Narrow Results

The condition for the formation of Dirac cones at arbitrary points in the Brillouin zone by the accidental degeneracy of two photonic bands was examined by the degenerate perturbation theory and group theory based on the spatial symmetry of two modes. The analysis was applied to a two-dimensional square-lattice photonic crystal with C_4v symmetry and the dispersion relation in the vicinity of the M point was examined. Exact agreement between the analytical and numerical calculation was obtained.

Breaking the time-reversal symmetry (TRS) on the surface of a three-dimensional topological insulator (TI) transforms its metallic surface into a Chern insulator. The TRS-broken surface states are essential for many exotic emergent particles in condensed matter. In this review, I will show broken TRS surface states of TI induced by magnetism and by light imaged with scanning microscopy and photoemission spectroscopy, respectively. Our capability to manipulate mesoscopic magnetic structures as well as to shape ultrafast light pulses makes broken-symmetry states in TI promising platforms to simulate elusive fundamental particles such as magnetic monopoles and Majorana fermions.

Here we present a short introduction into physics of Dirac materials. In particular we review main physical properties of various two-dimensional crystals such as graphene, silicene, germanene and others. We comment on the origin of their buckled two-dimensional shape, and address the issues created by Mermin-Wagner theorem prohibiting the existence of strictly two-dimensional, flat crystals. Then we describe main ideas which were leading to the discovery of two and three-dimensional topological insulators and Weyl fermions. We describe some of their outstanding electronic properties which have been originating due to the existence of the Dirac gapless spectrum. We also compare simplest devices made of Dirac materials. Analogies and differences between Dirac materials and optics are also discussed.