Samples of liquid crystals are characterized by a variety of topo-logical defects and can be exposed to external constraints such as extreme confining geometries. We explore the intrinsic structure of smectic colloidal liquid crystals dictated by the interplay be-tween intrinsic layering and the externally imposed boundary structure. Considering a topologically nontrivial annular confine-ment, a plethora of competing states is found with structures ranging from laminar states with mostly parallel layers to multiple smectic domains and arrays of edge dislocations, which we refer to as Shubnikov states in formal analogy to the characteristic of type-II superconductors. Our particle-resolved results, gained by a combination of real-space microscopy of colloidal rods and fun-damental-measure-based density functional theory of hard aniso-tropic bodies, agree on a quantitative level [1]. Using further insight from Monte-Carlo simulations, we present a general classification scheme of smectic topological defects in two [2] and three [3] spa-tial dimensions, which illustrates the coexistence of nematic and tetratic orientational order in spatially extended grain-boundary networks.

[1] R. Wittmann, L. B. G. Cortes, H. Löwen and D. G. A. L. Aarts, Nat. Commun. 12, 623 (2021).
[2] P. A. Monderkamp, R. Wittmann, L. B. G. Cortes, D. G. A. L. Aarts, F. Smallenburg and H. Löwen, Phys. Rev. Lett. 127, 198001 (2021).
[3] P. A. Monderkamp, R. Wittmann, M. te Vrugt, A. Voigt, R. Wittkowski and H. Löwen, arXiv preprint arXiv:2201.01736 (2022).