Electronic and optical properties of strained graphene and other strained 2D materials: a review

Abstract

Abstract. This review presents the state of the art in strain and rippleinduced effects on the electronic and optical properties of graphene. It starts by providing the crystallographic description of mechanical deformations, as well as the diffraction pattern for different kinds of representative deformation fields. Then, the focus turns to the unique elastic properties of graphene, and to how strain is produced. Thereafter, various theoretical approaches used to study the electronic properties of strained graphene are examined, discussing the advantages of each. These approaches provide a platform to describe exotic properties, such as a fractal spectrum related with quasicrystals, a mixed DiracSchrödinger behavior, emergent gravity, topological insulator states, in molecular graphene and other 2D discrete lattices. The physical consequences of strain on the optical properties are reviewed next, with a focus on the Raman spectrum. At the same time, recent advances to tune the optical conductivity of graphene by strain engineering are given, which open new paths in device applications. Finally, a brief review of strain effects in multilayered graphene and other promising 2D materials like silicene and materials based on other group-IV elements, phosphorene, dichalcogenide-and monochalcogenide-monolayers is presented, with a brief discussion of interplays among strain, thermal effects, and illumination in the latter material family.

Gravitation at the Josephson Junction

“…In real microscopic quantum systems, constrained motion is a result of a strong confining force (electrostatic, rigid chemical bonds, etc.). Therefore, confining potential formalism seems a physically more realistic approach to constraints [15][16][17][18][19][20][21][22][23][24][25].…”

“…, where , for = 1, 2, 3, are the principle curvatures of a threedimensional manifold embedded in R 4 [23][24][25].…”

“…In the previous section we have seen that the geometric field is equivalent to an electric field in the superconductor (15) the statement of which is analogous to the law of conservation of energy (25). Therefore, provided the superconducting element is homogeneous, we can expect int ( → ) = const and as a result of the perfect conductor aspect of the superconducting state, we can also expect a redistribution of the shift by the geometric field charges inside the superconductor in order to maintain the superconductor at a constant potential.…”

“…We may expect a backreaction on the entire junction as well. The kinetic energy of the bulk material can certainly be included in (25). The backreaction will increase with the increase in the difference between the interaction energy of the supercurrent with the electromagnetic field on both sides.…”

Quantitative relationship between polarization differences and the zone-averaged shift photocurrent

“…In particular, 2D materials have highly tunable electronic and optical properties [17][18][19][20] and are expected to generate large shift current [21][22][23] . We can identify three factors that determine the magnitude of the shift current: density of states, velocity matrix elements and shift-vector matrix elements.…”