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We propose classification schemes for characterizing two-dimensional topological phases with nontrivial weak indices. Here, weak implies that the Chern number in the corresponding phase is trivial, while the system shows edge states along specific boundaries. As concrete examples, we analyze differen
We have observed the quantum Hall effect (QHE) and Shubnikov-de Haas (SdH) oscillations in highly disordered graphene at magnetic fields up to 65 T. Disorder was introduced by hydrogenation of graphene up to a ratio H/C $approx 0.1%$. The analysis of
The metallic surface state of a topological insulator (TI) is not only topologically protected, but exhibits a remarkable property of inducing an effective vector potential on curved surfaces. For an electron in the surface state of a spherical or a
Negative longitudinal magnetoresistance, in the presence of an external magnetic field parallel to the direction of an applied current, has recently been experimentally verified in Weyl semimetals and topological insulators in the bulk conduction lim
We propose a topological quantum phase transition for quantum states with different Berry phases in hole-doped III-V semiconductor quantum wells with bulk and structure inversion asymmetry. The Berry phase of the occupied Bloch states can be characte
The paper examines weak localization (WL) of surface states with a quadratic band crossing in topological crystalline insulators. It is shown that the topology of the quadratic band crossing point dictates the negative sign of the WL conductivity cor