# Higher-Order Topological Insulators.

Ortix C.

Relazione su invito
II - Fisica della materia
GSSI Ex ISEF - Aula C - Mercoledì 25 h 10:00 - 13:00
In this contribution I will discuss the existence of higher-order topological insulators in: i) fourfold rotoinversion invariant bulk crystals, and ii) inversion-symmetric systems with or without an additional three fold rotation symmetry. These states of matter are characterized by a non-trivial $Z_{2}$ topological invariant, which we define in terms of symmetric hybrid Wannier functions of the filled bands, and can be readily calculated from the knowledge of the crystalline symmetry labels of the bulk band structure. The topological invariant determines the generic presence or absence of protected chiral gapless one-dimensional modes localized at the hinges between conventional gapped surfaces. I will also discuss the potential realisation of a higher-order topological insulating state in graphene multilayer stacks subject to external magnetic fields.