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Moving, merging, and annihilating Dirac points are studied theoretically in the tight-binding model on honeycomb lattice with up-to third-nearest-neighbor hoppings. We obtain a rich phase diagram of the topological phase transitions in the parameter space of direction-dependent hoppings. We obtain the conditions for the three Dirac points to merge and for the tricritical points. We find that only very small third-nearest-neighbor hoppings are enough for the existence of the merging of three-Dirac-points and the tricritical points, if the system is sufficiently anisotropic. The density of states is obtained to be D(e) a |e|1/3 when three Dirac points merge, and D(e) a |e|l/4 at the tricritical points. It is possible to realize these topological phase transitions in the ultracold atoms on the optical lattice, strained monolayer graphene, or strained bilayer graphene. [ABSTRACT FROM AUTHOR]

The edge states in a hybrid system of single-layer and double-layer graphene are studied theoretically in a tight-binding model. The edge states on one side of the interface between single-layer and double-layer graphene are shown to penetrate into the single-layer region when a perpendicular electric field is applied, while they are localized in the double-layer region without an electric field. The edge states on the other side of the interface are localized in the double-layer region independent of the electric field. This field-induced penetration of the edge states can be applied to switching devices. We also find a new type of edge state at the boundary between single-layer and double-layer graphene. [ABSTRACT FROM AUTHOR]

Dirac fermion systems form a unique Landau level at the Fermi level-the so-called zero mode-whose observation itself will provide strong evidence of the presence of Dirac dispersions. Here, we report the study of semimetallic black phosphorus under pressure by ^{31}P-nuclear magnetic resonance measurements in a wide range of magnetic field up to 24.0 T. We have found a field-induced giant enhancement of 1/T_{1}T, where 1/T_{1} is the nuclear spin lattice relaxation rate: 1/T_{1}T at 24.0 T reaches more than 20 times larger than that at 2.0 T. The increase in 1/T_{1}T above 6.5 T is approximately proportional to the squared field, implying a linear relationship between the density of states and the field. We also found that, while 1/T_{1}T at a constant field is independent of temperature in the low-temperature region, it steeply increases with temperature above 100 K. All these phenomena are well explained by considering the effect of Landau quantization on three-dimensional Dirac fermions. The present study demonstrates that 1/T_{1} is an excellent quantity to probe the zero-mode Landau level and to identify the dimensionality of the Dirac fermion system.