berry curvature

  1. J

    A Berry phase and parallel transport

    Hello. In the following(p.2): Berry uses parallel transport on a sphere to showcase the (an)holonomy angle of a vector when it is parallel transported over a closed loop on the sphere. A clearer illustration of this can be...
  2. J

    A Is the Berry connection compatible with the metric?

    Hello, Is the Berry connection compatible with the metric(covariant derivative of metric vanishes) in the same way that the Levi-Civita connection is compatible with the metric(as in Riemannanian Geometry and General Relativity)? Also, does it have torsion? It must either have torsion or not be...
  3. J

    A Is the Berry connection a Levi-Civita connection?

    Hello! I have learned Riemannian Geometry, so the only connection I have ever worked with is the Levi-Civita connection(covariant derivative of metric tensor vanishes and the Chrystoffel symbols are symmetric). When performing a parallel transport with the L-C connection, angles and lengths are...
  4. N

    A Is graphene a Weyl semimetal?

    I'm recently interested in the topological/Weyl semimetals, but I'm not an expert on the theory. Most papers just define Weyl semimetal as a material that have pairs of Weyl points with opposite Berry curvature. Here in graphene, the Berry curvature of the Dirac cones at K and K' point is also...