Key points are not available for this paper at this time.
The surface states of a d-dimensional conventional or first-order topological state of matter reside on a (d-1) dimensional boundary. However, its nth order incarnation, commonly known as a higher-order topological (HOT) phase, accommodates (d-n) dimensional boundary states, with corner and hinge modes standing as their representatives. Here, the authors introduce a general principle of systematically constructing the hierarchy of HOT phases by exploiting the symmetry of the system and the corresponding Clifford algebra. This procedure is applicable for insulating as well as gapless phases, and paves the route toward realizing a fourth-order nodal-loop semimetal, devoid of any surface bound state.
Călugăru et al. (Fri,) studied this question.