In mathematics and physics, a soliton is a nonlinear, self-reinforcing, localized wave packet that is strongly stable, in that it preserves its shape while propagating freely, at constant velocity, and recovers it even after collisions with other such localized wave packets. Its remarkable stability can be traced to a balanced cancellation of nonlinear and dispersive effects in the medium. Solitons were subsequently found to provide stable solutions of a wide class of weakly nonlinear dispersive partial differential equations describing physical systems.
In mathematics, physics, and art, moiré patterns or moiré fringes are large-scale interference patterns that can be produced when a partially opaque ruled pattern with transparent gaps is overlaid on another similar pattern. For the moiré interference pattern to appear, the two patterns must not be completely identical, but rather displaced, rotated, or have slightly different pitch.
A superlattice is a periodic structure of layers of two materials. Typically, the thickness of one layer is several nanometers. It can also refer to a lower-dimensional structure such as an array of quantum dots or quantum wells.
In condensed matter physics, Hofstadter's butterfly is a graph of the spectral properties of non-interacting two-dimensional electrons in a perpendicular magnetic field in a lattice. The fractal, self-similar nature of the spectrum was discovered in the 1976 Ph.D. work of Douglas Hofstadter and is one of the early examples of modern scientific data visualization. The name reflects the fact that, as Hofstadter wrote, "the large gaps [in the graph] form a very striking pattern somewhat resembling a butterfly."
A Wigner crystal is the solid (crystalline) phase of electrons first predicted by Eugene Wigner in 1934. A gas of electrons moving in a uniform, inert, neutralizing background will crystallize and form a lattice if the electron density is less than a critical value. This is because the potential energy dominates the kinetic energy at low densities, so the detailed spatial arrangement of the electrons becomes important. To minimize the potential energy, the electrons form a bcc lattice in 3D, a triangular lattice in 2D and an evenly spaced lattice in 1D. Most experimentally observed Wigner clusters exist due to the presence of the external confinement, i.e. external potential trap. As a consequence, deviations from the b.c.c or triangular lattice are observed. A crystalline state of the 2D electron gas can also be realized by applying a sufficiently strong magnetic field. However, it is still not clear whether it is the Wigner crystallization that has led to observation of insulating behaviour in magnetotransport measurements on 2D electron systems, since other candidates are present, such as Anderson localization.
A topological insulator is a material whose interior behaves as an electrical insulator while its surface behaves as an electrical conductor, meaning that electrons can only move along the surface of the material.
Superstripes is a generic name for a phase with spatial broken symmetry that favors the onset of superconducting or superfluid quantum order. This scenario emerged in the 1990s when non-homogeneous metallic heterostructures at the atomic limit with a broken spatial symmetry have been found to favor superconductivity. Before a broken spatial symmetry was expected to compete and suppress the superconducting order. The driving mechanism for the amplification of the superconductivity critical temperature in superstripes matter has been proposed to be the shape resonance in the energy gap parameters ∆n that is a type of Fano resonance for coexisting condensates.
Silicene is a two-dimensional allotrope of silicon, with a hexagonal honeycomb structure similar to that of graphene. Contrary to graphene, silicene is not flat, but has a periodically buckled topology; the coupling between layers in silicene is much stronger than in multilayered graphene; and the oxidized form of silicene, 2D silica, has a very different chemical structure from graphene oxide.
Bilayer graphene is a material consisting of two layers of graphene. One of the first reports of bilayer graphene was in the seminal 2004 Science paper by Geim and colleagues, in which they described devices "which contained just one, two, or three atomic layers"
Transition-metal dichalcogenide (TMD or TMDC) monolayers are atomically thin semiconductors of the type MX2, with M a transition-metal atom (Mo, W, etc.) and X a chalcogen atom (S, Se, or Te). One layer of M atoms is sandwiched between two layers of X atoms. They are part of the large family of so-called 2D materials, named so to emphasize their extraordinary thinness. For example, a MoS2 monolayer is only 6.5 Å thick. The key feature of these materials is the interaction of large atoms in the 2D structure as compared with first-row transition-metal dichalcogenides, e.g., WTe2 exhibits anomalous giant magnetoresistance and superconductivity.
