Band geometry plays a substantial role in topological lattice models. The Berry curvature, which resembles the effect of magnetic field reciprocal space, usually fluctuates throughout Brillouin zone. Motivated by analogy with Landau levels, constant curvature has been suggested as an ideal condition for realizing fractional Chern insulators. Here we show that while cannot be made two-band model...

In this paper, we provide state sum path integral definitions of exotic invertible topological phases proposed in the recent paper by Hsin, Ji, and Jian [arXiv:2105.09454 [cond-mat.str-el]. The phase has time-reversal $(T)$ symmetry, depends on a choice space-time structure called Wu structure. cannot be captured classification any bosonic or fermionic thus gives novel class phases. When $T$ sy...

Background: The “pasta” phase of nuclear matter may play an important role in the structure and evolution of neutron stars. Recent works suggest nuclear pasta has a high resistivity which could be explained by the presence of long-lived topological defects. The defects act as impurities that decrease thermal and electrical conductivity of the pasta. Purpose: To quantify how topological defects ...