Many-body effects in doped graphene on a piezoelectric substrate

We investigate the many-body properties of graphene on top of a piezoelectric substrate, focusing on the interaction between the graphene electrons and the piezoelectric acoustic phonons. We calculate the electron and phonon self-energies as well as the electron mobility limited by the substrate phonons. We emphasize the importance of the proper screening of the electron-phonon vertex and discuss the various limiting behaviors as a function of electron energy, temperature, and doping level. The effect on the graphene electrons of the piezoelectric acoustic phonons is compared with that of the intrinsic deformation acoustic phonons of graphene. Substrate phonons tend to dominate over intrinsic ones for low doping levels at high and low temperatures.Comment: 13 pages, 8 figure

Novel effects of strains in graphene and other two dimensional materials

The analysis of the electronic properties of strained or lattice deformed graphene combines ideas from classical condensed matter physics, soft matter, and geometrical aspects of quantum field theory (QFT) in curved spaces. Recent theoretical and experimental work shows the influence of strains in many properties of graphene not considered before, such as electronic transport, spin-orbit coupling, the formation of Moir\'e patterns, optics, ... There is also significant evidence of anharmonic effects, which can modify the structural properties of graphene. These phenomena are not restricted to graphene, and they are being intensively studied in other two dimensional materials, such as the metallic dichalcogenides. We review here recent developments related to the role of strains in the structural and electronic properties of graphene and other two dimensional compounds.Comment: 75 pages, 15 figures, review articl

Casimir Energy of a BEC: From Moderate Interactions to the Ideal Gas

Considering the Casimir effect due to phononic excitations of a weakly interacting dilute {BEC}, we derive a re-normalized expression for the zero temperature Casimir energy $\mathcal{E}_c$ of a {BEC} confined to a parallel plate geometry with periodic boundary conditions. Our expression is formally equivalent to the free energy of a bosonic field at finite temperature, with a nontrivial density of modes that we compute analytically. As a function of the interaction strength, $\mathcal{E}_c$ smoothly describes the transition from the weakly interacting Bogoliubov regime to the non-interacting ideal {BEC}. For the weakly interacting case, $\mathcal{E}_c$ reduces to leading order to the Casimir energy due to zero-point fluctuations of massless phonon modes. In the limit of an ideal Bose gas, our result correctly describes the Casimir energy going to zero.Comment: 12 pages, 3 figures, accepted for publication in JPA. New version with corrected typos and an additional appendi

Casimir force on interacting Bose-Einstein condensate

We have presented an analytic theory for the Casimir force on a Bose-Einstein condensate (BEC) which is confined between two parallel plates. We have considered Dirichlet boundary conditions for the condensate wave function as well as for the phonon field. We have shown that, the condensate wave function (which obeys the Gross-Pitaevskii equation) is responsible for the mean field part of Casimir force, which usually dominates over the quantum (fluctuations) part of the Casimir force.Comment: Accepted in Journal of Physics B: Atomic, Molecular and Optical Physic

Soziale Bedingungen von Schulleistungen: Zur Erfassung von Kontextmerkmalen durch Schüler-, Schul- und Elternfragebögen [Elektronische Ressource]

Author's comment: sine ann

Teachers’ appraisals of adjectives relating to mathematics tasks

Curricular implementations are unlikely to deliver the anticipated benefits for mathematics learners if written guidance to teachers is interpreted and enacted differently from the ways that policymakers and curriculum designers intend. One way in which this could happen is in relation to the mathematics tasks that teachers deploy in the classroom. Teachers and curriculum designers have developed an extensive vocabulary for describing tasks, using adjectives such as ‘rich’, ‘open’, ‘real-life’, ‘engaging’ and so on. But do teachers have a shared understanding of what these adjectives mean when they are applied to mathematics tasks? In Study 1 we investigated teachers’ appraisals of adjectives used to describe mathematics tasks, finding that task appraisals vary on seven dimensions, which we termed engagement, demand, routineness, strangeness, inquiry, context and interactivity. In Study 2, focusing on the five most prominent dimensions, we investigated whether teachers have a shared understanding of the meaning of adjectives when applied to mathematics tasks. We found that there was some agreement about inquiry and context, some disagreement about routineness, and clear disagreement about engagement and demand. We conclude that at least some adjectives commonly used to describe tasks are interpreted very differently by different teachers. Implications for how tasks might be discussed meaningfully by teachers, teacher educators and curriculum designers are highlighted

Electrically tunable transverse magnetic focusing in graphene

Author's final manuscript January 9, 2013Electrons in a periodic lattice can propagate without scattering for macroscopic distances despite the presence of the non-uniform Coulomb potential due to the nuclei. Such ballistic motion of electrons allows the use of a transverse magnetic field to focus electrons. This phenomenon, known as transverse magnetic focusing (TMF), has been used to study the Fermi surface of metals and semiconductor heterostructures, as well as to investigate Andreev reflection and spin–orbit interaction, and to detect composite fermions. Here we report on the experimental observation of TMF in high-mobility mono-, bi- and tri-layer graphene devices. The ability to tune the graphene carrier density enables us to investigate TMF continuously from the hole to the electron regime and analyse the resulting focusing fan. Moreover, by applying a transverse electric field to tri-layer graphene, we use TMF as a ballistic electron spectroscopy method to investigate controlled changes in the electronic structure of a material. Finally, we demonstrate that TMF survives in graphene up to 300 K, by far the highest temperature reported for any system, opening the door to new room-temperature applications based on electron-optics.National Science Foundation (U.S.) (CAREER Award DMR-0845287)United States. Office of Naval Research. GATE MURI Projec

Effects of tutor-related behaviours on the process of problem-based learning

Tutors in a Problem-Based Learning (PBL) curriculum are thought to play active roles in guiding students to develop frameworks for use in the construction of knowledge. This implies that both subject-matter expertise and the ability of tutors to facilitate the learning process must be important in helping students learn. This study examines the behavioural effects of tutors in terms of subject-matter expertise, social congruence and cognitive congruence on students’ learning process and on their final achievement. The extent of students’ learning at each PBL phase was estimated by tracking the number of relevant concepts recalled at the end of each learning phase, while student achievement was based on students’ ability to describe and elaborate upon the relationship between relevant concepts learned. By using Analysis of Covariance, social congruence of the tutor was found to have a significant influence on learning in each PBL phase while all of the tutor-related behaviours had a significant impact on student achievement. The results suggest that the ability of tutors to communicate informally with students and hence create a less threatening learning environment that promotes a free flow exchange of ideas, has a greater impact on learning at each of the PBL phases as compared to tutors’ subject-matter expertise and their ability to explain concepts in a way that is easily understood by students. The data presented indicates that these tutor-related behaviours are determinants of learning in a PBL curriculum, with social congruence having a greater influence on learning in the different PBL phases

All-Optical Generation of Surface Plasmons in Graphene

27 pages, 12 figures, includes supplementary materialarXiv is an e-print service in the fields of physics, mathematics, computer science, quantitative biology, quantitative finance and statistics.Here we present an all-optical plasmon coupling scheme, utilising the intrinsic nonlinear optical response of graphene. We demonstrate coupling of free-space, visible light pulses to the surface plasmons in a planar, un-patterned graphene sheet by using nonlinear wave mixing to match both the wavevector and energy of the surface wave. By carefully controlling the phase-matching conditions, we show that one can excite surface plasmons with a defined wavevector and direction across a large frequency range, with an estimated photon efficiency in our experiments approaching $10^{-5}$