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In an unconstrained elastic body, emergence of zero natural frequencies is an expectable outcome on account of the body's ability to purely translate or rotate with no structural deformation. Recent advances in literature have pushed such conventional definition and demonstrated properties transcending typical zero-frequency modes, such as localization of deformation at a structural edge or corner. In this paper, a spring–mass honeycomb lattice with an elastic foundation, referred to here as mechanical graphene, is designed to exhibit zero-frequency corner modes. A central element in the proposed design is the elastic foundation, and the zero-frequency corner modes are enabled by intricate modulation of the elastic-foundation's stiffness. These modes are proven to have their origins from the dynamics of a diatomic chain, made from a single strip of the mechanical graphene with free boundaries. Different shapes of finite mechanical graphene with free boundaries are considered and conditions leading to the manifestation of corner modes are correlated with the angle of corners and stiffness of springs supporting them. Finally, the effect of defects on zero-frequency corner modes is briefly discussed, demonstrating robustness against structural defects that are distant from corners. • The concept of zero-frequency corner modes in a mechanical graphene is introduced. • Elastic foundation of positive-negative springs enables zero-frequency corner modes. • Corner modes origin is connected to edge modes in a comparable diatomic lattice. • Corner modes only occur in mechanical graphene having 60°-angle corners. • Theory is verified numerically using different shapes of mechanical graphene. [Display omitted] [ABSTRACT FROM AUTHOR]

Next, the researchers applied different magnetic fields to the graphene to measure how its magnetoresistance changed. This is partly down to graphene's electrons and holes being highly mobile and therefore sensitive to tiny changes in an external magnetic field, the researchers write in their paper. Its unparalleled ability to increase or decrease its electrical resistance in response to a magnetic field could one day have applications for how we store data. [Extracted from the article]

The article discusses various research related to graphene, which are sheets of carbon that are one atom thick. Graphene have two-dimensional honeycomb lattice of carbon atoms that possess fantastic electrical conductivity and a strength that is 10 times of a steel. Research on graphene explored various issues including the fabrication of graphene photodetector, the role of nanoparticles in generating nanoribbons from graphene sheets and the relevance of graphene to the oil industry.

The theoretical basis leading to the creation of a light field with a hexagonal honeycomb structure resembling graphene is considered along with its experimental realization and its interaction with atoms. It is argued that associated with such a light field is an optical dipole potential which leads to the diffraction of the atoms, but the details depend on whether the transverse spread of the atomic wave packet is larger than the transverse dimensions of the optical lattice (resonant Kapitza-Dirac effect) or smaller (optical Stern-Gerlach effect). Another effect in this context involves the creation of gauge fields due to the Berry phase acquired by the atom moving in the light field. The experimental realization of the light field with a honeycomb hexagonal structure is described using holographic methods and we proceed to explore the atom diffraction in the Kapitza-Dirac regime as well as the optical Stern-Gerlach regime, leading to momentum distributions with characteristic but different hexagonal structures. The artificial gauge fields too are shown to have the same hexagonal spatial structure and their magnitude can be significantly large. The effects are discussed with reference to typical parameters for the atoms and the fields. [ABSTRACT FROM AUTHOR]

Abstract: Electronic, magnetic, and structural properties of graphene flakes depend sensitively upon the type of edge atoms. We present a simple software tool for determining the type of edge atoms in a honeycomb lattice. The algorithm is based on nearest neighbor counting. Whether an edge atom is of armchair or zigzag type is decided by the unique pattern of its nearest neighbors. Particular attention is paid to the practical aspects of using the tool, as additional features such as extracting out the edges from the lattice could help in analyzing images from transmission microscopy or other experimental probes. Ultimately, the tool in combination with density-functional theory or tight-binding method can also be helpful in correlating the properties of graphene flakes with the different armchair-to-zigzag ratios. Program summary: Program title: edgecount Catalogue identifier: AEIA_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEIA_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 66 685 No. of bytes in distributed program, including test data, etc.: 485 381 Distribution format: tar.gz Programming language: Fortran 90/95 Computer: Most UNIX-based platforms Operating system: Linux, Mac OS Classification: 16.1, 7.8 Nature of problem: Detection and classification of edge atoms in a finite patch of honeycomb lattice. Solution method: Build nearest neighbor (NN) list; assign types to edge atoms on the basis of their NN pattern. Running time: Typically ∼second(s) for all examples. [ABSTRACT FROM AUTHOR]

Abstract: The magnetic correlation in the Hubbard model on a honeycomb lattice is systematically studied by quantum Monte Carlo method. It is found that the magnetic order is qualitatively different in two filling regions separated by the Van Hove singularity around . A short-ranged ferromagnetic correlation is found in the low filling region, which is enhanced slightly by the on-site Coulomb interaction. The ferromagnetic fluctuation depends sensitively on the filling but is strengthened markedly as the next-nearest hoping integral increases. [Copyright &y& Elsevier]

Silicene-the silicon analogue to graphene-could have amazing electronic abilities [ABSTRACT FROM PUBLISHER]