Non-Abelian band topology in noninteracting metals

Electron energy bands of crystalline solids generically exhibit degeneracies called band-structure nodes. Here, we introduce non-Abelian topological charges that characterize line nodes inside the momentum space of crystalline metals with space-time inversion (𝒫𝒯) symmetry and with weak spin-orbit coupling. We show that these are quaternion charges, similar to those describing disclinations in biaxial nematics. Starting from two-band considerations, we develop the complete many-band description of nodes in the presence of 𝒫𝒯 and mirror symmetries, which allows us to investigate the topological stability of nodal chains in metals. The non-Abelian charges put strict constraints on the possible nodal-line configurations. Our analysis goes beyond the standard approach to band topology and implies the existence of one-dimensional topological phases not present in existing classifications.

Biaxial nematics of hard cuboids in an external field

By computer simulation, we model the phase behaviour of colloidal suspensions of board-like particles under the effect of an external field and assess the still disputed occurrence of the biaxial nematic (NB) liquid crystal phase.

Can multi-biaxial mesogenic mixtures favour biaxial nematics? A computer simulation study

A mixture of mesogens with different anisotropies favours the biaxial nematic phase.

Molecular field theory for biaxial nematics formed from liquid crystal dimers and inhibited by the twist-bend nematic

Theory shows the ability of flexible dimers to adopt bent and linear shapes facilitates the formation of biaxial nematic phases.

Equivalent variational approaches to biaxial liquid crystal dynamics

Within the framework of liquid crystal flows, the Qian and Sheng (QS) model (Qian and Sheng 1998 Phys. Rev. E. 58, 7475. ( doi:10.1103/PhysRevE.58.7475 )) for Q -tensor dynamics is compared with the Volovik and Kats (VK) theory (Volovik and Kats 1981 Sov. Phys. 54, 122–126) of biaxial nematics by using Hamilton’s variational principle. Under the assumption of rotational dynamics for the Q -tensor, the variational principles underling the two theories are equivalent and the conservative VK theory emerges as a specialization of the QS model. Also, after presenting a micropolar variant of the VK model, Rayleigh dissipation is included in the treatment. Finally, the treatment is extended to account for non-trivial eigenvalue dynamics in the VK model and this is done by considering the effect of scaling factors in the evolution of the Q -tensor.