391, from the Comunidad de Madrid through Grant MAD2D-CM, S2013/MIT-3007, from the Spanish Ministry of Economy and Competitiveness through Grants No. RYC-2011-09345, RYC-2016-20663, FIS2015-65706-P, FIS2016-80434-P (AEI/FEDER, EU) and the María de Maeztu Programme for Units of Excellence in R&D (MDM-2014-0377

Role Play As An Approach In Developing Students Communicative Competence

This study was conducted to examine the outcome of role play as an approach in developing the communicative competence of freshmen. Moreover, the focus of this study was on how the role-play as an approach was conducted; hence, necessary enhancement should be offered if needed. The information were gathered through Focused Group Discussion (FGD). Guide questions were prepared and validated; interviews were recorded, transcribed, interpreted and analyzed. Results revealed that role play as a type of communicative activity was a valuable classroom approach to assist students in developing their communicative competence and to provide the students an opportunity to practice the English language with fluency and accuracy. It was also discovered that role play was beneficial in developing students’ communicative competence provided that it was not done too long. It encouraged students to express themselves; provided self-confidence and opportunity for practicing the rules of social behavior; and allowed learners to use their learned language

Disorder-induced pseudodiffusive transport in graphene nanoribbons.

We study the transition from ballistic to diffusive and localized transport in graphene nanoribbons in the presence of binary disorder, which can be generated by chemical adsorbates or substitutional doping. We show that the interplay between the induced average doping (arising from the nonzero average of the disorder) and impurity scattering modifies the traditional picture of phase-coherent transport. Close to the Dirac point, intrinsic evanescent modes produced by the impurities dominate transport at short lengths giving rise to a regime analogous to pseudodiffusive transport in clean graphene, but without the requirement of heavily doped contacts. This intrinsic pseudodiffusive regime precedes the traditional ballistic, diffusive, and localized regimes. The last two regimes exhibit a strongly modified effective number of propagating modes and a mean free path which becomes anomalously large close to the Dirac point

Nonlocality of Majorana modes in hybrid nanowires

Spatial separation of Majorana zero modes distinguishes trivial from topological midgap states and is key to topological protection in quantum computing applications. Although signatures of Majorana zero modes in tunneling spectroscopy have been reported in numerous studies, a quantitative measure of the degree of separation, or nonlocality, of the emergent zero modes has not been reported. Here, we present results of an experimental study of nonlocality of emergent zero modes in superconductor-semiconductor hybrid nanowire devices. The approach takes advantage of recent theory showing that nonlocality can be measured from splitting due to hybridization of the zero mode in resonance with a quantum dot state at one end of the nanowire. From these splittings as well as anticrossing of the dot states, measured for even and odd occupied quantum dot states, we extract both the degree of nonlocality of the emergent zero mode, as well as the spin canting angles of the nonlocal zero mode. Depending on the device measured, we obtain either a moderate degree of nonlocality, suggesting a partially separated Andreev subgap state, or a highly nonlocal state consistent with a well-developed Majorana modeThis research was supported by Microsoft, the Danish National Research Foundation, the European Commission, and the Spanish Ministry of Economy and Competitiveness through Grants No. FIS2015-65706-P, No. FIS2015-64654-P, and No. FIS2016-80434-P (AEI/FEDER, EU), the Ramón y Cajal programme Grant No. RYC-2011-09345, and the María de Maeztu Programme for Units of Excellence in R&D (Grant No. MDM-2014-0377). C.M.M. acknowledges support from the Villum Foundation. M.-T.D. acknowledges support from State Key Laboratory of High Performance Computing, Chin

TEACH US THE WAY WE WANT: TEACHING APPROACH FOR SPECIAL NEEDS STUDENTS

This study was conducted to explore the learning of special needs students in reading and writing; determine their preferred teaching approaches; and obtain their suggestions to improve the teaching of both reading and writing modules. Focus Group Discussion (FGD) was conducted in obtaining pertinent information. Results regarding what the learners learned; and the best approach for teaching English revealed interesting insights which could guide special needs teachers. Suggestions which aimed at improving English teaching were also provided.     Article visualizations