In materials science, the term single-layer materials or 2D materials refers to crystalline solids consisting of a single layer of atoms. These materials are promising for some applications but remain the focus of research. Single-layer materials derived from single elements generally carry the -ene suffix in their names, e.g. graphene. Single-layer materials that are compounds of two or more elements have -ane or -ide suffixes. 2D materials can generally be categorized as either 2D allotropes of various elements or as compounds.
Band-gap engineering is the process of controlling or altering the band gap of a material. This is typically done to semiconductors by controlling the composition of alloys, constructing layered materials with alternating compositions, or by inducing strain either epitaxially or topologically. A band gap is the range in a solid where no electron state can exist. The band gap of insulators is much larger than in semiconductors. Conductors or metals have a much smaller or nonexistent band gap than semiconductors since the valence and conduction bands overlap. Controlling the band gap allows for the creation of desirable electrical properties.
A two-dimensional semiconductor is a type of natural semiconductor with thicknesses on the atomic scale. Geim and Novoselov et al. initiated the field in 2004 when they reported a new semiconducting material graphene, a flat monolayer of carbon atoms arranged in a 2D honeycomb lattice. A 2D monolayer semiconductor is significant because it exhibits stronger piezoelectric coupling than traditionally employed bulk forms. This coupling could enable applications. One research focus is on designing nanoelectronic components by the use of graphene as electrical conductor, hexagonal boron nitride as electrical insulator, and a transition metal dichalcogenide as semiconductor.
A rapidly increasing list of graphene production techniques have been developed to enable graphene's use in commercial applications.
Eva Yocheved Andrei is an American condensed matter physicist, a Distinguished Professor, and a Board of Governors Professor at Rutgers University. Her research focuses on emergent properties of matter arising from the collective behavior of many particles, especially low-dimensional phenomena under low temperatures and high magnetic fields.
Twistronics is the study of how the angle between layers of two-dimensional materials can change their electrical properties. Materials such as bilayer graphene have been shown to have vastly different electronic behavior, ranging from non-conductive to superconductive, that depends sensitively on the angle between the layers. The term was first introduced by the research group of Efthimios Kaxiras at Harvard University in their theoretical treatment of graphene superlattices.
Pablo Jarillo-Herrero is a Spanish physicist and current Cecil and Ida Green Professor of Physics at Massachusetts Institute of Technology (MIT).
Antonio Helio de Castro Neto is a Brazilian-born physicist. He is the founder and director of the Centre for Advanced 2D Materials at the National University of Singapore. He is a condensed matter theorist known for his work in the theory of metals, magnets, superconductors, graphene and two-dimensional materials. He is a distinguished professor in the Departments of Materials Science Engineering, and Physics and a professor at the Department of Electrical and Computer Engineering. He was elected as a fellow of the American Physical Society in 2003. In 2011 he was elected as a fellow of the American Association for the Advancement of Science.
Straintronics is the study of how folds and mechanically induced stresses in a layer of two-dimensional materials can change their electrical properties. It is distinct from twistronics in that the latter involves changes in the angle between two layers of 2D material. However, in such multi-layers if strain is applied to only one layers, which is called heterostrain, strain can have similar effect as twist in changing electronic properties. It is also distinct from, but similar to, the piezoelectric effects which are created by bending, twisting, or squeezing of certain material.
Fractional Chern insulators (FCIs) are lattice generalizations of the fractional quantum Hall effect that have been studied theoretically since 1993 and have been studied more intensely since early 2010. They were first predicted to exist in topological flat bands carrying Chern numbers. They can appear in topologically non-trivial band structures even in the absence of the large magnetic fields needed for the fractional quantum Hall effect. In principle, they can also occur in partially filled bands with trivial band structures if the inter-electron interaction is unusual. They promise physical realizations at lower magnetic fields, higher temperatures, and with shorter characteristic length scales compared to their continuum counterparts. FCIs were initially studied by adding electron-electron interactions to a fractionally filled Chern insulator, in one-body models where the Chern band is quasi-flat, at zero magnetic field. The FCIs exhibit a fractional quantized Hall conductance.
